Physics MCAT

A state trooper on the side of the road uses Doppler radar to track the speed of traffic that moves away from him. If the frequency of the outgoing radar, as measured by the trooper, is 10^10 Hz, then the frequency of the radar that bounces off the car and returns to the trooper is:

Always less than 10^10 Hz Doppler effect: Change in perceived frequency of wave as result of motion of source and/or observer along the line joining them Source moving away from detector, so observed frequency is less than actual frequency because it takes longer for the wave fronts to hit the observer

As the length of an inclined plane increases, the amount of force necessary to perform the same amount of work (moving object same displacement) _________ As the effort (required force) decreases in a pulley system, the effort distance __________ to generate the same amount of work

As the length of an inclined plane increases, the amount of force necessary to perform the same amount of work (moving object same displacement) deceases As the effort (required force) decreases in a pulley system, the effort distance increases to generate the same amount of work

Acceleration (a)

Rate of change of velocity that an object experiences as a result of some applied force Vector quantity Measured in SI units of m/s^2 Acceleration in direction opposite of initial velocity = deceleration Average acceleration (a with line over it) = delta v / delta t Instantaneous acceleration = average acceleration as delta t approaches 0 a with line over it = (Δv/Δt) limit as Δt-->0 On graph of velocity vs time, tangent to graph at any time (t) corresponds to slope of graph at that time, indicates instantaneous acceleration *If slope is positive, acceleration is positive and in same direction its velocity *If slope is negative, acceleration is negative and in opposite direction of velocity (deceleration)

Real Lenses

lenses with non-negligible thickness with real lenses, the focal length is related to the curvature of the lens surfaces and the index of refraction of the lens by the LENSMAKER'S EQUATION 1/f = (n-1)(1/r1 - 1/r2) where n is index of refraction of lens material, r1 is the radius of curvature of the first lens surface and r2 is the radius of curvature of the second lens surface The cornea is a real lens (primary source of refractive power) -> then passed to adaptive lens too change focal length before going to vitreous humor

Degrees to radians Radians to degrees

multiply by pi/180 *90 degrees X pi/180 = pi/2 multiply by 180/pi pi/2 X 180/pi = 90

Units of Heat 1 Cal = _______ cal = _______ J = ____ BTU

1 Cal = 1000 cal = 4184 J = 3.97 BTU

1 V =

1 J/C = 1 N*m/C Remember V = Ed, so if you are given a quantity in N/C and a quantity in Volts, dividing voltage by electric field (in N/C) will give us distance in meters because voltage = N*m/C

1 amu =

1.66 x 10^-27 g 1/12 the mass of 12 carbon atom

ln(10^6)

13.8 ln(x) = log(x)*2.303 2.303*log(10^6) 2.303 X 6 = About 14

A lamp with a 100 watt light bulb is turned on. How long does it take for the lamp to consume 3.6x10^5 joules?

3.6x10^3 s (P=W/t) P = 100 watts W = 3.6 X 10^5 joules t= 3.6 X 10^5 joules/ 100 W

Planck's Constant (h)

6.626 x 10^-34 J*s 4.14X10^-15 eV*s 1 J = 6.242 X 10^18 eV

Archimede's Principle

A body that is fully or partially immersed in a liquid will be buoyed up by a force that is equal to the weight of the liquid displaced by the body. Deals with buoyancy of objects placed in a fluid Any object placed in fluid will cause a volume to be displaced that is equal to the volume submerged, and because all fluids have density, the volume displaced will correspond to mass. The mass of the fluid displaced exerts a force equal to its own weight against the submerged object The force is direct upward and called the buoyant force: magnitude of force = density of fluid*volume of fluid displaced* g = density of fluid*volume submerged*g (Buoyant force = p fluid * V fluid * g = p fluid * V submerged * g) *DONT USE THE DENSITY OF THE OBJECT (if two objects dissipate the same volume, they experience the same magnitude of buoyant force even if they have different masses) Objects that don't sink will displace a volume of water equal to the objects weight -> An object will float if the average density is less then the density of fluid. It will sink if the average density is higher (cruise ships dont sink because the AVERAGE density is less than water) How much of a floating object lies below the surface? -Compare density or specific gravity (percent) -> percent of specific gravity says how much of an object is submerged (when the fluid is pure water with density of 1 g/cm^3) *density of ice = 0.92 g/cm^3 so 92% of volume is submerged (8% above surface) A specific gravity = 1 would be completely submerged but not sink We have specific gravity of about 1.1

Box Plot

Box bounded by Q1 and Q3, Q2 in line in the middle (median) *50% of data between Q1 and Q3, 25% in each box Whiskers = maximum and minimum values of data set (within 1.5X IQR) -> outliers shown outside of whiskers Shows range, median, quartiles, and outliers Useful for large amounts of data

Boyles Law and Gay-Lussacs Law

Boyle's Law: P1V1 = P2V2 Pressure and volume have inverse relationship: As one double the other is cut in half Gay-Lussac's Law: P1/T1 = P2/T2 Pressure and temperature have direct relationship: As one is doubled, the other is too

Ohm's Law

Calculates voltage drop between 2 points in a circuit V= voltage drop I= current R = Magnitude of resistance (Ohms) -Current proportional to emf (voltage)

If the work function of a metal is 6.622 × 10-20 J and a ray of electromagnetic radiation with a frequency of 1.0 × 1014 Hz is incident on the metal, what will be the speed of the electrons ejected from the metal? (Note: h = 6.626 × 10-34 J·s and me- = 9.1 × 10-31 kg)

Correct Answer: C Explanation: To determine the speed of the electrons ejected, we must first calculate their kinetic energy: k = hf -W (6.626 × 10-34 J*s)(1.0X10^14 Hz) - 6.622X10^-20 =0.004X10^-20 = 4X10^-23 Using the formula for the kinetic energy, we can now calculate the speed of the ejected electrons: k = 1/2 mv^2 -> v = sqr rt (2K/m) sqr rt (8X10^-23 / 9X10^-31) = sqr rt 10^8 = 10^4 m/s Notice the wide range in

Dynamic VS Static Pressure

Dynamic pressure is the pressure associated with flow, and is represented by (1/2)ρv². Static pressure is the pressure associated with position; static pressure is sacrificed for dynamic pressure during flow. (measured by pitot tube)

Linear Speed & Continuity Equation

Even though the flow rate is constant, the linear speed of fluid changes relative to cross-sectional area Linear speed is the measure of linear displacement of fluid particles in amount of time Flow rate = linear speed * cross-sectional area *Linear speed of fluid will increase with decreasing cross-sectional area Q = v1A1 = V2A2 = V3A3..... Where Q is flow rate, v1 and 2 are linear speeds at certain points, and A1 is cross-sectional area at point 1 This is called continuity equation: fluids flow quicker through narrow spaces -Arises from the conservation of mass of fluids (because liquids are incompressible) -With constant flow rate, there is inverse relationship between linear speed and cross-sectional area

If centripetal force is the magnetic force (Fc = FB) and a proton is moving 15 m/s through uniform magnetic field of 3.0 T, what is the radius of the circle that the proton moves in?

Fc = FB mv^2/r = qv B sin (theta) -> sin (90) = 1 r = mv/qB = (1.67X10^-27 kg)(15 m/s) / (1.60X10^-19)(3) r = 5X10^8 meters

Normal Distribution

The mean, median and mode are all the same at the center of the distribution Basis of the bell curve Approximately 68% of the distribution is within one standard deviation of the mean, 95% within 2, and 99% within 3 Counterpart of normal distribution is standard distribution Standard distribution = normal distribution with a mean of 0 and a standard deviation of one

Thermodynamics

The study of the flow of energy in the universe, as it relates to work, heat, entropy, and different forms of energy

Trigonometry What is tan (60 degrees) or (pi/3)

The values of sin and cosine range from -1 to 1, but the values of tangent go from - infinity to infinity Inverse sin or cosine of side lengths (Opp/Hyp for sin and adj/hyp for cosine) can give with angle values Know the two special right triangles: Angles = 90, 60, 30 and side lengths = 2, sqr rt 3, and 1 Angles 90, 45, and 45 and side lengths = sqr rt 2, 1, and 1 Note: tan of 90 is undefined because you can't divide by 0 (1/0) Sin increases from 0 to 90 degrees (starts at 0 goes to 1) and cosine decreases from 0 to 90 degrees What is tan (60 degrees) = (sqrrt 3/2) / (1/2) = sqrrt 3

An experiment with improperly tared (zeroed) mass balance would have what type of error?

This experiment would have inaccuracy (not valid) error but not imprecision error (it is reliable) The scale would reliably read the same weight, but the weight read would not be right. This would lead to bias

If at time t=0, there is a 2 mole sample of radioactive isotopes, how many nuclei remain after 45 minutes (3/4 of an hour), assuming decay constant = 2 hr^-1 and e^-3/2 = 0.22

Use n = n0*e^-λt n = n0 * e^-2*3/4 = 2 *0.22 so after 45 minutes, 0.44 moles remain. Multiply by avogadros number (6.02X10^23 nuclei/mol) = 2.64 X 10^23 nuclei

Three methods for calculating work

W = Fd cos theta (dot product of force and displacement vectors) W = P Δ V (area under a pressure-volume curve) W net = ΔK (Work-energy theorem)

Force on a Moving Charge

When a charge moves in a magnetic field, a magnetic force may be exerted on it, with the magnitude = FB = qvB sinθ where q = charge, v = magnitude of velocity, B is magnitude of magnetic field, θ= smallest angle between velocity vector (v) and magnetic field vector (B) -Sin means charge must have perpendicular component of velocity (If charge is parallel or antiparallel to magnetic field (B), sine (0) or sin (180) = 0, so there would be no force) *Magnetic fields only exert magnetic forces on other moving charges (assume presence of fixed and uniform external magnetic field *Charges can have both electrostatic and magnetic forces acting on them at the same time (the sum of these forces is called Lorentz force)

Unit Circle

a circle with a radius of 1, centered at the origin

v=fλ

wave speed = frequency x wavelength

Bimodal Distributions

2 or more peaks 2 peaks with valley in between = bimodal -Technically, you can have bimodal distribution with only one mode if one peak is slightly higher than the other, but even when peaks are different sizes, we still call it bimodal -Can sometimes be measured separately, but don't have to be

Energy

A systems ability to do work

Base units and derived units

Base units: Standard units around which system is designed Derived units: Created by association (Newton, a unit of force, is derived from kilograms, meters and seconds (1N = 1 Kg*m/s) -Other derived units: Joule (Kg*m^2/s^2) and Watt (Kg*m^2/s^2)

Graphs

Common Relationships for linear graphs: Linear, parabolic, Exponential, logarithmic Linear: Slope (m) = rise over run = change in y / change in x for any 2 points

A source of light (f = 6.0 × 1014 Hz) passes through three plane polarizers. The first two polarizers are in the same direction, while the third is rotated 90° with respect to the second polarizer. What is the frequency of the light that comes out of the third polarizer? A. Light will not pass through the third polarizer B. 3.0 × 1014 Hz C. 6.0 × 1014 Hz D. 9.0 × 1014 Hz

Correct Answer: A Explanation: Plane-polarized light is light in which the electric fields of all the waves are oriented in the same direction. Light passing through the first two polarizers will only contain rays with their electric field vectors in the same direction. When it reaches the third polarizer, however, the light will not be able to pass through because all the light rays will be oriented in the direction dictated by the first and second polarizers.

Two wooden balls of equal volume but different density are held beneath the surface of a container of water. Ball A has a density of .5 g/cm^3 and ball B has a density of .7 g/cm^3. When the balls are released, they will accelerate upward to the surface. What is the relationship between the acceleration of ball A and that of ball B? A. Ball A has the greater acceleration. B. Ball B has the greater acceleration. C. Balls A and B have the same acceleration. D. It cannot be determined from information given.

Correct Answer: A Explanation: Using Newton's second law, Fnet = ma, we obtain the following equation: Fbuoy - mg = ma Thus, a = Fbuoy - mg / m -> a = (Fbuoy /m) - g Both balls experience the same buoyant force because they are in the same liquid and have the same volume (Fbuoy = ρVg). Thus, the ball with the smaller mass experiences the greater acceleration. Because both balls have the same volume, the ball with the smaller density has the smaller mass (m = ρV), which is ball A.

A parachutist jumps from a plane. Beginning at the point when she reaches terminal velocity, which of the following is/are true? I. The jumper is in translational equilibrium. II. The jumper is not being acted upon by any forces. III. There is an equal amount of work being done by gravity and air resistance. A. I only B. I and III only C. II and III only D. I, II, and III

Correct Answer: B Explanation: At terminal velocity, the force of gravity and force of air resistance are equal in magnitude, leading to translational equilibrium. Thus, statement I is true. If these forces have the same magnitude and act over the same displacement, then the work performed is the same as well, making statement III true. Even though the net force is equal to zero, there are still forces acting on the parachutist, making statement II false.

If a defibrillator passes 15 A of current through a patient's body for 0.1 seconds, how much charge goes through the patient's skin? A. 0.15 C B. 1.5 C C. 15 C D. 150 C

Correct Answer: B Explanation: Electrical current is defined as charge flow, or in mathematical terms, charge transferred per time: I = Q / delta t A 15 A current that acts for 0.1 s will transfer 15 A × 0.1 s = 1.5 C of charge.

A 30 kg girl sits on a seesaw at a distance of 2 m from the fulcrum. Where must her father sit to balance the seesaw if he has a mass of 90 kg? A. 67 cm from the girl B. 67 cm from the fulcrum C. 133 cm from the girl D. 267 cm from the fulcrum

Correct Answer: B Explanation: In order for the seesaw to be balanced, the torque due to the girl (τg) must be exactly counteracted by the torque due to her father (τf). In other words, the magnitudes of these torques must be equal (τg = τf): rFsin(theta) = r2F2sin(theta)2 r*mg*sin(90) = r2*mg2*sin(90)2 2m * 30 kg = r * 90kg 0.67 m = r Because r represents the distance of each person from the fulcrum, the father must sit 67 cm from the fulcrum.

A certain 9 V battery is used as a power source to move a 2 C charge. How much work is done by the battery? A. 4.5 J B. 9 J C. 18 J D. 36 J

Correct Answer: C Explanation: Voltage (ΔV) is equal to the quotient of the amount of work done (W) divided by the charge of the particle on which the work is done (q), according to the equation V = delta U /q = W /q Because the voltage equals 9 V and the charge equals 2 C, the work done must equal 9 V × 2 C = 18 J.

Flow rate would__________ with increasing radius of tube or pressure gradient, and would ________- with increasing viscosity or length of tube

Flow rate would increase with increasing radius of tube or pressure gradient, and would decrease with increasing viscosity or length of tube Calculate the rate of flow for Laminar flow with Poiseuille's Law Q = Flow = (pi*r^4*Δ P) / (8nL) Where Q is rate of flow, r is radius of tube, ΔP is pressure gradient, n (eta) is viscosity, L is length of pipe

Newton's Third Law

For every action force there is an equal and opposite reaction force

Capacitors

Have ability to hold charge at particular voltage (stores amount of energy in the form of charge separation) (Example: AED, clouds in lightening storm) *MCAT focuses on parallel plate capacitors Capacitance: The ratio of the magnitude of the charge on one plate to the potential difference (voltage) across the capacitor C= Q/V (Q= +Q on positive plate + -Q on negative plate) Capacitance measured in Farads (1F = 1 C/V), but that's a lot, so it is usually measured in microfarads (1X10^-6 F) or picofarads (1X10^-9 F) Capacitance for parallel plate is dependent on geometry of conduction surfaces: C = ε0 (A/d) where ε0 is the permittivity of free space (8.85X10^-12 F/m) A is area of overlap of 2 plates, d is separation of two plates (separation sets up uniform electric field with parallel field vectors) Magnitude of parallel field vectors can be calculated from E = V/d (based from V= kQ/r and E = kQ/r^2 if we replace r with d) The direction of e field always goes from positive to negative *E field lines will always point in the direction a force would be exerted on a positive charge *Surface area, distance, and dielectric constant all contribute to capacitance If voltage source is removed, capacitor discharges, providing current opposite in direction to initial current

Superconductors

Special class of materials that are the one major exception to the rules of internal resistance Resistivity completely dissipates at low temps

A copper ball of density 8.9x10^3 kg/m^3 is dropped, first into a container filled with water, and then a container filled with oil. The density of water is 1x10^3 kg/m^3 and the density of oil is 700kg/m^3. Ignoring frictional forces, what describes the result of this experiment? *Property of Bouyant forces

The acceleration of the ball is less than g in both liquids and the greatest in oil. Downward force = gravity (same in both cases) Upward force = buoyant force Buoyant Force = Fb = PL*VB*g where PL is density of liquid, VB is volume of ball/volume of displaced liquid *For most part, larger volume = larger buoyant force when mass is equal Less dense liquid will decelerate the ball less Oil is less dense than water (1000 > 700)

Refraction

The bending of light as it passes from one medium to another and changes speed Speed of light through medium always less than its speed in vacuum (C = 3.00X10^8) -> but for the MCAT, lets just say the speed of light through air is about C too For a given medium (besides vacuum), speed is less than c n = c/v where c= speed of light in vacuum v is speed of light in medium n is dimensionless quantity called index of refraction Common media's indices of refraction: (n) Vacuum and air = 1 n Ice = 1.31 Water = 1.33 Acetone and ethanol = 1.36 Cornea and lens of human eye = 1.37-1.41 Glass = 1.48 - 1.93 Diamond = 2.42

Watt

Unit for power Watt = 1 joule/second Power = Watt/ time (sec)

Volume of a Cylinder Formula

V=πr²h

An object is placed in between the focal point and the surface of a thin covering lens. The image produced is:

Virtual and upright 1/I = 1/f - 1/o we know f>o, so 1/I is negative Negative indicates image is virtual Magnification = -I/o (I is negative and o is positive, so magnification is positive) positive magnification = upright

Specific Heat

When heat is added/removed from system, temp will change in proportion to amount of heat transfer unless system is undergoing a phase change where temp is constant Relationship between heat and temp = specific heat (c) Specific heat = amount of heat energy required to raise 1 g of substance by 1 deg C or unit K Specific heat of liquid water = 1 calorie per gram unit Kelvin (1 cal/g*K) = 4.184 J/g*K *Specific heat changes by phase The equation for heat transfer/that relates the heat gained or lost by object and change in temp is: q = mcΔT (mass* specific heat*change in temp in deg C or K)

A tractor pulls a log with a mass of 500 kg along the ground for 100 m. The rope (between the tractor and the log) makes an angle of 30° with the ground and is acted on by a tensile force of 5000 N. How much work does the tractor perform in this scenario? (Note: sin 30° = 0.5, cos 30° = 0.866, tan 30° = 0.577)

Work (W) = Fd cos(theta) 5000N * 100 m *cos (30) 500000*0.86 = between 400000 and 500000 = about 433 kJ

A baseball of mass 0.25 kg is thrown in the air with initial speed of 30 m/s, but because of air resistance (nonconservative force), the ball returns to the ground with a speed of 27 m/s. Find the work done by air resistance

Work of nonconservative = ΔE = ΔU + ΔK ΔU = 0 because initial and final heights are the same Work of nonconservative = ΔE = 0 + ΔK ΔK = 1/2 mv(final)^2 - 1/2 mv(initial)^2 1/2*0.25*(27^2 - 30^2) 1/8 * (729-900) 1/8* about -160 = -20 J Negative sign shows energy being dissipated from system

Isotope Decay Arithmetic and Nucleon Conservation

X and Y represent nuclear isotopes Parent nucleus (X) undergoes nuclear decay to form daughter nucleus (Y) When balancing nuclear reactions, the sum of atomic numbers must be same on both sides, and sum of mass numbers must be same on both side too Start by balancing number of protons (atomic number, on bottom)

cos30° sin30° tan30°

√3/2 1/2 √3/3

A wooden block floats in the ocean with half of its volume submerged. Find the density of the wood. Density of sea water = 1025 kg/m^3

(Buoyant force = p fluid * V fluid * g = p fluid * V submerged * g) p = density = m/v Volume of water displaced = volume of block /2 Because the block is floating, the buoyant force = the blocks weight Buoyant force = Weight of wood (Fg of wood) Weight of the wood = mass * g = density *volume * g Fg of wood (weight) = density * volume * g = density of water * (volume of wood/2) * g Cancel out g and volume of wood density of wood = density of water / 2 = 1025/2 = 512.5 kg/m^3

Simplify the following expressions: (a+b)^2 (a^2+ 2a^2)/ 5a^3 log (base a) a log (a^3) - log a

(a+b)^2 -> a^2 + 2ab + b^2 (a^2+ 2a^2)/ 5a^3 -> 3a^2 / 5a^3 -> 3/5a log (base a) a = 1 log (a^3) - log a -> log (a^3 / a) -> log a^2 -> 2 log a

Streamlines

-representations of molecular movements -indicate pathways followed by fluid particles as they move -The velocity vector of a fluid particle will always be tangential to streamline at any point -Streamlines never cross each other -If fluid in incompressible (which we can probably assume it is), the flow rate (volume per unit time) is constant for a closed system and is independent of cross-sectional area *If 4 liters pass a point in a certain amount of time, then 4 liters will pass all points in the same amount of time, even if diameter changes

Gauge Pressure

-the difference b/w the absolute pressure inside and the atmospheric pressure outside -The amount of pressure in a closed space above and beyond atmospheric pressure Gauge pressure = pressure exerted by a column of fluid + ambient pressure above the fluid - atmospheric pressure -When the atmospheric pressure is the only pressure above the fluid column, then gauge pressure = fluid pressure -When pressure at surface = 1 atm, gauge pressure = pgz ρ = rho = density of fluid g is acceleration due to gravity z is depth of object Pgauge = P-Patm = (P0 + ρgz) -Patm -When P0 = Patm, Pgauge = P-P0 = ρgz at a depth z

ATM to Pascals

1 atm = 101,325 Pa m^3 * Pa = Joules

Steps of the Scientific Method

1. Generate a testable question 2. Gather data and resources 3. Form a hypothesis (proposed explanation to testable question)(If-then statement) 4. Collect new data: experimentation, observation 5. Analyze the data 6. Interpret data 7. Publish / peer review 8. Verify results

Square root of 2 Square root of 3 Square root of 361 Square root of 256 Square root of 324 Square root of 289

1.414 1.732 19 16 18 17

Sin(30) Cos (0) Cos (90)

1/2 1 0

A circuit is set up with 3 resistors. One branch through R1 = 3 ohms, then splits into two branches (parallel) through R2 = 2 Ohms and R3 = 6 Ohms. What proportion of total current will pass through each, and what is total resistance

100% of current goes through 1st resistor. Ratio of resistance for R2 and R3 = 1:3, so 3X more current will go through R2 than R1 (3/4 current through R2, 1/4 through R1) Total resistance = 3 + 1.5 = 4.5 Ohms

A 1000 kg rocket ship, travelling at 100 m/s is acted upon by an average force of 20 kN applied in the direction of its motion for 8 s. What is the change in velocity of the rocket?

160 m/s The average force on the rocket equals its mass times the average acceleration; the average acceleration equals the change in velocity divided by the time over which the change occurs. So, the change in velocity equals the average force times the time divided by the mass: average acceleration (a) = Δ V / Δ t -> ΔV = aΔt a = f/m Δ V = fΔt/ m Δ V = 20000*8 / 1000 kg The new velocity of the rocket is 260, but the change in velocity is 160 m/s This equation is used because we are talking about AVERAGE force and AVERAGE acceleration

If a five meter board is inclined to 30 degrees above a horizontal surface, how high above the surface is the highest intint on the board?

2.5 m Angle of board is opposite to side being measured h*xsin(30) = height sin(30)=1/2

An ideal gas in a closed system undergoes a process in which it does 20 Joules of work. If, after the process, the internal energy of the gas is 10 Joules greater than it was before, then the amount of heat gained or lost by gas during the process is _________________.

30 Joules gained Delta U = Q - W (First law of thermodynamics ) So Q = Delta U + W W (work) = 20J Delta U = 10 J 10J +20J = 30 J GAINED (positive value)

A horizontal steel bar of uniform mass density and mass 5kg is supported by 2 vertical steel cables attached to the ends of the bar. When a 75kg mass hangs from the center of the bar, the tension in each cable is :

400N Downward force = (5kg + 75 kg) * about 9.8 = About 800 (divide by two because there are two cables) = about 400N

What is the electrical potential energy of a +2 C charge held at a distance (from a stationary charge) with a potential of 30 volts?

60 J Voltage (V) = k(constant) * Q (point charge)/r (distance from point charge) Electrical potential energy is U = k*Qq/r or U = V(voltage)*q(charge) U = 30V*2

System Types

A system is a portion of the universe that we are interested in observing or manipulating. The rest of the universe = surroundings 3 main types: Isolated systems: not capable of exchanging energy or matter with surroundings (total change in internal energy = 0) -Rare, bomb calorimeter, entire universe (because nothing surrounds the universe) *Calorimeters (like coffee cup calorimeters) are our best approximations of isolated systems, where neither energy nor matter is exchanged with the environment Closed Systems: Capable of exchanging energy but not matter (gases in vessels with moveable pistons Open system: Exchange both matter and energy with environment -Matter carries energy, and more may be transferred in the form of heat or work -Boiling pot of water, human beings, unconfined combustion reactions

In the figure below, six currents meet at point P. What is the magnitude and direction of the current between points P and x?

A. 2 A, toward x Correct Answer: A Explanation: Kirchhoff's junction rule states that the sum of all currents directed into a point is always equal to the sum of all currents directed out of the point. The currents directed into point P are 8 A, 2 A, and 3 A, so the sum is 13 A. The currents directed out of point P are 5 A and 6 A, so the total is 11 A. Because the two numbers must always be equal, an additional current of 2 A must be directed away from point P toward point x.

Relevant points in the three major temperature scales

Absolute 0: -460 deg F, -273 deg C, 0K Freezing point of water: 32 deg F, 0 deg C, 273 K Boiling point of water: 212 deg F, 100 deg C, 373 K

centrifugal force vs centripetal force

According to Newton's third law, these forces must have equal magnitude and opposite directions (antiparallel): they are equal and opposite in direction Centrifugal force is an apparent outward force during circular motion. It has been described as a reaction force according to Newton's third law the centripetal force is the force pulling the object towards the center of the circle..the centrifugal force is the force pulling it away from the center of the circle

Resistors in series

All current must pass sequentially through each resistor connected in linear arrangement Rs increases as more resistors are added (in series) As electrons flow through each resistor, energy is dissipated, and there is voltage drop associated with each resistor (voltage drops are additive ) Rs =R₁+R₂+R₃+... Voltage drops: Vs = V₁+V₂+V₃=V... Equivalent or resultant resistance: Sum of individual resistances When there si only one path to take, the current will stay the same through every resistor. Once you know the current, use V = IR to solve voltage drop across each resistor *for example, if you have 3 resistors, a (R1) = 3 ohms, b = 5, c = 7 in series, connected cell supplying 5V, the total R = 15 ohms. Them 5/15 = I = 1/3 So, the voltage drop across R1 = .33X3 = 1 ohm The voltage across R2 = 5X1/3 = 1.67 ohms Voltage drop across R3 = 7X1/3 = 2.333 (all should add up to 5)

Electromagnetic Waves

Changing magnetic field can cause change in electric field and vice versa Oscillations caused independent of matter, so EM waves can travel through vacuum Transverse: oscillating electric and magnetic field vectors are perpendicular to direction of propagation Electric and magnetic field are perpendicular to each other In a vacuum, all EM waves travel at the speed of light (3.00X10^8 m/s) -For MCAT, assume waves in air do too v = f*wavelength becomes C = f*wavelength where C is the speed of light The electric field oscillates up and down and the magnetic field oscillates into and out of page

__________ mirrors and ____________ lenses are both converging ___________ mirrors and __________ lenses are both diverging

Concave mirrors and convex lenses are both converging Convex mirrors and concave lenses are both diverging *For diverging lens (concave) and mirrors (convex) -> focal length is negative

Heat Transfer: (objects have to be in THERMAL contact, but not necessarily physical contact)(Does not require medium) Three means by which heat can transfer energy: Conduction, Convection, Radiation Imagine a thick metal container with two compartments. Compartment A is full of a hot gas, while compartment B is full of a cold gas. What is the primary mode of heat transfer in this system?

Conduction = direct transfer of energy via molecular collisions (use be direct physical contact)(metals ar best, gases not so much because there is more space (touching something hot) *When a metal spoon is placed in a pot of hot soup, the molecules in the soup collide with those on the surface of the spoon, thereby transferring heat by conduction. *A has direct contact with B, B has direct contact to C Convection = transfer of heat by the physical motion of a fluid over a material (only liquid and gases can transfer through this means)(if fluid has higher temp, it will transfer heat)(Can also be used to rapidly cool reaction via cold water bath) *fire warms the air above it, and the warmed air is less dense than the surrounding air, so it rises. A rising column of warm air means that heat is being transported in the air mass, which is simply the process of convection. The smoke particles ride along with the upward moving air current and create a plume of smoke. Radiation = the transfer of energy by electromagnetic waves (unlike conduction and convection, this can go through vacuum)(how the sun heats the earth) In this situation, heat will transfer from the warm gas to the metal and then to the cold gas. Choice (B), convection, requires flow of a fluid to cause heat transfer. In this case, the gas is not flowing, but rather is in contact with the metal. Choice (A), heat transfer through radiation, is also implausible not only because gases are unlikely to emit heat in the form of waves, but also because the radiation would be unlikely to penetrate the thick metal container. Enthalpy, choice (D), is not a form of heat transfer. Conduction, choice (C), is the most likely option; it happens when two substances make direct contact with one another. Here, gas A makes contact with the metal container, which makes contact with gas B.

Converging VS Diverging Lens

Converging lenses are needed for people who are farsighted (reading glasses) -Farsightedness = hyperopia -Objects farther away are seen clearly, while objects up close are blurry -Always thicker at center Diverging lenses (standard glasses) are needed by people who are nearsighted -you can see objects clearly Up Close, but objects farther away are blurry -Always thinner at center -nearsightedness = myopia Bifocal lenses are corrective lenses that have two distinct regions The eye has an optical power of around 60 diopters Most contact lens wearers have prescriptions between 0.25 and 8 diopters (+ and -), so even at tis worst the human eye can maintain its optical power at about 87% of maximum

When monochromatic light is refracted as it passes from air to glass, which of the following does NOT remain the same? (Note: Assume that the wave is fully transmitted.) A. Wavelength B. Frequency C. Amplitude D. Period

Correct Answer: A Explanation: As light rays travel from one medium to another, their wavelengths change. Even if we did not know this immediately, we can determine the answer through process of elimination. Frequency and period are inverses of each other, so if either of these quantities changes, the other would have to change as well, eliminating choices (B) and (D). Further, because the wave is fully transmitted, there is no absorption or reflection, and the amplitude (which is related to intensity) should not change, eliminating choice (C). When light is refracted, its speed changes; although the frequency does not change, the wavelength does.

Assume that having blonde hair and blue eyes are independent recessive traits. If one parent is a carrier for each gene while the other parent is homozygous recessive for both genes, what is the probability that the first two offspring will both have blonde hair and blue eyes? A. 6.25% B. 25% C. 43.75% D. 50%

Correct Answer: A Explanation: Because one parent is homozygous for both traits, we are only concerned with the other parent. This parent has a 50% chance of transmitting each independent trait, and thus a 25% chance of transmitting both (0.5 × 0.5 = 0.25). This probability is the same for both pregnancies because they are independent events; thus, the probability that both children exhibit both traits is 0.25 × 0.25 = 0.0625, or 6.25%

An experimenter is attempting to determine the internal energy of a well-known compound He cleans his glassware, completes the synthesis, calibrates a bomb calorimeter, and then uses it to measure the appropriate thermodynamic values. Which of the following errors did he make? A. He did not determine if the compound was novel or if the information has already been determined. B. He did not have a specific goal at the beginning of his research. C. He should not be involved in both the synthesis of the compound and later testing. D. He should have calibrated the calorimeter before the synthesis of the compound.

Correct Answer: A Explanation: The experimenter has not completed the initial phases of research. There was no data acquisition or refinement, and there was no indication that the question required an experiment to be answered. Were the experimenter doubtful of the validity of the reported value, an experiment could be appropriate—but there is no information to indicate that this is so. Based on the question stem, it is clear that the experimenter had a clear goal, eliminating choice (B). In human subjects research, tasks may be divided to facilitate blinding, but this is generally unnecessary in basic sciences research, eliminating choice (C). As long as the calorimeter was calibrated prior to its use, it does not matter when this calibration occurred relative to the synthesis of the compound, eliminating choice (D).

A firefighter jumps horizontally from a burning building with an initial speed of 1.5 m/s At what time is the angle between his velocity and acceleration vectors the greatest? A. The instant he jumps B. When he reaches terminal velocity C. Halfway through his fall D. Right before he lands on the ground

Correct Answer: A Explanation: The firefighter's acceleration is always directed downward, whereas his velocity starts out horizontal and gradually rotates downwards as his downward velocity increases. Therefore, as time progresses, the angle between his velocity and acceleration decreases, which means that the maximum angle occurs at the instant he jumps.

The value of 200^0.25 is closest to: A. 4 B. 14 C. 50 D. 800

Correct Answer: A Explanation: The fourth root of a number, or a number raised to the one-quarter power, is the square root of the square root of that number: 200^(1/4) = 200^(1/2)(1/2) = sqrrt of sqrrt of 200 -> sqrrt of 200 = about 14 (because 14^2 = 196), now take the square root of that -> therefore, the fourth root of 200 should be a bit less than 4.

All of the following statements about the photoelectric effect are true EXCEPT: A. the intensity of the light beam does not affect the photocurrent. B. the kinetic energies of the emitted electrons do not depend on the light intensity. C. a weak beam of light of frequency greater than the threshold frequency yields more current than an intense beam of light of frequency lower than the threshold frequency. D. for light of a given frequency, the kinetic energy of emitted electrons increases as the value of the work function decreases.

Correct Answer: A Explanation: The greater the intensity, the greater the number of incident photons and, therefore, the greater the number of photoelectrons that will be ejected from the metal surface (provided that the frequency of the light remains above the threshold). This means a larger current. Remember that the frequency of the light (assuming it is above the threshold frequency) will determine the kinetic energy of the ejected electrons; the intensity of the light determines the number of electrons ejected per time (the current).

A hydraulic lever is used to lift a heavy hospital bed, requiring an amount of work W. When the same bed with a patient is lifted, the work required is doubled. How can the cross-sectional area of the platform on which the bed is lifted be changed so that the pressure on the hydraulic lever remains constant? A. The cross-sectional area must be doubled. B. The cross-sectional area must be halved. C. The cross-sectional area must be divided by four. D. The cross-sectional area must remain constant.

Correct Answer: A Explanation: This question tests our understanding of Pascal's principle, which states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel. We are told that the work required to lift the bed with the patient is double the work needed to lift just the bed. In other words, the force required doubles when both the bed and the patient have to be lifted. To maintain the same pressure, we must double the cross-sectional area of the platform of the hydraulic lever on which the patient and the bed are lifted.

The entropy of a system can: A. never decrease. B. decrease when the entropy of the surroundings increases by at least as much. C. decrease when the system is isolated and the process is irreversible. D. decrease during an adiabatic reversible process.

Correct Answer: B Explanation: The entropy of a system can decrease as long as the entropy of its surroundings increases by at least as much. On the other hand, the entropy of an isolated system increases for all real (irreversible) processes. This adheres to the second law of thermodynamics, which says that energy will be dispersed and entropy of the universe will remain constant or increase during all processes.

Which of the following describes the image formed by an object placed in front of a convex lens at a distance smaller than the focal length? A. Virtual and inverted B. Virtual and upright C. Real and upright D. Real and inverted

Correct Answer: B Explanation: The image produced by a convex lens can be either real or virtual. It is real if the object is placed at a distance greater than the focal point, and virtual if the object is placed at a distance less than the focal point (between the focal point and the lens). Remember that for a single mirror or lens, an image that is real must be inverted and one that is virtual must be upright. In this question, the object is placed in front of the focal point, so the image must be virtual and, therefore, upright. We could also determine this from the optics equation. If f > o, then 1/f - 1/o is negative, and i is therefore negative (virtual).

In a sample of hospital patients, the mean age is found to be significantly lower than the median. Which of the following best describes this distribution? A. Skewed right B. Skewed left C. Normal distribution D. Bimodal distribution

Correct Answer: B Explanation: The mean is to the left of the median, which implies that the tail of the distribution is on the left side; therefore, this distribution is skewed left. It would be expected that there would be a low plateau on the left side of the distribution, which accounts for the shift in the mean.

What is the wavelength of a photon that causes an electron to be emitted from a metal with a kinetic energy of 50 J? (Note: The work function of the metal is 16 J, and h = 6.626 × 10-34 J·s) A. 1.0 × 10-34 m B. 3.0 × 10-27 m C. 3.0 × 10-26 m D. 1.0 × 1035 m

Correct Answer: B Explanation: To determine the wavelength of the light ray, first calculate its frequency from the photoelectric effect equation: K = hf - W -> f = K+w/ h = 50 J + 16 J / 6.626 × 10-34 J·s = 6.6X10^1 / 6.6 X 10^-34 = 10^35 Hz Next, determine the wavelength of the incident ray of light by relating the frequency to the speed of light: C = f*wavelength Wavelength = c/f =3X10^8 / 10^35 Hz -> 3X10^-27 m

If the gravitational potential energy of an object has doubled in the absence of nonconservative forces, which of the following must be true, assuming the total mechanical energy of the object is constant? A. The object has been lifted to twice its initial height. B. The kinetic energy of the object has been halved. C. The kinetic energy has decreased by the same quantity as the potential energy has increased. D. The mass of the object has doubled.

Correct Answer: C Explanation: In the absence of nonconservative forces, all changes potential energy must be met by an equal change in kinetic energy. Note that it is the difference in potential energy that is the same as the difference in kinetic energy, not the proportionality, eliminating choice (B). Both choices (A) and (D) could be true statements but do not necessarily have to be—the object's mass could have been quadrupled while its height was halved.

Current Voltage Electromotive force (emf) Conductivity

Current: Movement of positive charge through conductive material over time (amperes: C/S) Voltage: Potential difference between two points (V: J/C) Electromotive force (emf): Potential difference of the voltage source for a circuit, usually a battery (also measured in Volts) Conductivity: Reciprocal of resistance, measure of permissiveness to current flow (measured in Siemens (S))

Measures of Central Tendency

Describe the middle of a sample (but how we define the middle can vary): Mean/ arithmetic mean: (equation shown in image): The average, adding up all individual values and dividing the result by the number of values -n = number of data points in the set -Good indicators of central tendency when all values fairly close -Not so good for Outlier -> can shift mean towards one end of the range - Good for normal distribution Median: (n+1)/2 where n is the number of data values -Midpoint: Half of the data points are greater than the value and half are smaller -MUST FIRST LISTED VALUES IN ORDER -Least susceptible to outliers, but not good for large range or multiple modes IF THE MEAN AND MEDIAN ARE FAR APART FROM EACH OTHER, THIS IMPLIES OUTLIERS OR SKEWED DISTRIBUTION -If mean and median are close it implies symmetrical distribution Mode: Number that appears most often in a set of data -There may be multiple or none -Seen as peaks Outliers: result from 1 of 3 causes: 1. True statistical anomaly / anomalous result 2. Measurement error 3. Distribution not approximated by normal distribution (skewed with long tail) *Decision of what should be done with outliers should be made before study begins *When outliers are an indication that data set may not approximate normal distribution, repeated samples or larger samples will generally demonstrate if this is true *Existence of outliers say if mean is appropriate measure

Geometrical Optics

Describes Behavior of light at the boundary of a medium or interface between two media -it determines the lights behavior in regards to reflection and refraction, as well as the applications mirrors and lenses. When light travels through a homogeneous medium, it travels it straight line: Rectilinear Propogation

In a reversible process, 5.46X10^4 J of heat used to change 200g block of ice into water at 273K,w hat is change in entropy *Heat of fusion of ice = 333 J/g

During phase change temp is constant (at 273 in this case) ΔS = Qrev /T = 5.46X10^4 / 273 = 2X10^2 J/g = ΔS q = mL = 200g * 333J/g = 6.66X10^4 (this is amount of energy in joules needed to melt ice, which we didn't reach, so the ice did not melt completely and temp remained constant

Gamma Decay

Emission of γ rays (gamma rays), which are high frequency, high energy photons They don't carry a charge and lower energy of parent nucleus without changing mass or atomic number High energy state of parent shown with asterisk No changes occur in mass number or atomic number, only a γ ray is emitted *Note: Gamma radiation produces electromagnetic radiation (rather than nuclear fragments), so it can be detected on an atomic absorption spectrum

Describe: A. Dispersion B. Refraction C. Diffraction D. Polarization

Even though the light is traveling through a prism, the change in the light's direction is caused by refraction, not dispersion. Dispersion involves the breaking up of polychromatic light into its component wavelengths because the degree of refraction depends on the wavelength. We are told that the incident light is monochromatic or, in other words, of only one wavelength; therefore, light will not be dispersed, eliminating choice (A). Diffraction, choice (C), describes the spreading of light waves as they pass through a small opening. Polarization, choice (D), is the alignment of the electric field component of light waves. *image shown is refraction

Silver has a melting point of 962 deg C and a heat of fusion of 1.05X10^5 J/kg Specific heat of silver = 233 J/kg*K How much heat is required to completely melt 1kg silver with initial temp of 20 deg C?

First you have to heat the chain up to the melting point: q = mcΔT The specific heat uses Kelvins, so everything needs to be converted to K 962 + 273 = 1235 Initial temp = 293 Change in temp = 942 q = 1kg * 233* 942 -> 1 * 230 * 950 -> about 200 * 1000 = 2X10^5 J So, you have to add that much heat to get chain to the melting point, but it is still in solid phase. Now, use q =mL to melt it 1kg * 1.05X10^5 J/kg = 1.05*10^5 J Total heat needed = about 200 kJ + 105 kJ = little over 300 kJ

Sign Convention for a single mirror

For MCAT, O is almost always positive If O is positive, image with single lens or mirror = UV NO IR -> Upright images are Virtual, No image if Object is focal length away, Inverted images are always Real m (magnification) tells you if the image is inverted (negative m) or not (positive m). Then, the absolute value of m tells you if the image is enlarged ( | m | > 1) or not

Heat and the second law of thermodynamics

Heat: Process of energy transfer between two objects at different temperatures -Will continue until the 2 objects come into thermal equilibrium at same temp *Work and heat are the only 2 ways energy can be transferred Second Law of thermodynamics: Objects in thermal contact and not in thermal equilibrium will exchange heat energy so object with higher temp will give off heat energy to object with lower temp until both have same temp at thermal equilibrium (energy constantly being dispersed) *Heat won't spontaneously transfer energy from cold to warm object without work being done on the system Unit for heat = Joule (J) (or calorie (cal), nutritional Calorie (Cal) = 1000 calories , or British thermal unit (BTU)) calorie = about of heat required to raise 1 g of water 1 degree Celsius (1 Calorie (1000 calories)= heat to raise 1 kg of water 1 deg C) 1 Cal = 1000 cal = 4184 J = 3.97 BTU

Consider two resistors wired in parallel with R1 = 5 ohms and R2 = 10 ohms. If the voltage across them is 10V, what is the current through each of the 2 resistors?

How to start: Find total voltage (10V) , total resistance, and then use that to find total current Parallel: 1/Rp = 1/5 + 1/10 = 2/10 + 1/ 10 = 3/10 Rp = 10/3 So that is our total resistance. Because it is parallel, we know 10 V is going to stay the same through out each. Now we need to find current V= IR (Ohm's Law) I = V/R Total current (Ip) = 10 / 10/3 = 3 Amps (So we know that I 1 + I2 = 3A) I1 = 10 / 5 = 2 Amps I2 = 10/10 = 1 Amp Note, 1+2 = 3 amps, and the resistor with smaller resistance has bigger current

A detector with a surface area of 1 square meter is placed 1 meter from a blender. It measures the average power of the blenders sound as being 10^-3 W. Find the intensity and sound level of the blender, and the ratio of the intensities of the blender and a jet engine. (Assume Bjet=150dB)

I - P/A = 10^-3 / 1 m^2 = 10^-3 W/m^2 B (sound level)= 10 log (Intensity/threshold of hearing) = 10*lof (10^-3/10^-12) = 10X 9 = 90 dB Ratio of 2 sound intensities: B of jet = B of blender + 10 log (I jet / I blender) 150 dB = 90 dB (I jet/ I blender) 6 = log (I jet/ I blender) (I jet/ I blender) = 10^6 Jet engine is 1,000,000X more intense than blender

Kinetic energy of ejected electrons

If frequency of photon on metal is at threshold frequency for metal, electron barely escapes If it is above threshold for metal, excess energy converted to kinetic energy in ejected electron Calculate max kinetic energy of ejected electron: K max = hf - W where W is work function of metal h is Planck's constant (6.626X10^-34 J*s) the work function is the minimum required to eject electron: W = h*fT -Think of it like activation energy: Must be matched or exceeded for escape of electron So K max = hf - h*fT) *fT is threshold frequency These formulas solve for maximum kinetic energy of electron rather than exact kinetic energy because actual energy can be anywhere from 0 to K max depending on subatomic interactions. K max is only achieved when all possible energy from photon is transferred to ejected electrons

Randomization and Blinding Without blinding, the placebo effect would be greatly reduced in the ______________ but still present in ______________ group

In human subjects research, there are both experimental and observational studies *Observational research does not involve manipulation of the subjects environment -> Generally less conclusive and more subjective than experimental research (which does involve manipulation of subject or environment) Experimental Approach: Randomization is the method used to control for difference between subject groups in biomedical research -Blinding: Perception biased by knowing what group subject is in -SIngle Blind: only patient or assessor (person who performs assessments) is blinded Double blind: Everyone is blinded (investigator, subject, assessor) Without blinding, the placebo effect would be greatly reduced in the control group (because they know they aren't getting anything) but still present in treatment group

Incompressible fluids (liquids) demonstrate an __________ relationship between their dynamic pressure (function of speed) and there static pressure

Incompresible fluids (liquids) demonstrate an inverse relationship between their dynamic pressure (function of speed) and there static pressure Bernoulli's equation says if more energy dedicated toward fluid movement then less energy dedicated toward static pressure Static pressure is the pressure associated with position; static pressure is sacrificed for dynamic pressure during flow. (measured by pitot tube)

Objects A and B are submerged at a depth of 1 m in a liquid with a specific gravity of 0.877. Given that the density of object B is one-third that of object A and that the gauge pressure of object A is 3 atm, what is the gauge pressure of object B? (Note: Assume atmospheric pressure is 1 atm and 9.8 m/s^2 = g) A. 1 atm B. 2 atm C. 3 atm D. 9 atm

Kinda a trick question Correct Answer: C Explanation: The absolute and gauge pressures depend only on the density of the fluid, not that of the object. When the pressure at the surface is equal to atmospheric pressure, the gauge pressure is given by Pgauge = ρgz, where ρ represents the density of the fluid, not the object. If 2 objects are at the same depth, they must have the same gauge pressure.

Exponential Decay

Let n be the number of radioactive nuclei that haven't been decayed yet. The rate of nuclei decay (Δn/Δt) = - λ * n where λ = decay constant Tells us how the number of radioactive nuclei changes with time: Exponential decay: n = n0*e^-λt where n0 = number of undecayed nuclei at time t = 0 Decay constant is related to half life by: λ = ln 2/ (T 1/2) = 0.693 / (T 1/2) Y-axis: Percentage of radioactive nuclei remaining X-axis: Number of half lives

Sound

Longitudinal wave transmitted by oscillation of particles in deformable medium (a medium that can change shape when external pressure applied) Can travel through solids, liquids, and gases but not through vacuum Given by: v = Square root of (B/p) where B is bulk modulus (measure of mediums resistance to compression) and p is density of medium -Bulk modulus increases from gas to liquid to solid -Bulk modulus increases WAY more than density -Sound travels fastest through solid (with low density) and slowest through (dense) gas Sound produced by mechanical disturbances in particles along waves direction of propagation -Particles don't actually travel along with the wave, but they vibrate/oscillate around eq position, which causes small regions of compression to alternate with small regions of Rarefaction (Decompression) source of any sound is ultimately mechanical vibration Pitch (frequency) at which air column vibrates is determined by length of air column (can be changed by covering holes) -Pair of membranes stretched across larynx that vibrate = vocal cords *Males have larger and thicker vocal chords = lower voice

Intensity and Loudness (Volume) of Sound

Loudness/volume is how we perceive intensity (Subjective, depends on physical factors) Sound intensity on the other hand, is objectively measurable Intensity is average rate of energy transfer per area across surface perpendicular to wave: power transported per unit area Units for intensity = watts/square meter (W/m^2) I = P/A P is power produced by the source and A is the area over which the power is spread Power = Intensity * Area Intensity is proportional to the square of the amplitude (doubling amplitude = 4 times the intensity) Sound waves spread sound over larger and larger areas the further they travel from the source *Intensity inversely proportional to square of distance

A diver is 20 m below the surface. What is the gauge pressure? What is absolute pressure? The density of sea water = 1025 kg/m^3

Note: the SI unit for gravity is 9.8 m/s^2 = 9.8 N/kg Since the pressure at the surface (P0) = Patm, we can say gauge pressure = density* g *z =1000 kg/m^3 * 9.8 N/kg * 20 m = 20000 N/m^2 = 2X10^5 Pascal Absolute pressure = Patm + pgz (gauge pressure) (where p = rho = density) 1.013X10^5 pascal + 2X10^5 Pascal = about 3X10^5 pascal

Fusion

Nuclear fission and fusion both release energy Size or reactant particles: Small (hydrogen, helium) Increase in nuclear mass Small nuclei combine to form larger nucleus -How many stars power themselves (including sun) -> 4 hydrogen nuclei to make 1 helium nucleus produces 3.85 X 10^26 joules / second (385 yottawatts) Fusion power plants (less common) generate energy from deuterium (2 over 1 H) and lithium nuclei

Fission

Nuclear fission and fusion both release energy large nucleus into smaller nuclei (size of reactant particles: Large (Lanthanides, actinides) (decrease in nuclear mass) -spontaneous fission rarely occurs -Absorption of low energy neutron can be induced in certain nuclei -Releasing neutrons causes chain reaction that causes nearby atoms to undergo fission (induced fusion: powers most commercial nuclear power plants)

Work-Energy Theorem

Offers direct relationship between the work done by all forces acting on object and the change in kinetic energy of object Net work done by forces = change in objects kinetic energy Wnet = ΔK = K final - K initial ΔU = heat transferred into system (Q) - mechanical work done by the system (W)

Power (lens)

P = 1/f Power (P) measured in diopters, f = focal length in meters P and f are positive for converging lens (convex) and negative for diverging lens (concave)

Plane Mirrors

Parallel incident light rays remain parallel after reflection from plane mirror (flat, reflective surface that causes neither convergence or divergence Light does not converge at all, so it always produces virtual images Most common mirrors in our house: images appear to be behind the plane in which the mirror lies. Think of place mirrors as spherical mirrors with infinite radius of curvature r = f = infinity so 1/o + 1/I = 0 (i = -o) Virtual image is at distance behind mirror = to distance of object in front of mirror

A hydraulic press has a piston of radius 5 cm, pushing on enclosed fluid. A 50 kg weight rests on piston. Another piston has radius of 20 cm. What force is needed on larger piston to keep the press in equilibrium? g = 10 m/s^2

Pascal's Principle: P = F1/A1 = F2/A2 First get kg into Newtons for force 50X10 = 500 N = F1 F2 = F1 (A2/A1) F2 = 500 (pi*r^2 / pi*r^2) F2 = 500 (r1 / r2)^2 500 (20/5)^2 500X16 = 8000 N

Frequency and Pitch

Pitch: Our perception of frequency lower frequency = lower pitch higher frequency = higher pitch Range of hearing = 20 Hz - 20000 Hz Below 20 Hz = infrasonic waves (frequency lower than humans can hear) Above 20000 Hz = ultrasonic waves (dog whistles, and ultrasound machines)

Windows measure 2.0X3.5 meters. Storm lowers pressure outside window to 0.997 atm while pressure inside remains at 1 atm. What is net force pushing on window

Pnet = Fnet/A -> Fnet = Pnet * A where P=pressure, F = magnitude of normal force vector, and A is area Measured in pascal (Pa) = newton per square meter (a N/m^2) *Convert pascal to atm (1 atm = 1.013 X10^5 pascal) Fnet = 1X10^5 * (1-0.997) * (2X3.5) =10^5*0.003*7 10^5 * 3X10^-3 * 7 21X10^2 2100 N

Positive Control and Negative control

Positive: ensures a change in the dependent variable when it is expected (receives treatment with known result) Negative: ensures no change in the dependent variable when no change is expected (used to assess for placebo effect) Experimental group falls in between these 2 extremes Controls help establish casualty by demonstrating that the outcome does not occur in the absence of intervention. Controls are used to keep the manipulations of systems as similar as possible, or as a known standard to judge experimental manipulation against

Electric Potential (measured in volts)(not the same as electric potential energy)

Ratio of magnitude of charge's electric potential energy to magnitude of charge -Not the same as voltage, which is the potential difference, or measure of the change is electrical potential between two points, provides indication of tendency toward movement in one direction or other V = U/q where V is the electric potential measured in volts (V) and 1 V = 1 J/C Even with no test charge (q), we can use V = kQ/r -Scalar quantity, sign determined by sign of Q -V inversely proportional to distance from Q There is potential difference between two points that are different distances from Q (Lets say Va and Vb). This potential difference = voltage (Vb-Va) Potential difference = Delta V = Vb-Va = Wab/q where Wab is work needed to move q through e field from a to b -Conservative force -The + end of battery is high potential end, minus is low potential need. Positive charges move from + to - (current) and negative charges move from - to + Given an electric dipole, the electrical potential is zero: B. anywhere on any perpendicular bisector of the dipole axis and at infinity. Charges move to decrease electric potential energy -For a positive test charge (q), this means going from high potential energy (a) to low potential energy (b), so b-a is negative number. Looking at equation, Delta V = Vb-Va = Wab/q, is Vb-Va is negative, and q is positive, Wab has to be negative. -If work is negative, this is a decrease in electric potential energy -Negative test charge: going from low to high, so Vb-Va is positive. But, in order for Wab/q to be positive too, when q is negative work also has to be negative, which again represents decrease in electric potential energy SO: Positive charges move in direction to decrease their electrical potential (negative voltage), whereas negative charges move in direction to increase electrical potential (positive voltage). But, in both cases, electric potential ENERGY is decreasing

Ray diagrams for convex (diverging) mirrors

Ray that strikes parallel to axis appears to be reflected through focal point (F). A ray that appears to pass through the focal point is reflected back parallel to axis. Ray towards center of mirror reflects back at the same angle relative to the normal Single diverging mirror only forms virtual, upright and smaller image -The further away the object, the smaller the image will be -Think of security mirrors and mirrors in passenger side

Semilog and log-log graphs

Semilog graphs: Linear, which makes them easier to interpret than curved log graph *usually, x-axis stays the same, butt he y - axis assigns spacing based on ration (10, 100, 1000, ....) *can be multiples of any number as long as it is consistent *Look for weird spacing between points on the y axis, like the tiny tick marks will be very condensed towards the next number *Image shown Log-log: Both axes given different axis to create linear plot: still constant ratio

Energy Dispersion: Entropy

Second law of thermodynamics states that energy spontaneously disperses from being localized to becoming spread out if not hindered *entropy isn't just disorder, it is the measure of spontaneous dispersal of energy at certain temp (how much energy is spread out, how widely) *If water remains at melting point, it has same kinetic energy as ice, but different number of micro states (both have same temp and kinetic energy, but liquid has more micro states and thus higher entropy = less organized than ice) The equation for calculating the change in entropy = ΔS = Q of rev (Qrev) / T where ΔS = change in entropy (units = J/ mol* K), Qrev = heat gained or lost in a reversible process, and T is temp in kelvin *When energy is distributed into system at given temp, entropy increases (energy out of system = entropy decrease) The entropy of a system will NEVER DECREASE (it either increases or remains 0) Energy spontaneously disperses, but it can also be localized or concentrated (but this won't happen spontaneously in a closed system) *work usually has to be done to concentrate energy *unidirectional limitation on the movement of energy = "times arrow" *Energy is a closed system will spontaneously spread out and entropy will increase if not hindered *So basically, the second law says that entropy of the universe (which is a closed, expanding system) is increasing ΔS of universe = ΔS of system + ΔS of surroundings > 0 Every Natural process is ultimately irreversible Unnatural process: put hot and cold object together, and the hot object gets hotter and the cold object gets colder Under highly controlled conditions, certain equilibrium processes such as phase changes can be treated as essentially reversible Reversible reaction: Process requires an infinite amount of time (goes REAL slowly): Requires that system is always in equilibrium and no energy is lost or dissipated (no real processes are truly reversible, we can only approximate) So, a reversible process is defined as a process that can spontaneously reverse course *Process of freezing and melting water is chemically reversible

Which of the following accurately depicts the field lines created by a proton that is moving toward the right on this page?

The answer is D You should know that the field lines for a positively charged particle will always point away from the particle in a radial pattern, regardless of the direction in which the particle is moving. This is because field lines point in the direction a positive test charge would move in that field (that is, the direction that a force would be exerted on a positive test charge in that field).

Potential Energy stored in a capacitor

U = 1/2 CV^2

If two objects are traveling toward each other, how does the apparent frequency differ from the original frequency? Traveling away from each other? One following the other?

Use Doppler equation Travling toward = top sign used Apparent frequency is higher than actual frequency f' = f (V+VD/ V-VS) Away = bottom sign used Apparent frequency lower than original frequency f' = f (V-VD/ V+VS) Following: Either f' = f (V+VD/ V+VS) or f' = f (V-VD/ V-VS)

Helium nucleus should theoretically have mass of 4.03190 but it has mass of 4.00260 amu. What is the mass defect and binding energy of nucleus? C^2 = 932 MeV/amu

Use E = mC^2 4.03190- 4.00260 = 0.02930 amu = mass defect 0.02930 amu * 932 MeV/amu = about 27 MeV

H2O molecule has dipole moment of 1.85 D Calculate electrical potential due to water molecule 89 nm away along the axis of the dipole *Because it is along the axis, cos(0) = 1 *k = 9*10^9 1 D (Debye) = 3.34X10^-30 C*m

Use V (electric potential) = kqd /r^2 *cos theta = (9X10^9)(qd = p (dipole moment in C*m) / (89X10^-9)^2 =(9X10^9)(1.85X(3.34X10^-30 C*m)) / (8.9X10^-8)^2 9*2*3X10^-21 / 9*9X10^-16 = 6/9 X 10^-5 About 0.67 X10^-5 or 6.7X10^-6 V

Ultrasound

Uses high frequency sound waves outside range of human hearing to compare the relative densities of tissues *Consists of transmitter that generates pressure gradient (also functions as receiver that processes reflected sound) Calculate distance based upon travel time of the reflected sound. Speed of wave and travel time are known, used to generate graphical representations of borders by calculating traversed distance Relies on reflection: Interface between 2 objects is necessary to visualize everything *Transmitter (sender) generates wave, which reflects off of an object and return to the transmitter (also functions as receiver) -Do not function simultaneously Doppler ultrasound used to determine flow of blood Ultrasounds can increase blood flow to sire of injury Can create friction and heat Can also break up kidney stones and used in dental cleaning

Single Slit Diffraction

When light passes through narrow opening, light seems to spread out -More narrow slit = more spread out light If a lens is between narrow slit and screen, we see bright central fringe with alternating dark and bright fringes on each side Central bright fringe (maximum) is twice as wide as bright fringes on side, and as slit narrows the central maximum becomes wider The location of dark fringes (minima) = a sin θ = n*wavelength where a = width of slit, θ is angle between line drawn from center of lens to dark fringe and axis of lens, n is integer indicating # of fringe, wavelength is wavelength of incident wave *bright fringes halfway between dark fringes

Radioactive Decay

a naturally occurring spontaneous decay of certain nuclei accompanied by the emission of specific particles Know how to answer: 1. Integer arithmetic of particle and isotope species 2. Radioactive half-life problems 3. Exponential decay curves and decay constants

4 core ethical tenets

beneficence: Obligation to act in patients best interest nonmaleficence: Obligation to avoid things where potential harm outweighs good autonomy: Respect Patient's decisions justice: Responsibility to treat people fairly and and distribute care

Third Law of Thermodynamics

entropy of a perfectly organized crystal at absolute zero is zero

Ray Diagrams for concave (converging) mirrors

3 important rays to draw: If rays don't intersect, extend them to the other side to create virtual image Concave mirror: Ray that strikes parallel to axis is reflected back through focal point (F). A ray that passes through the focal point is reflected back parallel to axis. Ray towards center of mirror reflects back at the same angle relative to the normal A) the object is behind F -> image is real, inverted, and magnified B) Object placed at F -> Any time object is at focal point of converging mirror, the reflected rays will be parallel and the image will be at infinity (no image is formed because reflected rays are parallel) C) Object between F and mirror -> image is virtual, upright, and magnified (rays appear to converge behind mirror, but they don't)

tan^-1 (1)

45 degrees pi/4

A circuit consist of a 12 V battery and two resistors of resistance 3 Ω and 4Ω in parallel with the battery. The ratio of the current in the 3Ω resistor to that in the 4Ω resistor is :

4:3 Current: I = V/R 12V/3 Ω = 4A (first) 12V/4 Ω = 3A 4A/3A = 4/3

A plane mirror of height 1 m has the property that is reflects light rays that are perpendicular to its surface back in the same direction they came. The focal length of such a mirror is:

Infinity Focal length is distance from mirror to focal point (point at w which reflected rays of light converge/appear to diverge from) Mirror does not allow convergence, so no theoretical focal point

Plane Polarized (Linearly Polarized) Light

Light in which the electric fields of all waves are oriented in the same direction (electric field vectors and magnetic field vectors are parallel) *Side note: the plane of electric field identifies the plane of polarization *Unpolarized light has random orientation (like sunlight or lightbulb) *Plane-polarized light used in classification of stereoisomers : The optical activity of a compound due to chiral centers cause plane polarized light to rotate counterclockwise or clockwise (specific rotation) Filters called polarizers used in cameras and sunglasses that allow only light with electric field pointing in specific direction to enter -When second polarizer is perpendicular to the first, no light gets through The electric fields of unpolarized light waves exists in all 3 dimensions: The direction of the wave's propagation is surrounded by electric fields in every plane perpendicular to that direction. Polarizing light limits the electric field's oscillation to only 2 dimensions. Circular polarization: Rarely seen in nature-> results from interaction of light with certain pigments or highly specialized filters -Has uniform amplitude but continuously changing direction which causes helical orientation Helix has average e field vectors and magnetic field vectors that are still perpendicular to each other, but maxima fall on outer border of helix (image) Plane polarization has no effect on wavelength or frequency or speed, but polarization DOES affect amount of light passing through a medium and intensity

Multiplying Vectors by Scalars

Magnitude will change Direction will either be parallel or antiparallel to original direction *If vector A is multiplied by the scalar value (n), a new vector (B) is created such that B = nA *Magnitude of B = magnitude of A * absolute value of n (|n|) *Direction of vector B: Look at sign on n (if n is positive, B and A go in same direction. If B is negative, B and A are in opposite directions (If vector A multiplied by scalar +3, vector B is three times as long as A and points in the same direction)

The ejection fraction is the proportion of the blood volume in the left ventricle expelled with each contraction of the heart. A patient is known to have an ejection fraction of 0.6 (only 60% of blood expelled from left ventricle per heart beat), a cardiac output of 5 L/min and a heart rate of 80 beats/min. What is the volume of blood in person's left ventricle just prior to contraction?

5 L/min / 80 Beats/min = 1/16 L/beat 1/16 * 0.6 = 0.1 Liters

Temperature A change of 10 K is equal to a change of __°C. One degree Celsius is equal to ___ degrees Fahrenheit; therefore, 10°C = __°F.

A change of 10 K is equal to a change of 10°C. One degree Celsius is equal to 1.8 degrees Fahrenheit; therefore, 10°C = 18°F. Temperature: Physical, qualitative property of matter proportional to the average kinetic energy of particles that make up substance Difference in temp determines the direction of heat flow (Heat from higher temp to lower temp) *Heat refers to transfer of thermal energy (from high temp to low temp) *If no heat flow occurs, temps are = and objects in thermal equilibrium Celcius and Fahrenheit are oldest scales because they are based on phase changes (0 and 100 for Celsius and 32 and 212 for F) Kelvin most used for science, 0 K is absolute 0 (theoretical point temp at which there is no thermal energy) -Freezing point = 273.15 K Although the scale for Celsius and Kelvin have different 0 reference points, the size of their units are the same (1 deg C = 1 K) *But, there are 180 degrees difference from freezing to boiling in Fahrenheit, so the size of Fahrenheit unit is smaller! F = 9/5 C + 32 C= 5/9 (F - 32) K = C + 273 Body temp is 98.6 F or 37 degC *Length, volume, solubility, conductivity all change as function of temp *

A long horizontal piece of pipe with varying cross sectional area is filled with a fluid of density 1.02 g/cm3 and fitted with movable pistons on each end (oriented perpendicularly to the pipe).The piston on th eleft end has a cross sectional area of A1 and the piston on the right end has a cross sectional area of A2. If a pressure of P0 is applied to the piston on the left end, then the pressure experienced by the piston at the right end is :

P0 Pascal's Principle: Change in pressure applied to enclosed fluid is transmitted undiminished to every part of fluid and to walls. If pressure is added, pressure will travel undiminished through pipe -Pressure stays the same, but force will vary in direct proportion with the area P = F1/A1 = F2/A2

Coulumb's Law

Quantifies the magnitude of the electrostatic force (Fe) between 2 charges (q1 and q2) F=kq1q2/r^2 r is distance between charges k = Coulumb's constant (electrostatic constant) = 8.99X10^9 N*m^2/C^2 = 1/4pi*E0 where E0 = permittivity of free space = 8.85 X10^-12 C^2/N*m^2 *If the distance is doubled, the square of the distance is quadrupled, and the force is reduced to 1/4 original value *Force proportional to charge magnitudes *Force magnitude inversely proportional to r^2

Gravity

Attractive force felt by all forms of matter All objects exert gravitational force Unique because it can be both a constant and a vector Usually not very significant, except on planetary level Magnitude of gravitational force (Fg) = (G*m1*m2)/ r^2 where G is universal gravitational constant (6.67X10^-11 N*m^2/kg^2) m1 and m2 are masses of 2 objects r is distance between their centers of mass *magnitude of force inversely related to square of distance (if r is halved, Fg will quadruple) *If m1 is tripled, Fg will triple Acceleration due to gravity decreases with height above earth and increases the closer to earths center of mass one gets *Near Earth's surface, g = 10 m/s^2

The radioactive isotope of lead, Pb, decays to the radioactive isotope bismuth, Bi. The decay process responsible for this decay is

Beta-minus decay A neutron in parent atom becomes proton in daughter atom Bi is daughter atom (has one more proton than Pb, which is parent atom) Neutron in Pb becomes proton in Bi Isotope = Same element, different number of neutrons = different mass number

Fundamental Measurements

British/Imperial System: FPS: Foot, pound (lb), second -Used only in US -Later derived slug as unit of mass, because pound is weight measurement Metric System: MKS: Meters, kilograms, seconds or CGS: Centimeters, grams, seconds -SI units include metric system and 4 other base units Length may be given in angstroms (1 A = 10^-10 m) or nanometers (1 nm = 10^-9 m) Energy on atomic scale can be electron-volts (1eV = 1.6X10^-19 J = amount of energy gained by electron accelerating through a potential difference of one volt)

Thermal expansion

Rising temp = increasing length of solid , decrease = decrease The amount of length change is proportional to the original length of the solid and the increase in temp according to: ΔL=αLΔT Where ΔL = change in length, a (alpha) = coefficient of linear expansion (constant, usually with units of K^-1 or deg C^-1), L = original length, ΔT is change in temp *Negative answer = decrease in length *Expansion result of increase in dimension at all point. If object initially longer, it will experience greater expansion *THIS GIVES YOU CHANGE IN length, not final length For liquids: Formula for volumetric thermal expansion for liquids and solids: ΔV = B(beta)*VΔT where ΔV is change in volume, beta = coefficient of volumetric expansion, V is original volume (constant that characterizes specific materials volume changes as temp changes -> its value = 3X coefficient of linear expansion (alpha) so that B = 3a)

Negatively charged electrons are electrostatically attracted and gravitationally attracted to positively charged protons. What is the ratio of the electrostatic force to gravitational force between electron and proton? mass of proton = 1.67X10^-27 kg mass of electron = 9.11X10^-31 kg e- = 1.6X10^-19 C k = 0X10^9 N*m^2/ C^2 G = 6.67 X10^-11 N*m^2 /kg

Fe = kq1q2/r^2 Fg = Gm1m2/r^2 Divide these 2, we get: kq1q2/Gm1m2 Plug in and simplify, we get 9*1.6*1.6*10^-29 / 6.67 * 1.6*9*10^-69 1.6X10^-29/6.67X10^-69 .25X 10^40 = 2.5X10^39 *note:: electrostatic attraction is stronger than gravitational attraction by A LOT

A ball is thrown vertically up into the air from a window ledge 30 meters above the group with an initial velocity of 10 m/s Find velocity and position after 2 seconds Find distance and time when ball at max height

Find velocity and position after 2 seconds v = v0 +at 10 + (-9.8)(2) = -9.6 = velocity at 10 seconds Position at 2 seconds = y = V0t + at^2/2 10*2 + (-9.8)(2)^2 / 2 20-19.6 = 0.4 m above the ledge Distance at max height: v^2 = v0^2 + 2ay 0 = 10^2 + 2(-9.8)(y) y = about 5 m Time at max height: v = v0+at 0 = 10 + (-9.8)(t) t = about 1 second *The amount of time that an object takes to get to max height = same time it takes for object to fall back to starting height (assuming negligible air resistance) (Because you can solve for time to reach max height by setting final velocity to 0, you can ,multiply by 2 to get total time in flight (velocity is has in x direction remains constant throughout time in flight -> by multiplying time by velocity in x-direction, you can find horizontal distance traveled)

Terms for Phase Changes

Solid to liquid: Fusion or melting (occurs at melting point)(Corresponding heat of transfer = heat of fusion) Liquid to solid: freezing or solidification (occurs at melting point)(Corresponding heat of transfer = heat of fusion) Liquid to gas: Evaporation or vaporization or boiling (Occurs at boiling point)(Corresponding heat of transfer = heat of vaporization) Gas to liquid: Condensation (Occurs at boiling point)(Corresponding heat of transfer = heat of vaporization) Solid to gas: sublimation Gas to solid: deposition

What does each nuclear reaction emit, and what are ΔZ and ΔA Alpha Decay Beta-Negative decay Beta-Positive decay Gamma Decay Electron Capture

Alpha Decay: Emits (4 over 2) He, ΔZ (atomic number = number of protons) = +2 and ΔA= +4 (mass number) Beta-Negative decay: Emits electron (B- or e-) and antineutrino (v with line over it), ΔZ = +1 and ΔA = 0 (stays same) Beta-Positive decay: Emits positron (B+ or e+) and neutrino (v with line over it), ΔZ = -1 and ΔA = 0 (stays same) Gamma Decay: Emits gamma ray (y), ΔZ and ΔA don't change Electron Capture: Emits nothing, but absorbs electron from inner shell), ΔZ=-1 and ΔA= 0 (no change)

Suppose an excited parent isotope (A over Z) X* gamma decays to (A' over Z') X which undergoes position emission to form (A'' over Z'') Y, which in turn alpha decays to (A'' over Z'') Z. If Z is americium -241, what is (A over Z) X*

Americium is 95 on periodic table. Work backwards:The last reaction is the following alpha decay: (A'' over Z'') Y -> (241 over 95) Am + (4 over 2) alpha new atomic number = 97, mass number 245 (241 + 4) This is Bk 245 Then: (A' over Z') X -> (245 over 97) Bk + (0 over +1) Beta+ New atomic number = 98 (californium) and mass number stays 245. Adding gamma ray in last step makes it high energy form, so we get: (A over Z) X* = (245 over 98) Cf *

Atmospheric Pressure

Changes with altitude Below sea level = more than 1 atm of pressure Above sea level (in the mountains) = less than 1 atm (decimal, like .93 atm or something *Atmospheric pressure impacts hemoglobins affinity for oxygen and boiling of liquids Note: Right now, about 2X10^5 Newtons of force are pushing on us

Current (I)

Flow of charge between two points at different electrical potentials connected by conductor, like copper wire -Movement of positive charge from high potential end to low potential end (in reality though, its negatively charged electrons that move in circuit from low to high potential ) Magnitude of I = amount of charge (Q) passing through conductor per unit time Δt I = Q/Δt Measured in ampere ( 1 A = 1 Coulomb / second) Current is direction of positive flow (from higher electrical potential to lower electrical potential -Direction of current is opposite of actual electron flow (Which is from low potential to high potential, reducing their potential energy) *regions around the positive charges are considered high potential, and regions around the negative charges, low potential. Since electrons are negative they should be repelled by the negative charge and attracted by the positive charge, move from regions of low potential to the regions with high potential (and because the negative charge of electron is then close to positive charge, there is less electrical potential energy, which is the energy of how far electron can "fall" (less space to fall = less energy, and there is less space to fall now because e- is right by +) Positive charge moves from points with high potential to points with lower potential. Negative charge moves to points with higher potential. Positive charge moves to a lower potential energy. Negative charge moves to a lower potential energy. ANYWAY: Current is opposite to the direction of electron flow (electrons go from low to high, current goes from high to low electrical potential) 2 patterns of currents: DC (charge flows in one direction)(house hold batteries) and AC (Charge flow changes directions periodically ) (Used for longer distances ) *Current only flows in conductive materials A potential difference (voltage) can be produced by electric generator, a galvanic (voltaic) cell, a battery, etc. When no charge is moving between two terminals with different potential values, the voltage is called the electromotive force (emf)(not actually a force, it is a potential difference (voltage) and has units of Volts (J/C)). -emf = pressure to move that results in current

Beat Frequency

Frequency of periodic increase in volume: f of beat = |f₁-f₂| where f1 and f2 represent the 2 frequencies that are close in pitch and f of beat represents beat frequency that results

Total Internal Reflection

Going from medium with higher index of refraction to lower index of refraction (water to air), the refracted angle will be larger than incident angle (θ2 > θ1) (refracted light bends away from normal) As the incident angle is increased (θ1), the refracted angle also increases , eventually reaching critical angle (θc) where refracted angle (θ2) = 90 degrees (light rays pass along interface between the 2 media) Snell's Law: If θ2 = 90 degrees θc = sin ^-1 (n2/n1) Total internal reflection: All right incident on boundary is reflected back into original material, results with any angle of incidence greater then critical angle (θc) -Occurs as light goes from medium with higher refractive index to lower refractive index At the incident angle of θc, the refracted angle = 90 degrees. When the incident angle is above 90 degrees, total internal reflection occurs

Find the gravitational force between an electron and a proton that are 10^-11 m apart Mass of proton = 1.67X10^-27 kg Mass of electron = 9.11X10^-31 kg

Magnitude of gravitational force (Fg) = (G*m1*m2)/ r^2 G is universal gravitational constant (6.67X10^-11 N*m^2/kg^2) Fg = (6.67X10^-11 N*m^2/kg^2)(1.67X10^-27 kg)(9.11X10^-31 kg) / (10^-11 m )^2 (6.5X10^-11)(1.5X10^-27)(9X10^31)/ 10^-22 100X10^-69 / 10^-22 100X10^-47 Fg = 10^-45 N

The first four energy levels of a hypothetical atom are listed on the answer card. What is the frequency of light emitted when the atom makes a transition from the n=4 to the n=2 level of this atom? (h=4.1x10^-15 eVs) n=4 -2.6 eV n=2 -4.2 eV

E = hf h = 4.1X10^-15 E = energy of photon f = frequency n=4-n=2 = 1.6 eV f = [Delta E] /h 1.6 eV/ 4.1X10^-15 = 3.9 X 10^14

A projectile of mass 20kg is shot at an angle of 60 degrees to the horizontal at a speed of 100 m/s. What is the total mechanical energy of the projectile at its highest point?

1X 10^5 J At top, projectile has potential energy (from its height) and kinetic energy (from its speed) No dissipative force = total energy at top = energy at the beginning when all of the energy is kinetic KE = 1/2 mv^2 = 1/2(20)(100)^2

Molecular Forces in Liquids: Cohesion and Adhesion

Surface tension: Causes liquid to form thin, strong layer at liquid surface -results from cohesion (occurs between molecules with the same properties) (the attractive force that a molecule of liquid feels towards molecules of the same liquid) -At the surface, molecules only have strong attractive forces pulling from below (instead of from all sides which balance out) -Pulls the surface of the liquid towards center -> establishes tension , so when small indentation is made on surface, the cohesion leads to net upward force Adhesion: another force liquids experience -the attractive force that a molecule of liquid feels towards molecules of some other substance -Cause water droplets to form on windshield even though gravity pulling down -In containers, this causes meniscus (Concave meniscus occurs when liquid crawls up the sides of the tube a tiny bit because adhesive forces are bigger than cohesive)(A convex/backwards meniscus is less common, tiny mountain, occurs when cohesive forces are greater than adhesive, like mercury)

Thermodynamic Processes *Note: Work accomplished by change in displacement is not likely to be motivated by heat transfer, and any heat transfer that does occur is most likely a result of friction dissipating mechanical energy from system

System foes from initial equilibrium with initial pressure, temp, and volume to new equilibrium state with new pressure, temp, and volume Isothermal (ΔU =change in internal energy = 0): no temperature change/constant temp/no change in internal energy (First law of thermodynamics (ΔU = Q-W) reduces to Q=W) Isobaric: Constant pressure (First law of thermodynamics reduces to multiple possible forms) Isovolumetric/Isochoric: Constant volume = no change in work (W=0)(First law of thermodynamics reduces to ΔU= Q) *Work = PΔV Adiabatic (Q=0): no heat exchange (First law of thermodynamics reduces to ΔU= -W) Closed loop process graph: Work is area inside the loop

Capacitors in Series

Total capacitance decreases (have to share voltage drop, can't store as much charge) -Similar to decrease in resistance seen in parallel resistors -Cs decreases as more capacitors are added -Capacitors must store voltage drop in the loop so each can't store as much charge -Capacitors in series act like 1 equivalent capacitor with much larger distance between plates (more distance = smaller capacitance) 1/Cs = 1/C1 +1/C2 +1/C3...... *Total voltage is the sum of individual voltages (like resistors in series)

Wave Phase

Waves passing through same space can be described by how in step or out of step they are by calculating phase difference 2 Waves with same frequency, wavelength, and amplitude and that pass through same space at same time are in phase if crests and troughs coincide/line up -Perfectly in phase = phase difference of 0 -Out of phase: Trough of one wave lines up with crest of another, phase difference = 1/2 a wave (λ/2 or 180 degrees (one cycle = one wavelength = 360)(waves can also be out of phase by any other fraction of cycle)

A train traveling south at 216km/hr is sounding its whistle while passing by a stationary observer. The whistle emits a sound at a frequency of 1400hz. What is the frequency heard by the stationary observer when the train is moving toward the observer, and when the train has passed the observer? (speed of sound in air=340m/s)

Well first, convert 216 km/hr to m/s 216 * 1000m/3600sec = 215X0.35 = about 60 m/s Now use doppler equation Train moving toward detector = top sign used in denominator, but vD = 0 because object not moving so we get: f' = f* (v/v-vs) where v = 340 m/s and vs = 60 m/s and f = 1400 Hz = 1700 Hz Now, when the train is moving away, everything stays the same except the bottom sign is used for the train because it is going AWAY from detector 1400* (340/ 340+60 ) = 1400(17/20) = about 1200 Hz

Skewed distributions

When the spread of data is not symmetrical meaning the data clusters to one end. The mode is located at the highest point, then the median and finally the mean. (mean is more susceptible to outliers, mode really isn't affected by outliers, and median can be (so it is in the middle)) The direction of skew is determined by tail, not the bulk of distribution: The visual shift in data opposite direction of skew -Negatively skewed distribution has tail on left (negative side) -Positively skewed distribution has tail on right

Principle of Superposition

When waves interact with each other, the displacement of the resultant wave at any point is the sum of the displacements of the two interacting waves -When waves are perfectly in phase (they match up), the displacements add together and the sum of resultant is = to sum of amplitudes of other two waves (Constructive interference) *If two waves with = amplitude are 180 degrees out of phase, resultant wave has 0 amplitude 2 waves perfectly in phase = amplitude is sum of amplitudes 2 Waves perfectly out of phase: amplitude is difference in amplitudes (0) * If two waves are 180° out of phase, what is the amplitude of the resultant wave if the amplitudes of the original waves are 5 cm and 3 cm? 2 cm *Partially constructive/destructive interference -> resultant is sum of displacement of two waves (don't perfectly add together because they are not perfectly in phase, so the amplitude of the resultant wave is not quite the sum of the two waves amplitudes. Noise cancelling headphones capture environmental sound and produce a wave about 180 degrees out of phase = cancelling ambient sound

A gas in a cylinder kept at constant pressure of 3.6.X10^5 Pa while 300 kJ of heat are added cause gas to expand from 1 to 1.5 m^3. Find work done and change in internal temperature (ΔU)

Work = PΔV (3.6X10^5)(0.5) = 1.8X10^5 J ΔU = Q-W Where Q is energy transferred into system as heat and W is work ΔU = 3X10^5 J - 1.8X10^5 J = 1.2X10^5J = 120 kJ

Finding the Resultant (R) of V1 + V2 + V3

Using Component method: 1. Resolve the vectors to be added onto their X- and Y- components 2. Add the X-components and Y-components to get the resultant Rx and Ry 3. Find magnitude using pythagorean theorem 4. Find direction (theta) by using theta = tan^-1 (RY/ RX)

Force (F)

Vector quantity that is experienced was pushing or pulling on objects Every velocity is motivated by force Objects don't have to be touching (gravity, electrostatic forces between point charges) Measured in Newtons (N) = kg*m/s^2

Velocity (V)

Vector: Magnitude measured as rate of change of displacement in given unit of time (Meters/second) Velocity vector same direction as displacement vector Speed (v) is the rate of actual distance traveled in given unit of time Instantaneous speed always (scalar) = to magnitude of objects instantaneous velocity (measure of average velocity as change in time (delta t) approaches 0) *Average speed not always = to magnitude of average velocity because average v is ration of displacement over time, whereas average speed accounts for actual distance traveled *Average velocity = change in distance over change in time Earth's orbit: d = 9.4 X 10^8 km per year, but x = 0 SO average speed = 9.4 X 10^8 km / 3.16X10^7 s = 29.8 km/s and average velocity = 0km/ 3.16 X 10^7 = 0 Main points: *Instantaneous speed is magnitude of the instantaneous velocity vector (Instantaneous velocity is the velocity at a specific instant in time. This can be different to the average velocity if the velocity isn't constant.) *Average speed and average velocity may be unrelated because speed does not depend on displacement, but on total distance/time *Distance will always be equal to or larger in magnitude than displacement Velocity is rate of change of displacement of object. Displacement is a function of velocity acting over a period of time v = limit as t -> 0 of delta x/delta t where v = instantaneous velocity, delta x = change in position, delta t = change in time

Fluid Dynamics: study of fluids in motion Viscosity (n)

Viscosity: The resistance of a fluid to flow -Measure of fluids internal resistance to flow (more viscosity = more energy lost during flow) Increased viscosity = increase in viscous drag (nonconservative force, analogous to air resistance) Thin fluids (gases, water, dilute aqueous solutions) have low viscous drag & low viscosity = flow easily (its really easy for objects to move through)(less energy lost) High viscosity: Lots of viscous drag (difficult for objects to move through): blood, honey, oil All fluids have some viscosity (pretty much) (lower viscosity = more "ideal" fluid) Ideal fluid = no viscosity = INVISCID Units = Pascal-second = Pa*s = N*s/m^2 Unless stated, assume no viscus drag *Assume conservation of energy in low-viscosity fluids with laminar flow (low internal resistance)

Sound Wave Terminology: Wave speed Frequency Angular frequency Period Equilibrium position Amplitude Traveling waves Standing waves

Wave speed is rate at which wave transmits energy or matter (product of frequency and wavelength) Frequency is measure of how often waveform passes point in space (Hz) Angular frequency = frequency measured in radians/second Period is time needed to complete one wave cycle Equilibrium position is point with 0 displacement Amplitude is maximum displacement from equilibrium position Traveling waves have nodes and antinodes that move with wave propagation Standing waves have defined nodes and antinodes that don't move

A projectile is fired from ground level with an initial velocity of 50 m/s and an initial angle of elevation of 37 deg C. Assuming g= -10 m/s and sin37 = 0.6 and cos 37 = 0.8, find: Projectile total time in flight Total horizontal distance traveled

Y component of velocity = v0*sin37 = 50m/s * 0.6 = 30 m/s y = v0*t + at^2 /2 0 = 30t +-10t^2 / 2 5t^2 = 30t t^2 =6t t = 6 and 0, so at 6 and 0 seconds the height is 0 (total time in height = 0) Horizontal distance: Only consider x component now: V0*cos37 = 50*.8 = 40 m/s x = v0*t + at^2 /2 x = 40*6 + 0*36 / 2 (there is only acceleration in y direction because of gravity, but only looking a horizontal, gravity doesn't matter) 240 + 0 = 240 m

Hill's Criteria (9)

describe the components of an observed relationship that increase the likelihood of causality in the relationship -First criteria has to be present -More criteria = more likelihood -Not proven, can determine correlation, not causation *Correlation quantified with correlation coefficient between -1 and +1 (-1 = strong negative correlation, 0 = no correlation, +1 = strong positive correlation ) Temporality: Exposure (independent variable) must be before outcome Strength: More variability in outcome variable explained by variability in study variable Dose-Response Relationship: Proportional relationship Consistency : Similar in multiple settings Plausibility: Reasonable mechanism, supported by literature Consideration of alternative explanations : Confounders Experiment : Can an experiment be performed to determine casualty 100% Specificity: Change in outcome only produced by change in independent variable Coherence : Consistent with current state of knowledge

Doppler effect

f' = f (V +/- VD)/ (V -/+ Vs) where f' is perceived frequency, f is actual emitted frequency, V = speed of sound in the medium VD = speed of the detector Vs = speed of the source Upper sign (+ in numerator and - in denominator): Top = toward (if source or detector (you) is moving toward object you would use a +) Bottom sign (- in numerator and + in denominator): away (if detector moving away from other object, you would use a - in the numerator) *Treat numerator (detector) and denominator (source) separately when deciding if top or bottom sign Ambulance example: You are driving and hear an ambulance coming from behind you. You are the detector, and you are moving away from the source, so even though the ambulance is getting closer, use the bottom sign (-) on top. But, from the ambulance perspective (denominator), they are doing towards you (detector), so they use top sign, which is also a minus So the equation would look like: f' = f (v-vD)/(v-vS) because VS>VD and f' > f Now, if the ambulance passes you: (f'<f) (Vs>vD) Detector is going towards sound, so use the top sign Sound is going away from detector (in the denominator use the bottom sign, which is +) So the equation is f' = f (v+vD)/(v+vS) *Change from f'> to f'< is perceived as drop in pitch Applies to all waves (including light) -If source of light (or whatever wave it is) is moving toward detector, observed frequency will increase (perceived frequency = f' > actual frequency (f)) -Blue shift (blue is at high-frequency end) -If source is moving away, observed frequency will decrease (red shift) (f'<f) *a decrease in velocity would be associated with a decrease in frequency. *As ambulance passes, you hear a distinct drop in the sound *Doppler effect describes the difference between the actual frequency of a sound and its perceived frequency *imagine sound waves in front of moving object as being compressed Increasing pitch and frequency *ambulance going toward car)), and sound waves behind are stretched out (decreasing pitch and frequency) Echolocation: Animal serves as source and detector A difference of zero between the perceived and the emitted frequencies implies that the source of the sound is not moving relative to the object

Diffraction Gratings X-Ray diffraction

multiple slits arranged in patterns; produce colorful patterns due to interference between different wavelengths Example: CD or DVD Thin films can also cause interference (soap bubbles or oil puddles) -Interference here between reflected rays, not diffracted rays X-ray diffraction uses bending of light rays to create model of molecules (often combined with x-ray crystallography) during protein analyses

Density (p)

the ratio of the mass of a substance to the volume of the substance Scalar quantity (no direction) Density (p = rho) = mass (m) / volume (V) In units of kg/ m^3 or g/mL or g/cm^3 *millimeter = cubic centimeter 1 g/cm^3 = 1000 kg/m^3 (even though you would think it would be the other way around, but there are 1000 L in a cubic meter The weight of any volume with known density can be calculated by multiplying density (p) by volume and acceleration due to gravity Weight (Fg) = p(density)*V*g Density of fluid compared to that of pure water at 1 atm and 4 deg C (specific gravity) -> at 1 atm and 4 deg C, water has density = 1 g/cm^3 Specific gravity (SG) = p (density) / 1 g/cm^3 -Density of object / density of water -Unitless number / dimensionless -Can determine if object will sink or float

sin 45°

√2/2 = 0.71 So, if you were asked sin^-1 (0.75), you know it is around 45 degrees, but slightly above (49 degrees)

Vectors and Scalars

-Vectors have both magnitude and direction (displacement, velocity, acceleration, and force) -Represented by arrows (length usually proportional to magnitude of the vector quantity -Magnitude of displacement between two vectors can be shown as |A| -Scalars have only magnitude (no direction) (distance, speed, energy, pressure, mass) Distance vs displacement: The earth travels distance of 940 million kilometers per year, but circular path means displacement is 0 -Generally represented by italics

A spring with a 5kg weight attached is in harmonic motion. As the mass passes through the equilibrium position, x0, the mass has 40 J of kinetic energy. At x=20 cm, the spring has 20 J of kinetic energy. The spring constant for the spring is:

1000 N/m Spring forces are conservative Total energy = KE +PE TE= 40 J since X0 is where all of the energy in KE So, at any given point, KE+PE = 40 J At 20 cm, KE = 20J so PE must = 20J Equation for potential energy of spring systems = PE = 1/2 kx^s 20 J = 1/2 k (0.2)^2 20 = .5k * 0.04 40 = 0.04k k= 1000 N/m

Vector Subtraction

Adding a vector with equal magnitude but opposite direction to the first vector *flipping the direction of the vector being subtracted and then adding tip to tail

First Law of Thermodynamics

Change in the total internal energy of a system = amount of energy transferred in the form of heat - amount of energy transferred from system in form of work Energy can be transferred and transformed, but it cannot be created or destroyed. ΔU= Q-W where ΔU is change in internal energy, Q =heat energy transferred to the body, and W is work done by system Q = ΔU + W ΔU positive = increasing temp, negative value = decreasing temp Heat (Q) positive = heat flows into system, negative = heat flows out of system Work (W) positive = Work is done by the system (expansion), negative = work is done on the system (compression) Presence of nonconservative forces doesn't matter because all energy transfer accounted for (whatever we "lose" we "find" somewhere else) Summary: The 1st law says that increase in total internal energy of system is caused by transferring heat into the system or performing work on the system. Decrease in total IE caused by when heat is lost from system and work is done by the system

Two blocks are in static equilibrium (image on next card) If block A has a mass of 15 kg and the coefficient of static friction between block A and the surface = 0.2, what is the maximum of block B?

Free body diagrams: Block A: Normal force (N)(always perpendicular to surface) straight up, static friction (fs) to the right, T to the left, F=mg down *Static friction = μs*N Block B: T up, F = mg down Net force = 0 for both because they are at equilibrium (not moving), so T = Force of block B downwards = fs (to the right) So, fs = T and T = Force of B downwards Force of B downwards = mg fs = mg μs*N = mg N (up) = F (down) = mg μs*mg (of block A) = mg (of block B) μs* mass of block a = mass of block B 0.2 *15 kg = 3.0 kg = mass of. block B

A circuit consist of a 6 V battery attached to a 12uF parallel plate capacitor. While the capacitor is charging, the voltage across the capacitor is _______________ and ______________ than 6 V.

Increasing and less than 6V Capacitor = 2 plate system that stores charge Still charging = impossible for charge to be 6V or greater

Work

Not energy, but a measure of energy transfer (the other form of energy transfer is heat) *Only the way by which energy is transferred *Side note: In your muscles, potential energy in phosphate bonds of ATP converted to mechanical energy, exerting force. On chemical level, PE in ATP harnessed by heat transfer -This is dot product, means that it is function of cosine of angle between vectors, and means that only forces parallel or antiparallel to the displacement vector will do work (transfer energy)

Power

Rate at which energy is transferred from one system to another (how fast work happens) P = W/t = ΔE/t W is work, which equals change in energy (ΔE) t is time over which work is done Power is measured in Watts (W) = (J/second) In electrical power, we use P = IV where I is current and V is electrical potential difference)

Speed vs. Velocity

Speed is the distance an object travels per unit of time and velocity is speed in a given direction. (Distance/time vs displacement/time) Speed is a scalar quantity and velocity is a vector Velocity can be positive or negative, speed can only be positive

Centripetal Acceleration (ac) Centripetal Force (Fc) Centrifugal force

The acceleration of an object that travels in a circle; always directed towards the center of the circle if the object is in uniform circular motion ac = v^/r Centripetal force generates centripetal acceleration (both vectors, acceleration always in same direction as net force)(this acceleration keeps object in circular pathway) *No more centripetal force = object exits circle path and assumes path along tangent line Fc = m*v^2 / r (equation for centripetal force) So, because force = ma, centripetal acceleration = v^2 /r where Fc is magnitude of the centripetal force, m is mass, v is speed, and r is the radius of the circular path *Centripetal force Usually the result of gravity, tension, or a normal force

An elevator is designed to carry a maximum weight of 9800 N (including its own weight), and to move upward at a speed of 5 m/s after an initial period of acceleration. What is the relationship between the maximum tension in the elevator cable and the maximum weight of the elevator while the elevator is accelerating upward? A. The tension is greater than 9800 N. B. The tension is less than 9800 N. C. The tension equals 9800 N. D. It cannot be determined from the information given.

The forces on the elevator are the tension upward and the weight downward, so the net force on the elevator is the difference between the two. For the elevator to accelerate upwards, the tension in the cable will have to be greater than the maximum weight so that there is a net force directed upwards.

Suppose the liquid used in a thermometer has a volume expansion coefficient that is less than that of the thermometer tube itself. What happens to the change in temperature?

The liquid level falls when temp rises Volume expansion = amount of expansion = proportional to the volume of substance * increase in temp Delta V = change volume B = coefficient of volume expansion V= original volume Delta T = change in temp Liquid has lower volume expansion coefficient than thermometer tube means that with same delta T, liquid in tube will not expand as much as tube itself. Tube will be expanding and liquid level will appear to drop because tube expanding faster than liquid

A car is traveling at 40 km/hr and the driver puts on the brakes, bringing the car to rest in a time of 6 s. What is the magnitude of the average acceleration of the car?

The magnitude of the average acceleration is the change in velocity divided by the time. The velocity changes by =40 km/hr because the car comes to rest. average acceleration = ΔV/Δt (40 km/hr) / (6 sec* 1 hour /3600) 40/1/600 = 40*600 =24000 km/hr^2

An 80 kg diver leaps from a 10m cliff into sea. Find potential energy at top of cliff and when he is 2m underwater, with sea level = datum

U=mgh U = 80*9.8*10 = 8000 J 2 meters underwater: U = 80*9.8*-2 = -1600 J

Total Mechanical Energy

the sum of kinetic and potential energy E = U + K The first law of thermodynamics accounts for conservation of mechanical energy (never created or destroyed, just transferred) *BUT this does not mean total mechanical energy remains constant (energy is transferred away in things like heat and stuff) Conservation of Mechanical Energy: In the absence of nonconservative forces (like frictional force), the sum of the kinetic and potential energies will be constant Conservative forces are path independent and do not dissipate energy (two most common for MCAT are gravitational and electrostatic) *Elastic forces approximated to be conservative, unless MCAT throws in spring problem where frictional forces are not ignored How to determine if force is conservative: If the change in energy around any round trip is zero (object comes back to starting point), or if the change in energy is equal despite taking any path between two points, then the force is conservative *Mechanical energy remains CONSTANT *basically means system gives back an amount of usable energy equal to amount taken away *Object loses potential energy when it falls but gains same amount back when lifted back to original height, regardless if return path is same as descent path *At all points during fall through vacuum, there is perfect conservation of PE into KE *Change in energy of system moving from one setup to another: Object undergoes displacement: If energy change is equal regardless of path taken, then the forces are conservative *Conservative forces like gravity and electrostatic forces and (usually) elastic forces conserve mechanical energy. Non conservative forces like friction and air resistance dissipate mechanical energy as thermal or chemical energy When work done by non-conservative forces is 0 or there are none, total mechanical energy of system (U+K) remains constant ΔE = ΔU+ΔK = 0 When nonconservative forces (fiction, air resistance, viscous drag (Resistance force from fluid viscosity)) are present, total mechanical e energy not conserved: W of nonconservative = ΔE = ΔU + ΔK where Wnonconservative = work done by nonconservative forces only = amount "lost" from system (really its just transformed) *Nonconservative forces are path dependent (longer distance =. more energy dissipated) *MECHANICAL ENERGY DECREASES (energy dissipated)

Newton's Three Laws

(1) Fnet = ma = 0 where fnet is net force: An object at rest will stay at rest unless acted upon by an unbalanced force and an object in motion will stay in motion with the same speed and in the same direction unless acted upon by an unbalanced outside force; also known as Law of Inertia. (2) Fnet = ma: Acceleration is produced when a force acts on mass and the greater the mass of the object being accelerated, the greater amount of force is needed to accelerate that object. -An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector (No acceleration will occur when vector sum of forces results in cancellation of forces -Net force and acceleration vector point in same direction (3) Fab = -Fab: For every action there is an equal and opposite reaction. Car driven at constant velocity crashes into wall: First law: Prior to collision, vehicle has constant velocity so there is no acceleration or net force Second Law: Collision with wall = sudden deceleration -Acceleration means there is net force (massXacceleration) Third law: car exerts force on wall, and wall exerts = force back in opposite direction

Electric Dipoles

*Seperation of charge within molecule such that there is percent or temporary region of equal and opposite charges at a particular distance *2 equal and opposite charges being separated a small distance d from each other (+q and -q separated by d) -Can be temporary or permanent -For a collection of charges, electrical potential (P) = scalar sum of potentials *V = kq (r2-r1)/r1*r2 If the point is far away from dipole, r1*r2 is about equal to r^2, and r1-r2 is about equal to d cos theta SO, V = kqd/r^2 cosθ and the product of charge and d = dipole moment (p) -SI unit of dipole moment: C*m p =q*d Dipole moment is vector *vector pointing from the - charge to the + charge *Note: In the image, -q and +q are actually source charges, even though they are represented by lowercase q

Perpendicular Bisector of the Dipole

*equipotential line that lies halfway b/w +q and -q (angle between plane and dipole axis = 90 so cos 90 = 0) *electrical potential at any point along this line is zero E field on this can be approximated as E = P/r^3 *lines point in direction opposite of p *Translational equilibrium: Charges are equal and opposite, so forces acting on the charges will be = in magnitude and opposite in direction -No rotational equilibrium (Torques are in the same direction, either both clockwise or counterclockwise) *However, there is net torque about center of dipole axis (T) = pE sin(theta) Where p = magnitude of dipole moment (qd), E is magnitude of uniform external electric field, theta is angle dipole moment makes with e-field *Torque will raise dipole to reorient/rotate itself so that its dipole moment, p aligns with e field (E)

Pressure and boiling point

- Remember: Temperature will not change until liquid is completely vaporized -The boiling point of a liquid depends on the atmospheric pressure. Higher the atmospheric pressure, higher the boiling point. At the top of Mount Everest, water boils at a much lower temperature than 100, because the atmospheric pressure there is much less than that at sea level. (This also means that it takes a longer time to cook food at the top of Everest than at sea level.) Pressure cookers cook food in lesser time because the temperature of boiling water inside it is much higher than 100 degrees due to increased pressure. - At higher elevation atmospheric pressure decreases hence the boiling point decreases

Closed Pipes

- closed at one end and open at the other -closed end has node and open end has antinode First harmonic has 1 node (closed end) and 1 antinode at open end In a sinusoidal wave, the distance from node to antinode = 1/4 of wavelength Unlike strings and open pipes, harmonic in closed pipe = number of quarter wavelengths: There can only be odd numbers (because node to node is half wavelength, and your closed end and open end are never going to be the same thing) First harmonic = wavelength 4X length of pipe, so λ = L*4 or L = λ/4 Third harmonic: L = 3λ /4 (3 quarter wavelengths) Fifth harmonic (second overtone) = L = 5λ/4 λ = 4L/n f = nv/4L n: can only be odd integers (1,3,5) v: wave speed -when presented w/ a closed pipe, count the # of quarter wavelengths contained in the pipe to determine the harmonic

Electric Potential Energy (Joules)

-Fourth form of potential energy (in addition to gravitational, elastic, and chemical) -Dependent on the relative portion of one charge to another -U = kQq/r -Like charges = positive answer (unlike charges (one positive and one negative) mean electric potential energy is negative) -Electric potential energy = Amount of work necessary to bring charge from however far away to a point. -Fe = kQq/r^2 and W = Fd*cos theta, so if we assume force and displacement vectors to be parallel: ΔU = W = Fd*cos(theta) = Fr*1 = kQq/r *Consider negative point charge and positive test charge -> attractive, so the closer they are the more stable they are, so they have negative potential energy (increasingly negative the closer they are, further from 0 because there is increasingly smaller electric potential energy as they become more stable -Like charges become more stable as they move farther away (magnitude of electrical potential energy becomes smaller and smaller positive number) *Electric potential energy increases when opposite charges move farther away or when like charges move close. Energy will decrease when opposite c charges come close or like charges move away

Turbulent Flow

-rough and disorderly -causes the formation of eddies (swirls of fluid of varying sizes, typically occur at downstream side of obstacle obstructing laminar flow) -In unobstructed fluid flow, turbulence can arise when speed exceeds critical speed (depends on physical properties, like viscosity and diameter)(In this case, laminar flow only in thin layer of fluid adjacent to the wall, called the boundary layer) -Boundary layer: Flow speed immediately at wall = 0 and increases uniformly throughout layer, but beyond boundary layer, the motion goes crazy -Alot of energy is dissipated because of increased frictional forces -Equations like Bernoullis equation can't be applied in turbulent flow systems Critical speed (vc) can be calculated by: N sub R * n / p*D where NsubR is constant (Reynolds number), n (eta) is viscosity, p (rho) is density and D is diameter

Laminar Flow

-smooth and orderly (smooth lines around object) -often modeled as layers of fluid that flow parallel to each other Upward force = buoyant force, downward force = gravity *If the maximum buoyant force is larger than the force of gravity on the object, it will float. This is true if the object is less dense than the fluid it is in *NOTE: Layers may not have same linear speed (layer closest to wall may be slower) Calculate the rate of flow for Laminar flow with Poiseuille's Law Q = Flow = (pi*r^4*Δ P) / (8nL) Where Q is rate of flow, r is radius of tube, ΔP is pressure gradient, n (eta) is viscosity, L is length of pipe *Relationship between radius and pressure gradient is inverse and exponential (more radius = less pressure assuming constant flow rate) Fluids with low viscosity and laminar flow can be approximated to be conservative systems (total mechanical energy of system is constant if we discount small viscous drag forces that occur in all real liquids)

State Functions

-thermodynamic properties that are a function of only the current equilibrium state of a system -independent of the path taken to get to a particular equilibrium state -internal energy (U), pressure, density (lowercase p), temp., volume, entropy (S), enthalpy (H), gibbs free energy (G) On the other hand, process functions (like work and heat) describe the path taken to get from one state to another

Absolute (hydrostatic) Pressure

-total pressure that is exerted on an object that is submerged in a fluid (remember fluids are both liquids and gases) P = P0 + ρgz where P is absolute pressure P0: incident or ambient pressure (pressure at the surface)(this isn't always 1 atm depending on fluid system, or if the system is in a closed container ρ = rho = density of fluid g is acceleration due to gravity z is depth of object z: depth of the object g: acceleration due to gravity

.A 10kg object slides down an incline that has a coefficient of friction of 0.3. As the angle of incline increases, the frictional force does what?

.Decreases Frictional Force = MeowF *N (normal force) -Direction of frictional force always opposes movement (once the instantaneous velocity vector is known (or net force in the case of static friction) the frictional force must be in the opposite direction) Flat surface (theta= 0) means that FN*Cos (theta)= FN because cos(0) = 1 As theta increases, FN approaches 0 as the plane surface becomes vertical, so as the angle increases , the frictional force decreases

500 calories of heat are applied to a 10g cube of ice that is at an initial temperature of 0 degrees celsius. What is the change in temperature of the ice due to this amount of heat? (Note: The heat of fusion of water is 80cal/g and the specific heat of water is 1 cal/gCelsius)

0 degrees C Solid state to liquid requires heat of fusion (80 cal/g) Temp will not increase until it is in liquid state 10g * 80 cal/g = 800 cal to melt cube 500 calories is not enough to melt the cube, so nothing will happen

mile to meters to feet

1 mile : 1609 meters 1 mile = 5280 feet *1 inch = 2.5 cm There are about 30.5 cm in a foot

Rules for Significant Figures: 34,600. 0.0003201 1.10 525,600

1. Non-zero digits are always significant. 2. Any zeros between two significant digits are significant. 3. Any 0 to the left of the first nonzero digit are "leading zeros" and are not significant 4. If there are zeros to the right and there is a decimal they are significant, but no decimal = non-significant -For example, 3490 has 3 SF and 3490.0 has 5 SF 5. The last digit in measurements is usually an estimation and is not significant (7.45 meters only has 2 sig figs technically because 5 is estimation) 6. Trailing zeros with decimals are significant and need to be preserved in scientific notation (100.0 is written as 1.000 X10^2 while 100 is 1 X 10^2). 7. For answer choices, round to number that is the same as the lest number of significant figures in X or division (addition and - maintain SF) 34,600. (5 SF) 0.0003201 (4 SF) 1.10 (3 SF) 525,600 (4 SF)

In the circuit below, what is the voltage drop across the 2/3 resistor? One circuit, R1 and R23 in series, R2 and R3 in parallel R1 = 1/2 Ohms R2 = 2 Ohms R3 = 2/3 Ohms V = 10 V

5V To determine the voltage drop across the 2/3 resistor, start by calculating the total resistance in the circuit. For the resistors in parallel, the total resistance is 1/ Rp = 1/2 ohms + 3/2 ohms -> Rp = 1/2 ohms The total resistance in the circuit is the sum of the remaining resistor and the equivalent resistance of the other two: Rs = 1/2 ohms + 1/2 ohms = 1 ohms Now that we know the equivalent resistance, we can calculate the total current using Ohm's law: I = V/R = 10V/ 1 ohm = 10A Finally, we can determine the voltage drop across the parallel resistors. The voltage drop across the 1/2 ohm resistor must be 10 A * 1/2 ohms = 5V Therefore, there must be a 5 V drop across both the 2/3 resistor and 2 ohm resistor, according to Kirchhoff's loop rule. Each of these resistors forms a complete loop in combination with the 1/2 ohm resistor and 10 V voltage source, and the net potential difference around any closed loop must be 0 V.

An ideal calorimeter is filled with 2 quarts of water at an initial temperature of 20 degrees 20 Celsius. The water is then brought to a boil in a time of 5 minutes. Another calorimeter is filled with 3 quart of water at an initial temperature of 20 degrees Celsius and an identical heat source is used to heat the water. How much time is required to bring the 3 quarts of water to boil?

7.5 minutes Equation for heat energy: Delta Q = mc*delta T Delta Q = heat gained or lost m = mass c= constant (specific heat) Delta T = change in temp c and T are = for both, so more more water takes longer to boil 1.5X5 min = 7.5 min

Friction

A force that opposes motion/movement of objects -Other forces can speed up or slow down, but friction can only oppose objects motion (cause it to slow down/become stationary) 2 Types: Static and kinetic Static friction (fs): exists between stationary object and surface upon which it rests. Inequality that describes magnitude of static friction = 0 less than or equal to fs less than or equal to msN (0<fs<msN) where ms (meow s ) is coefficient of static friction (unitless quantity dependent on two materials in contact) and N is magnitude of normal force (component of force between 2 objects in contact that is perpendicular to plane of contact between object and surface) *Range for static friction = 0 (object resting on surface with no applied force) to MsN *Contact points are the places where friction occurs between two rough surfaces sliding past each other. If the normal load (force that squeezes the 2 together) rises, the total area of contact increases. That increase governs degree of friction Kinetic friction (fk): between sliding object and surface *Magnitude: fk = man where mk is coefficient of kinetic friction and N is normal force *Unlike static, kinetic friction will have constant value for any given combination of a coefficient of kinetic friction and normal force *Amount of surface area in contact or velocity don't matter *Ms is ALWAYS larger than Mk (So, max value of static friction will always be greater than constant for kinetic friction: Object will "stick" until they start moving, then they slide -> it is always easier to keep an object from sliding (kinetic friction) than it is to start sliding an object (static friction))

Equipotential Lines

A line on which the potential at every point is the same -Potential difference between any 2 points is 0 -No voltage between 2 points =no acceleration along line, but there is potential difference between different set of eq lines which can cause particles to move and accelerate -Looks like a bunch of concentric (same center) circles surrounding source charge -Conservative force -No work done to move q from one point on eq line to another (work depends on the potential difference of the 2 lines, and not the pathway taken between them -Gravitational potential energy is unchanged Look at the image: SO Q is positive (so b has lower electrical potential than a), and q (an electron) is negative (so b has higher electrical potential energy than a) -Electron has to gain energy to move farther away because it actually wants to come closer

Resistance / Resistivity

A material's opposition to the flow of electric current/charge *The electrical equivalent of friction, air resistance, or viscous drag (all oppose motion) *High resistance = insulators *All appliances function as resistors (like lightbulbs) Resistance of resistor is dependent on resistivity, length, cross-sectional area, and temp R (Ohms) = pL/A Where p (rho) is resistivity (measured in meters X ohms), L is length of resistor, and A is cross-sectional area (m^2) Resistivity is the number that characterizes the intrinsic resistance to current flow -Resistance is directly proportional to length and resistivity (longer resistor = more resistance) -Inverse relationship between resistance and area (more area = less resistance, because it increases the number of pathways through resistor (conduction pathways)) -Wider area, more current can flow -More conductors have greater resistance at high temperatures (intrinsic quality) Electrical resistance results in energy loss, which reflects a drop in electrical potential. Voltage drop can be calculated with Ohm's Law (V=IR As current moves through resistors, the voltage drops some in each resistor, but the current (sum of currents for divided circuit) is constant (current has to pass through each resistor because no charge is gained or lost) -Even conductors have some resistance to current and cause some voltage drop -Everything has some internal resistance (r int), so voltage reduced some amount from theoretical emf. The actual voltage of cell = V = Ecell - i*r int where V is voltage, E cell = emf of cell, i is current through cell, r int = internal resistance Internal resistance is 0 and emf=voltage when cell is not actually driving current (like when switch is open) *The internal resistance will lower the available voltage for the circuit. Lowering the available voltage will also lower the current When current is not 0 (switch not open), internal resistance is not negligible and voltage is less than emf VOLTAGE CANT BE MORE THAN EMF Discharging cell supplies current that flows from positive (high potential end) to negative (lower potential end) -Secondary batteries can be recharged (current driven towards positive end)(cell acts galvanic/voltaic when discharging and electrolytic when recharging)

What are the magnitudes and directions of the resultant vectors from the following cross products: C = A x B and D = B x A ?A: X = -3 N, Y = 0B: X = 0, Y = +4 m

A × B = |A||B|sinθA × B = |-3||+4|sin(90) = 12 x 1 = 12 N m C is 12 N m into the page, and D is 12 N m out of the page. For C, index finger points to left (negative) and middle finger points up (+4 is positive Y axis). This points you thumb away from you (into page) For D, Index finger (+4 is positive Y axis) pointing up, middle finger left (negative), which means thumb pointing towards you (out of page) Into page is circle with x in it (the tail of an arrow being shot into page) and out of page is circle with dot in it (Arrow being fired at you)

A 10 Ω resistor carries a current that varies as a function of time as shown. How much energy has been dissipated by the resistor after 5 s?

A. 40 J B. 50 J C. 80 J D. 120 J Correct Answer: D Explanation: Power is energy dissipated per unit time; therefore, the energy dissipated is E = PΔt. In the five-second interval during which the resistor is active, it has a 2 A current for three of those seconds. The power dissipated by a resistor R carrying a current I is P = I2R. Therefore, the energy dissipated is E = I2RΔt =(2 A)2(10 ?)(3 s)= 4 × 10 × 3 = 120 J

The pulley system shown on the back of the card has an efficiency of 80%. A person is lifting a mass of 200 kg with the pulley A. Find distance through which the effort must move to raise the loss 4m B. Find effort required to lift load C. Find the work done by the person lifting the load through a height of 4 meters

A. To move 4 m, all 6 supporting ropes must shorten by 4m 6*4m = 24, meaning the effort must move through a distance of 24 m B. Efficiency = (load*load distance)/ (effort * effort distance) *Don't forget to convert mass to load / weight (200 kg * 9.8 = 2000) 80% = 2000*4 / effort * 24 0.8 = 8000/effort*24 -> 20 = 8000/effort -> Effort = 8000/20 = 400 N C. Work done by person = work in Work in = effort * effort distance = 400N * 24 = about 9600 J of work done by person

The force of friction acting on an object is 50N, and the net force on that objet is also 50N. The object is ________________________. If there is no net force acting on an object, the velocity is __________ and the acceleration is _

Accelerating Net force acting on object = object is accelerating Net force + frictional force = 100N of force opposing friction If there is no net force acting on an object, the velocity is constant and the acceleration is 0

Circuit Laws

An electric circuit is conducting path that has one or more voltage sources (like a battery) connected to one or more passive circuit elements (resistors). Kirchhoff's laws are two rules that deal with conservation of charge and energy within a circuit Kirchhoff's Junction Rule: At any point in a circuit, the use of currents directed into points = sum of currents directed away from point I into junction = I leaving junction -number of electrons entering and leaving point are the same Kirchhoff's Loop Rule: -Closed circuit loop: Sum of voltage sources = sum of voltage (potential) drops -Consequence of conservation of energy -Kirchhoff's loop rule states that the total potential difference around any closed loop of a circuit is 0 V. -No excess energy appears or disappears (but it can change forms) -terms of voltage (J/C) -V source = V drop -If all of the voltage was not "used up" in each loop, it would build up after each trip (which is impossible) -Only true for closed loop

Inclined Plane A 5g block slides down frictionless incline at 30 degrees. Find the normal force and acceleration of block (sin30 = 0.5, sin60 = 0.866, cos30 = .866, cos60 = 0.5

Another example of motion in two dimensions Best to divide force vectors into components that are parallel and perpendicular to plane Fg,|| (parallel) = mg sin(θ) (component of gravity parallel to the plane) Fg,_| (perpendicular) = mg cosθ (oriented into plane) Block in example has two forces acting on it: Normal force (perpendicular to surface) and gravity (straight down) -Acceleration is parallel to plane We want to find normal force (perpendicular) and acceleration (parallel), we should split gravity into parallel and perpendicular components No acceleration in perpendicular dimension means magnitude of normal force must be equal to that of the perpendicular component of gravity |N| = | Fg, perpendicular | = mg cosθ = 5kg*9.8*0.866 =about 43 N Acceleration can be determined now in parallel direction. Only force in this dimension is parallel component of force of gravity, so it is net force Fnet,|| = Fg,|| = m*a|| (parallel acceleration) mgsinθ = m*a|| =9.8*sin30 = 9.8*0.5 = 4.9 m/s^2

Magnetic Field

Any moving charge, whether its a single electron or a current, creates a magnetic field (measured in Tesla (T)) 1T = 1 N*s/m*C -Sometimes measured in gauss (1T = 10^4 gauss) because teslas are really large Fo a long, straight, current carrying wire, magnitude of magnetic field produced by I (current) in the wire at a perpendicular distance (r) from the wire = B= Mu0 (meow 0) * I / 2 pi r where B = magnetic field at distance (r) from wire Mu0 = Permeability of free space (4piX10^-7 T*m/A) I = current Inverse relationship between the magnitude of the magnetic field and the distance from current -Straight wires create magnetic field in concentric (same center) rings, with direction of field vectors determined with right hand rule (thumb in direction of current, wrap fingers around invisible wire, fingers mimic circular field lines For Circular loop carrying wire with radius r, magnitude of magnetic field at center of circular loop = B = Mu0*I/2r The first equation gives magnitude of magnetic field at any perpendicular distance from wire, and second expression gives magnitude of magnetic field only at center of loop If an object were placed 5 meters to the left of a current carrying wire or in the center of a circle with a radius of 5 meters, the object placed in the center would have a larger magnetic field because the denominator of the loop equation does/t include pi, so you are dividing by a smaller number

A seesaw with a mass of 5kg has one block of mass 10 kg two meters to the left of the fulcrum and another block 0.5 m to the right of the fulcrum If seesaw in equilibrium, what is mass of block 2 and force exerted by fulcrum?

Balanced seesaw implies rotational equilibrium (also in translational equilibrium) Positive (counterclockwise) torque exerted by block 1 = magnitude to negative (clockwise) torque exerted by block 2 Normal force and weight of seesaw eliminated because lever arms = 0 Torque 1 = torque 2 r1F1*sin(theta1) = r2F2*sin(theta2) r1*mg*sin90 = r2*mg*sin90 r1m1=r2m2 ->2m*10kg/0.5m = m2 m2 = 40 kg Normal force = Force of seesaw+blocks (mass of seesaw + mass of block 1 + mass of block 2) *g (5+10+40)*10m/s^2 = 550N

A weight lifter lifts a 275 kg barbell from the ground to a height of 2.4 m. How much work has he done in lifting the barbell, and how much work is required to hold the weight at that height?

Because the weight of the barbell (force acting downward) is mg = 275 kg * 10 m/s^2 or about 2750 N, it follows that the weightlifter must exert an equal and opposite force of 2750 N on the barbell. The work done in lifting the barbell is therefore W = Fd cos θ = (2750 N)(2.4 m)(cos 0) ≈ 7000 J. Using the same equation, it follows that the work done to hold the barbell in place is W = Fd cos θ = (2750 N)(0 m)(cos θ) = 0 J. Because the barbell is held in place and there is no displacement, the work done is zero.

Bernoulli's equation is the reason for the upward force that permits airplane flight. Which statement best summarizes the equation's relationship to flight? A. The speed of airflow is equal on the top and bottom of a wing, resulting in nonturbulent flight. B. The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a net upward force on the wing, in turn resulting in flight. C. The speed of airflow on the flat bottom of the wing is greater than over the curved top of the wing, resulting in more pressure below the wing and the production of a net upward force on the wing, in turn resulting in flight. D. The weight of the wing is directly proportional to the weight of the air it displaces.

Bernoulli's equation is the reason for the upward force that permits airplane flight. Which statement best summarizes the equation's relationship to flight? A. The speed of airflow is equal on the top and bottom of a wing, resulting in nonturbulent flight. B. The speed of airflow is greater over the curved top of the wing, resulting in less pressure on the top of the wing and the production of a net upward force on the wing, in turn resulting in flight. C. The speed of airflow on the flat bottom of the wing is greater than over the curved top of the wing, resulting in more pressure below the wing and the production of a net upward force on the wing, in turn resulting in flight. D. The weight of the wing is directly proportional to the weight of the air it displaces. Correct Answer: B Explanation: Airplane wings have curved upper surfaces and flat lower surfaces, which causes the air to flow faster over the top of the wing because it has further to travel to the edge of the wing than the air over the flat bottom surface. Increased air speed will mean lower pressure within the fluid. This will result in higher pressure below the wing and an upward force.

Error Sources: Bias (3 types) and Confounding

Bias is systematic error, so it doesn't impact precision, but skews data Bias results flaws of data collection Confounding is an error during analysis Most prevalent type of bias = selection bias: Subjects not representative of target population -Could include one gender being more prevalent -Measurement and assessment of selection bias occurs before any intervention Detection Bias: Inconsistent use of knowledge (finding one variable (like hypertension) increases likelihood of finding second variable (diabetes). Both more common in obsession, so physician might use more obese population, inflating true value of secondary measurement Observation bias: Hawthorne effect (Observation bias) -> behavior more likely just because you are being studied -Exercising more when you start taking weight loss drug -Occurs before data analysis, so it is example of bias Confounding: Data analysis error -Third party variables = confounding variables/confounders *Bias is error in data collection, confounding is error in data analysis *Bias is systematic (unidirectional) error that occurs during selection of subjects or measurement and collection of data *Confounding: Association is erroneously drawn between 2 variables because of shared connection to a third variable

Capacitors in parallel

C=C₁+C₂+C₃+... Produce resultant capacitance = to sum of individual capacitors Cp increases as more capacitors are added Voltage across each parallel same and equal as voltage across the source (same as resistors in parallel)

The only time you have a real image produced by a mirror is when:

Case 1: Converging (concave) mirror Distance of object >focal length (object outside of focal length) f is positive real and inverted di positive (image on same side of mirror as object) Magnification: Negative (inverted) *For lenses, only case 1 has real image too, and do>f and it has positive di and negative magnification, but it is a converging CONVEX lens Case 2 (converging mirror)(concave) F-positive di<f Image inside focal length Virtual rays don't actually go behind the mirror di negative (behind mirror) Magnification: Positive, m>1 (not inverted)(not negative) term-262Like a make up mirror Case 3 Diverging mirror (convex mirror) F=negative (behind the mirror) virtual Di negative (behind mirror) Magnification: Positive (not inverted), but, m<1 means smaller than object

Three Types of Lenses

Case 1: distance to image was positive (di>o so object on opposite side), m negative means its inverted (real image, rays actually do converge on other side)(Object outside of focal length = negative m) Case 2 is a magnifying glass (di<0, same side as object) (virtual image)(not inverted, larger image)(image on same side as object)(light rays appear to come from behind, negative distance)(Positive magnification because image is larger) Both case 1 and 2 have positive focal lengths, are for convex/converging lenses For converging lens, you can have object inside focal length (real image that is inverted) or outside focal length (virtual, inverted) Case 3: Diverging (Concave) lens: object and image on same side Doesn't matter if object is inside or outside focal length Virtual image, di is negative (same side as object) Positive m = not inverted, m<1 means its smaller Concave = NEGATIVE FOCAL LENGTHS Virtual images are typically on same side and not inverted Note: If object = focal distance (o = 2f because lenses have 2 focal points), you have a real inverted image that is the same size, but for mirrors, if o = f you have no image

The voltage across the terminals of an isolated 3μF capacitor is 4V. If piece of ceramic have dielectric constant k=2, placed between plates, what is new charge, capacitance, and voltage. A 3μF capacitor is connected to a 4V battery (no longer isolated). If piece of ceramic have dielectric constant k=2, placed between plates, what is new charge, capacitance, and voltage.

Charge: Adding dielectric has no effect on charge in isolated capacitor (no new charge, same as before) Q = CV -> 3μF * 4 = 12 μC Capacitance: C'= kC C' = 2*3μF = 6 μF New Voltage: V = Q/C, so V' = Q'/C' V = 12 μC/ 6 μF = 2 V Next question: Capacitance: C' = kC C' = 2*3μF = 6 μF Voltage: Voltage held constant by battery, so it stays sat 4 V Charge: Q = CV -> Q' = C'V' Q' = 6 μF * 4V = 24 μC

Fluid Physiology in Circulatory and Respiratory System

Circulatory system = closed loop, non constant flow rate (result of valves, gravity, elasticity of vessels) -Nonconsistent = pulse -Loss of circulation volume from oncotic/osmotic and hydrostatic pressures -Blood volume entering heart always = to volume leaving -As blood flows away from heart, vessels have increasing resistance up to capillaries , but total resistance decreases because there are more vessels in parallel (equivalent resistance lower for capillaries in parallel than for aorta) *The speed of blood in the aorta is much higher than the speed of blood through a capillary bed because the cross-sectional area of all the capillaries added together is much greater than the cross-sectional area of the aorta. -The continuity equation states that the flow rate of a fluid must remain constant from one cross-section to another. In other words, when an ideal fluid flows from a pipe with a large cross-sectional area to one that is narrower, its speed decreases. This can be illustrated through the equation A1ν1 = A2ν2. If blood flows much more slowly through the capillaries, we can infer that the cross-sectional area is larger. This might seem surprising at first glance, but given that each blood vessel divides into thousands of little capillaries, it is not hard to imagine that adding the cross-sectional areas of each capillary from an entire capillary bed results in an area that is larger than the cross-sectional area of the aorta. *Arterial circulation motivated by heart *Venous circulation has 3X volume of arterial circulation and is motivated by skeletal muscles and expansion of heart Respiratory system: during inspiration, there is negative pressure gradient that moves air into lungs -During expiration, gradient reverses -When air reaches the alveoli, there is basically no speed -Total resistance increases as air leaves body despite increase in diameter of airways because there are fewer airways in parallel (exhale = ribs fall, diaphragm moves up, volume of chest decreases = increase in pressure in lungs) Note: The continuity equation can not be applied to human circulation

Bernoulli's equation

Conservation of energy / volume = relationship between pressure, velocity and height *The sum of the static pressure and the dynamic pressure will be constant between any two points in a closed system -More dynamic pressure (faster flow) = less static pressure -Think about it like this, at slower speeds (wider tube), the water kinda spreads out more so more pressure is exerted on the walls of the tube. At high speeds (narrower tube), its like a more condensed, tiny super fast stream with less pressure being exerted on the walls of the tube Dividing conservation of energy by volume = Bernoulli's equation P₁+ρv₁²/2+ρgh₁=P₂+ρv₂²/2+ρgh₂, where P=absolute pressure of fluid, v = linear speed, g= acceleration due to gravity, ρ=density, and h=height relative to datum 1/2 p(density)v^2 sometimes called dynamic pressure (pressure associated with movement of fluid) Pressure can be thought of as ratio of energy per cubic meter (energy density) -J/ m^3 = N*m /m^3 = N/m^2 Systems at higher pressure have higher energy density Static Pressure: P+ pgh Overall, Bernoulli's equation says if more energy dedicated toward fluid movement then less energy dedicated toward static pressure Pitot tube: Specialized measurement devices that determine speed of fluid flow by determining difference between static and dynamic pressure of fluid at given points along tube -Stagnation pressure (when velocity is 0 at one point) = Pressure + 1/2 rho*v^2 -> Velocity 1 = square root (2(stagnation pressure - Pressure at point 1)/ density) Venturi flow meter: Image shown -Average height remains constant, so pgh remains constant -As cross-sectional area remains decreases from 1 to 2, the linear speed must increase -As dynamic pressure increases (pressure associated with movement of fluid), the absolute pressure must decrease. -With lower absolute pressure, the column of fluid sticking up from tube will be lower at point 2 (Venturi effect) *water will flow the fastest and the hydrostatic pressure will have its lowest value where the horizontal pipe is narrowest (will result in lowest water level); this is called the Venturi effect

An office building with a bathroom 40 m above the ground has its water supply enter the building at ground level through a pipe with an inner diameter of 4 cm. If the linear speed at the ground floor is 2 m/s and at the bathroom is 8 m/s, determine the cross-sectional area of the pipe in the bathroom. If the pressure in the bathroom is 3 x 10⁵ Pa, what is the required pressure at ground level?

Continuity equation: Q = v₁A₁ = v₂A₂ A₂ = A₁v₁/v₂ = πr₁²v₁/v₂ = π(0.02)²(2)/8 A₂ = about 3.14X10^-4 m^2 Bernoulli's equation: P₁ + (1/2)ρv₁² + ρgh₁ = P₂ + (1/2)ρv₂² + ρgh₂ P₁ = P₂ + ρ [ (v₂² -v₁²/2) + g(h₂ -h₁) ]= 3 x 10⁵ + 1000 kg/m^3 [ (8² - 2²/2) + (9.8)(40) ] 3X10^5 +1000 ((60/2) +400) = about 7.3X10^5

Convex and concave mirrors Diffraction and interference

Convex, diverging: image still right side up but distoreted, smaller, wider field of vision (security mirrors and passenger side car mirrors) -Parallel light reflected in multiple directions (larger vision field) Concave and convex mirrors produce images by reflection, and concave and convex lenses produce images by refraction Thin slit experiments (diffraction) Diffraction is spreading out of light as it passes through narrow opening or around obstacle -Interference = fringes in slit Diffraction and interference = evidence for wave theory of light diffraction. When light passes through a narrow opening, the light waves spread out; as the slit narrows, the light waves spread out even more. When a lens is placed between the narrow slit and the screen, a pattern consisting of alternating bright and dark fringes can be observed on the screen. As the slit becomes narrower, the central maximum (the brightest and most central fringe) becomes wider. This can also be seen in the equation for the position of dark fringes in a slit-lens setup (a sin θ = nλ). As a, the width of the slit, decreases, sin θ must increase because nλ is constant for a given fringe. If sin θ increases, θ necessarily increases, implying that the fringes are spreading further apart.

A study is performed on a new medication. Subjects in the experimental group are told about the potential side effects of the medication, while subjects in the placebo group are not. The subjects have no contact with each other and do not know in which group they are placed. The side effects end up being significantly more severe in the treatment group, when seen by the same assessor physician. This is most likely caused by which of the following? A. Physician unblinding only B. Patient unblinding only C. Both physician and patient unblinding D. Both physician and patient blinding

Correct Answer: A Explanation: Because the same physician sees both the control groups and the experimental groups, there is the potential for the physician to realize which of the groups is receiving which treatment—especially if the subject mentions expected side effects. In this study, patients were not told which group they were in, but if they were assigned to the medication group, they were told about its side effects. If the patients talked to each other they could experience patient unblinding, but we are told they have no communication with each other.

Monochromatic red light is allowed to pass between two different media. If the incident angle in medium 1 is 30° and the incident angle in medium 2 is 45°, what is the relationship between the speed of the light in medium 2 compared to that in medium 1? A. V2 = V1(sqrrt 2) B. V2 (sqrrt 2) = V1 C. V2 = V1 (sqrrt 3) D. V2 (sqrrt 3) = V1

Correct Answer: A Explanation: First, the color of the light is irrelevant here; the ratio would be the same even if the specific color were not mentioned. Second, recall Snell's Law: n1 sin θ1 = n2 sin θ2. Although we don't know the value of n for either medium, you do know the simple relationship n = c/v Replacing n in Snell's law, and canceling out c from both sides, we get: c/v1 sinθ1 = c/v2 sinθ2 sin 30 / v1 = sin 45/ v2 1/2v1 = sqrrt 2/ 2v2 V2 = V1*sqrrt 2

A consumer is comparing two new cars. Car A exerts 250 horsepower, while Car B exerts 300 horsepower. The consumer is most concerned about the peak velocity that the car can reach. Which of the following statements would best inform the consumer's decision? (Note: 1 horsepower = 745.7 W) A. Car A and Car B both have unlimited velocities, ignoring nonconservative forces. B. Car A will reach its peak velocity more quickly than Car B. C. Car A will dissipate less energy to the surroundings than Car B. D. Car A will have a lower peak velocity than Car B.

Correct Answer: A Explanation: Horsepower is a unit of power, as evidenced by the name and the conversion factor given in the question stem. Power is a rate of energy expenditure over time. Given unlimited time, both cars are capable of unlimited increases in (kinetic) energy, meaning that they have unlimited maximum velocities. The fact that Car B has a higher power rating means that it will reach any given velocity faster than Car A, eliminating choice (B). There is not enough information to make any judgments on the efficiency of the cars, eliminating choice (C). While it may take longer for Car A to reach a given velocity, both cars have unlimited maximum velocities according to the information given in the stem, eliminating choice (D).

During uniform circular motion, which of the following relationships is necessarily true? A. No work is done. B. The centripetal force does work. C. The velocity does work. D. Potential energy depends on position of the object around the circle.

Correct Answer: A Explanation: In uniform circular motion, the displacement vector and force vector are always perpendicular; therefore, no work is done. Potential energy is constant for an object in uniform circular motion, whether it is the gravitational potential energy of a satellite orbiting the Earth or the electrical potential energy of an electron orbiting the nucleus of an atom. In both cases, potential energy does not change and does not depend on the position of the object around the circle, eliminating choice (D).

A charge of 2 μC flows from the positive terminal of a 6 V battery, through a 100 Ω resistor, and back through the battery to the positive terminal. What is the total potential difference experienced by the charge? A. 0 V B. 0.002 V C. 0.2 V D. 6 V

Correct Answer: A Explanation: Kirchhoff's loop rule states that the total potential difference around any closed loop of a circuit is 0 V. Another way of saying this is that the voltage gained in the battery (6 V) will be used up through the resistors. Because this charge both started and ended at the positive terminal, its total potential difference is therefore 0 V. 6 V, choice (D), is the voltage gained in the battery as well as the voltage drop in the resistors—creating a net sum of 0 V.

Josh, who has a mass of 80 kg, and Sarah, who has a mass of 50 kg, jump off a 20 m tall building and land on a fire net. The net compresses, and they bounce back up at the same time. Which of the following statements is NOT true? A. Sarah will bounce higher than Josh. B. For Josh, the change in speed from the start of the jump to contacting the net is 20 m/s C. Josh will experience a greater force upon impact than Sarah. D. The energy in this event is converted from potential to kinetic to elastic to kinetic.

Correct Answer: A Explanation: Sarah will not bounce higher than Josh. Assuming that mechanical energy is conserved, Sarah and Josh will start with a given amount of potential energy, which is converted into kinetic energy, then elastic potential energy, then kinetic energy again with no loss of energy from the system, eliminating choice (D). By this logic, both individuals should return to the same starting height. Josh starts with U = mgh = 80 * 10 * 20 = 16,000 J of potential energy. At the moment he hits the net, all of this potential energy has been converted into kinetic energy. Therefore, K = 1/2 mv^2 -> v = sqr rt (2K/m) = square root (2X16000 / 80) = square root of 400 = 20 m/s eliminating choice (B). Josh will experience a greater force upon impact because the net exerts a force proportional to weight; the higher the weight, the larger the force exerted by the net, eliminating choice (C).

A water tower operator is interested in increasing the pressure of a column of water that is applied to a piston. She hopes that increasing the pressure will increase the force being applied to the piston. The only way to increase the pressure is to alter the speed of the water as it flows through the pipe to the piston. How should the speed of the water be changed to increase the pressure and force? A. Increase the speed B. Decrease the speed C. Release water intermittently against the pipe D. The speed of water will not change pressure at the piston.

Correct Answer: B Explanation: This is a basic interpretation of Bernoulli's equation that states, at equal heights, speed and pressure of a fluid are inversely related (the Venturi effect). Decreasing the speed of the water will therefore increase its pressure. An increase in pressure over a given area will result in increased force being transmitted to the piston.

A ray of light (f = 5 × 1014 Hz) travels from air into crystal into chromium. If the indices of refraction of air, crystal, and chromium are 1, 2, and 3, respectively, and the incident angle is 30°, then which of the following describes the frequency and the angle of refraction in the chromium? A. 5 × 1014 Hz; 9.6° B. 5 × 1014 Hz; 57° C. 1.0 × 1010 Hz; 9.6° D. 1.0 × 1010 Hz; 57°

Correct Answer: A Explanation: This question contains two parts—we have to determine the frequency and the angle of refraction of the light ray. The first part, however, is straightforward because the frequency of a light ray traveling from one medium to another does not change. Because the frequency must be 5 × 1014 Hz, we can eliminate choices (C) and (D). For the angle of refraction, we can either calculate it or determine it using logic. First, the light ray goes from air into crystal; that is, from a low index of refraction to a higher one. According to Snell's law, the angle of refraction will be smaller than the incident angle (closer to the normal). When the light ray moves from crystal to chromium, it again goes from a lower index of refraction into a higher one, thus making the angle of refraction even smaller, eliminating choice (B). This question could also be answered by calculation using Snell's law, but the calculations are time consuming and unnecessary.

How many moles of electrons pass through a circuit containing a 100 V battery and a 2 Ω resistor over a period of 10 seconds? (Note: F = 9.65 X 10^4 C/mol e-) A. 5.18 × 10-3 moles B. 500 moles C. 5.18 × 103 moles D. 5.2 × 106 moles

Correct Answer: A Explanation: To determine the moles of charge that pass through the circuit over a period of 10 s, we will have to calculate the amount of charge running through the circuit. Charge is simply current times time, and the current can be calculated using Ohm's law: V= IR and I = Q/delta t, so Q = V* delta t /R Q = 500 C Then, calculate the number of moles of charge that this represents by using the Faraday constant and approximating F as 10^5 C/mol e- 500 C / 10^5 = 5X 10^-3 mol e-

As the confidence level increases, a confidence interval: A. becomes wider. B. becomes thinner. C. shifts to higher values. D. shifts to lower values.

Correct Answer: A Explanation: To increase the confidence level, one must increase the size of the confidence interval to make it more likely that the true value of the mean is within the range. Therefore, the confidence interval must become wider.

A transformer is a device that takes an input voltage and produces an output voltage that can be either larger or smaller than the input voltage, depending on the transformer design. Although the voltage is changed by the transformer, energy is not, so the input power equals the output power. A particular transformer produces an output voltage that is 300 percent of the input voltage. What is the ratio of the output current to the input current? A. 1:03 B. 3:01 C. 0.25 D. 300:01:00

Correct Answer: A Explanation: We are told that transformers conserve energy so that the output power equals the input power. Thus Pout= Pin, or IoutVout = IinVin. There is therefore an inverse proportionality between current and voltage. If the output voltage is 300% of the input voltage (3 times its amount), then the output current must be 1/3 of the input voltage. This can be represented as a 1:3 ratio.

A hypothesis test was correctly conducted and the experimenter failed to reject the null hypothesis. Which of the following must be true? I. The p-value was greater than α. II. A type I error did not occur. III. The power of the study was too small. A. I only B. II only C. I and II only D. I and III only

Correct Answer: B Explanation: A type I error occurs when the null hypothesis is incorrectly rejected. Because we failed to reject the null hypothesis, this could not have occurred. Statement I is incorrect because in a two-sided test, the p-value only needs to exceed alpha/2 Statement III is incorrect because we lack information about power in the question stem. In addition, a study could be extremely well-powered and still fail to reject the null hypothesis if no difference truly exists between two populations.

A 95% confidence interval will fall within what distance from the mean? A. ±σ B. ±2σ C. ±3σ D. ±4σ

Correct Answer: B Explanation: Approximately 95% of values fall within two standard deviations (±2σ) of the mean for a normal distribution. A confidence interval is constructed using the same values. Approximately 68% of the values are within one standard deviation, and 99% are within three standard deviations, eliminating the other answer choices.

Mechanical advantage and efficiency are both ratios. Which of the following is true regarding the quantities used in these ratios? A. Mechanical advantage compares values of work; efficiency compares values of power. B. Mechanical advantage compares values of forces; efficiency compares values of work. C. Mechanical advantage compares values of power; efficiency compares values of energy. D. Mechanical advantage compares values of work; efficiency compares values of forces.

Correct Answer: B Explanation: Mechanical advantage is a ratio of the output force generated given a particular input force. Efficiency is a ratio of the useful work performed by a system compared to the work performed on the system.

In some forms of otosclerosis, the stapedial foot plate, which transmits vibrations from the bones of the middle ear to the fluid within the cochlea, can become fixed in position. This limits the displacement of the stapedial foot plate during vibration. Based on this mechanism, which of the following symptoms would most likely be seen in an individual with otosclerosis? A. An increase in the perceived volume of sounds B. A decrease in the perceived volume of sounds C. An increase in the perceived pitch of sounds D. A decrease in the perceived pitch of sounds

Correct Answer: B Explanation: Saying that the stapedial footplate has limited displacement during vibration is another way of stating that the amplitude of the vibration has been decreased. Because amplitude is related to intensity, and intensity is related to sound level, the perceived sound level (volume) will be decreased as well. Pitch, described in choices (C) and (D), is related to the frequency of a sound, not its amplitude.

A graph of an exponential decay process is created. The y-axis is the natural logarithm of the ratio of the number of intact nuclei at a given time to the number of intact nuclei at time t = 0. The x-axis is time. What does the slope of such a graph represent? A. λ B. - λ C. e^-λt

Correct Answer: B Explanation: The expression n = n0*e^-λt is equivalent to (n/n0) = e^-λt Taking the natural logarithm of both sides, we get: ln (n/n0) = - λ*t From this expression, it is clear that plotting ln (n/n0) vs. t will give a straight line with a slope of -λ.

A large cylinder is filled with equal volumes of two immiscible fluids. A balloon is submerged in the first fluid; the gauge pressure in the balloon at the deepest point in the first fluid is found to be 3 atm. Next, the balloon is lowered all the way to the bottom of the second fluid, where the hydrostatic pressure in the balloon reads 8 atm. What is the ratio of the gauge pressure accounted for by the first fluid to the gauge pressure accounted for by the second fluid? A. 1:03 B. 3:04 C. 3:05 D. 3:08

Correct Answer: B Explanation: The first step in answering this question is defining the different types of pressures. Atmospheric pressure is the pressure at the top of the first fluid exerted by air (at sea level, it is equal to 1 atm). Gauge pressure is the pressure inside the balloon above and beyond atmospheric pressure; gauge pressure is the total (absolute or hydrostatic) pressure inside the balloon minus the atmospheric pressure. Gauge pressure depends on the density of the fluid, the constant of gravity, and the depth at which the object is submerged. Hydrostatic or absolute pressure is the total pressure in the balloon (that is, the gauge pressure and the atmospheric pressure together). Because we are given the gauge pressure at the bottom of the first fluid as 3 atm, our task now is to calculate the gauge pressure accounted for by the second fluid. The hydrostatic pressure at the bottom of the cylinder is 8 atm. One of these atmospheres is atmospheric pressure pushing on the fluids. Another 3 atmospheres are accounted for by the first fluid that is pushing on the second fluid. Thus, the gauge pressure due to the second fluid is 8 - 1 - 3 = 4 atm. The ratio of the gauge pressures is therefore 3:4.

If the electric field at a distance r away from charge Q is 36 N/C, what is the ratio of the electric fields at r, 2r, and 3r? A. 9:03:01 B. 36:09:04 C. 36:18:09 D. 36:18:12

Correct Answer: B Explanation: The first step in answering this question is to remember that the magnitude of the electric field is inversely proportional to the square of the distance: E = kQ/r^2 Therefore, if the electric field at radius r (Er) is 36 N/C, then the electric field at radius 2r will be E of 2r = kQ/(2r(^2 36/ 4r^2 -> 9N/C Similarly, the electric field at radius 3r is equal to 36/(3r)^2 = 36/9r^2 = 4 Therefore, the ratio of Er:E2r:E3r is 36:9:4.

Which of the following statements is true of movement on a plane with friction? I. Acceleration is a function of applied force only. II. More force is needed to accelerate a stationary object than a moving object. III. The force of friction is independent of the mass of objects. A. I only B. II only C. I and II only D. I and III only

Correct Answer: B Explanation: The presence of friction does not change the impact of Newton's laws. A net force must still be applied to cause motion. This net force is not necessarily equal to an applied force, as friction and gravity also act on the object; thus, statement I is eliminated. Static friction opposes the movement of stationary objects, and is necessarily greater than the force of kinetic friction; thus, statement II is correct. Statement III is false because the normal force is related to mass, and friction is related to the normal force.

The resistance of two conductors of equal cross-sectional area and equal lengths are compared, and are found to be in the ratio 1:2. The resistivities of the materials from which they are constructed must therefore be in what ratio? A. 1:01 B. 1:02 C. 2:01 D. 4:01

Correct Answer: B Explanation: The resistance of a resistor is given by the formula R = pL/A Thus, there is a direct proportionality between resistance and resistivity. Because the other variables are equal between the two resistors, we can determine that if R1:R2 is a 1:2 ratio, then ρ1: ρ2 is also a 1:2 ratio.

A 10 kg wagon rests on a frictionless inclined plane. The plane makes an angle of 30° with the horizontal. Approximately how large is the force required to keep the wagon from sliding down the plane? A. 10 N B. 49 N C. 85 N D. 98 N Note: sin 30 = 0.5

Correct Answer: B Explanation: The static force of friction acts parallel to the plane and is in the opposite direction from the parallel component of gravity in this setup. Because the wagon is in equilibrium, these two forces are equal in magnitude. Remember that gravity is often split into components in inclined plane problems. Rather than splitting into x- and y-components, however, it is more convenient to split the gravity vector into parallel and perpendicular components. The parallel component of gravity is given by the expression mg sin θ. Plugging in the values from the question, both the parallel component of gravity and static force of friction must be equal to 10*10m/s^2* (sin 30°) = 49 N.

An anchor made of iron weighs 833 N on the deck of a ship. If the anchor is now suspended in seawater by a massless chain, what is the tension in the chain? (Note: The density of iron is 7800 kg/m^3 and the density of seawater is 1025 kg/m^3) A. 100 N B. 724 N C. 833 N D. 957 N

Correct Answer: B Explanation: The tension in the chain is the difference between the anchor's weight and the buoyant force because the object is in translational equilibrium: T= Fg - Fbuoy. The object's weight is 833 N, and the buoyant force can be found using Archimedes' principle. The magnitude of the buoyant force is equal to the weight of the seawater that the anchor displaces: Fbuoy = ρw*Vw*g Because the anchor is submerged entirely, the volume of the water displaced is equal to the volume of the anchor, which is equal to its mass divided by its density V = mass/density We are not given the anchor's mass, but its value must be the magnitude of the weight of the anchor divided by g. Putting all of this together, we can obtain the buoyant force: Buoyant force = p fluid * V fluid * g = p fluid * V submerged * g =p(density of water)* (mass/density of anchor)*g = density of water * (weight/ density of anchor* g) = weight (density of water/density of anchor) 833 (weight of anchor) * (1025 / 7800) = about 100 N Lastly, we can obtain the tension from the initial equation T = Fg - Fbuoy: T = 833 N - 109 N = 724 N

A 2000 kg experimental car can accelerate from 0 to 30 m/s in 6 s. What is the average power of the engine needed to achieve this acceleration? A. 150 W B. 150 kW C. 900 W D. 900 kW

Correct Answer: B Explanation: The work done by the engine is equal to the change in kinetic energy of the car: W = delta K = 1/2m(vf^2 - vi^2) 1000*30^2 = 900000 J The average power therefore is Power = W / t P = 900,000 / 6 = 150,000 W

A 150 pound man must be given a drug that is dosed at 1.5 mg drug / kg body mass Approximately how many milligrams of the drug should be administered per dose? (Note: 1 lb = 4.45 N) A. 33 mg B. 67 mg C. 100 mg D. 225 mg

Correct Answer: C Explanation: Because grams are a unit of mass and pounds are a unit of force, we must first convert pounds to newtons, and then divide by the acceleration due to gravity to find kilograms. The weight of the person in newtons is 150 lb X 4.45 N/lb = 667.5 N = 667.5 kg*m/s^2 This corresponds to a mass of: 667.5 kg*m/s^2/ 9.8 m/s^2 = 67 kg Now, we can determine the dose: 67 kg (1.5 mg drug/ kg body mass) = 100 mg

A child is practicing the first overtone on his flute. If his brother covers one end of the flute for a brief second, how will the sound change, assuming that the new pitch represents the first overtone in the new setup? A. The pitch of the sound will go up. B. The pitch of the sound will go down. C. The pitch of the sound will not change. D. The change in the pitch depends on the starting pitch.

Correct Answer: B Explanation: This question is testing our understanding of pipes open at one or both ends. To begin, remember that high-frequency sounds have a high pitch and low-frequency sounds have a low pitch. The pipe in this example begins as one that is open on both ends, and then one end is closed off. Our task, therefore, is to determine how the frequency of the second harmonic differs between a pipe that is open at both ends from one of equal length that is open at only one end. For a pipe of length L open at both ends, the wavelength for the second harmonic (first overtone) is equal to L: Wavelength = 2L/n = 2L/2 = L In contrast, for a pipe open at one end and closed at the other, the wavelength is equal to : 4L/3 Keep in mind that the first overtone for a closed pipe corresponds to the third harmonic, not the second. Thus, when the brother covers one end of the flute, the wavelength increases. Given that the wavelength and the frequency of a sound are inversely proportional, an increase in wavelength corresponds to a decrease in frequency. Therefore, when the brother covers one end of the flute, the sound produced by the instrument will be slightly lower in pitch than the original sound.

At what temperature do the Fahrenheit and Celsius scales give equal values? A. 0 K B. 233 K C. 273 K D. 313 K

Correct Answer: B Explanation: This question requires not only unit conversions, but algebra as well. Given that F = 9/5 C + 32 the temperature T can calculated as: T = 9/5 T + 32 -> -4/5 T = 32 -> T = -5/4 (32) = -40 However, the answers are given in kelvin. -40°C + 273 = 233 K.

In an adiabatic compression process, the internal energy of the gas: A. increases because the work done on the gas is negative. B. increases because the work done on the gas is positive. C. decreases because the work done on the gas is negative. D. decreases because the work done on the gas is positive.

Correct Answer: B Explanation: To answer the question, make sure you understand all the terms. An adiabatic process means that there is no exchange of heat; in other words, Q = 0. When a gas is compressed, positive work is being done on the gas (rather than by the gas), so the value for work done by the gas will be negative (W < 0). Based on this, we can determine how the internal energy of the gas changes by using the first law of thermodynamics (ΔU = Q ? W). If Q = 0 and W is negative, then ΔU is positive.

When a hydrogen atom electron falls to the ground state from the n = 2 state, 10.2 eV of energy is emitted. What is the wavelength of this radiation? (Note: 1 eV = 1.60 × 10-19 J, and h = 6.626 × 10-34 J·s.) A. 5.76 × 10-9 m B. 1.22 × 10-7 m C. 3.45 × 10-7 m D. 2.5 × 1015 m

Correct Answer: B Explanation: To solve this question correctly, one must be careful with the units. First, convert 10.2 eV to joules: 10 eV * (1.60X10^-19 J/eV) = 1.6X10^-18 J Next, to determine the wavelength of the radiation, first find the frequency: E = hf -> f = E/h (1.60 × 10-19 J)/(6.626 × 10-34 J·s) = .25 * 10^16 -> 2.5X10^15 Hz Lastly, from the wave equation c = f λ, we can calculate the wavelength of the radiation: λ = c/f -> (3X10^8)/(2.5X10^!5) = 1.2X10^-7 m

In experiment A, a student mixes ink with water and notices that the two liquids mix evenly. In experiment B, the student mixes oil with water; in this case, the liquids separate into two different layers. The entropy change is: A. positive in experiment A and negative in experiment B. B. positive in experiment A and zero in experiment B. C. negative in experiment A and positive in experiment B. D. zero in experiment A and negative in experiment B.

Correct Answer: B Explanation: When the ink randomly intersperses throughout the water, the final state is more disordered than the initial state, so the entropy change of the system is positive. When the oil separates from the water, the final state is just as ordered as the initial state (because the oil and the water are still completely separate), so the entropy change is zero. You can also answer this question by noticing the reversibility of the two experiments. Experiment A has a positive entropy change because it is irreversible, while experiment B has no entropy change because the reaction is reversible. According to the second law of thermodynamics, the overall entropy change can never be negative in a thermodynamic process that moves from one equilibrium state to another.

Using the appropriate number of significant digits, what is the answer to the following math problem? (Note: Assume all numbers are the results of measurements.) 3.060 × 4.10 + 200. = A. 210 B. 213 C. 212.5 D. 212.55

Correct Answer: B Explanation: While all digits are preserved during calculations, the final determination of the number of digits is made by both significant figures and decimal places. During multiplication, the answer is maintained to the smallest number of significant digits. During addition, it is maintained to the smallest number of decimal places. By following the order of operations, addition is the last operation; thus we cannot have a decimal in our answer choice. Because multiplication occurred earlier, the result of that multiplication may be shortened according to the two significant figures in 4.10, but not the entire answer.

Two fluids, A and B, have densities of x and 2x, respectively. They are tested independently to assess absolute pressure at varying depths. At what depths will the pressure below the surface of these two fluids be equal? A. Whenever the depth of fluid A is one-half that of fluid B B. Whenever the depth of fluid A equals that of fluid B C. Whenever the depth of fluid A is 2 times that of fluid B D. Whenever the depth of fluid A is 4 times that of fluid B

Correct Answer: C Explanation: A is less dense The equation for absolute (hydrostatic) pressure is P = Po + ρgz, where Po is the pressure at the surface, ρ is the density of the fluid, g is acceleration due to gravity, and z is the depth in the fluid. If the density of fluid B is twice that of fluid A, then the depth in fluid A will have to be twice that in fluid B to obtain the same absolute pressure: P = Po + ρgz = P = Po + ρgz x*gz = 2x*gz z = 2z

A certain carbon nucleus dissociates completely into α particles. How many particles are formed? A. 1 B. 2 C. 3 D. 4

Correct Answer: C Explanation: A typical carbon nucleus contains 6 protons and 6 neutrons. An α particle contains 2 protons and 2 neutrons. Therefore, one carbon nucleus can dissociate into 6/2 =3 alpha particles.

The energy stored in a fully charged capacitor is given by U = 1/2 CV^2. In a typical cardiac defibrillator, a capacitor charged to 7500 V has a stored energy of 400 J. Based on this information, what is the charge on the capacitor in the cardiac defibrillator? A. 1.1 × 10-5 C B. 5 × 10-2 C C. 1.1 × 10-1 C? D. 3.1 × 106 C

Correct Answer: C Explanation: Because the question is asking us to calculate the charge on the capacitor, use the formula Q = CV. We are given V = 7500 V and can calculate C from the formula for energy, U = 1/2 CV^2 = 1/2 (Q/V)V^2 = QV/2 Q = 2U/V = 2*400J/7500 V Thus, the charge is close to 0.1 C, which is closest to choice (C).

Which of the following processes is LEAST likely to be accompanied by a change in temperature? A. The kinetic energy of a gas is increased through a chemical reaction. B. Energy is transferred to a solid via electromagnetic waves. C. A boiling liquid is heated on a hot plate. D. A warm gas is mixed with a cold gas.

Correct Answer: C Explanation: If a substance is undergoing a phase change, any added heat will be used toward overcoming the heat of transformation of the phase change. During the phase change, the temperature will remain constant. Temperature is a measure of the kinetic energy of the molecules in a sample, so a change in kinetic energy, choice (A), is essentially the same thing as a change in temperature. The heat transfer by radiation described in choice (B) will definitely change the temperature of the solid as long as it is not in the process of melting. Choice (D) describes heat transfer by convection, in which the warm gas will transfer heat to the cold gas until they both reach an intermediate temperature

An opera singer has two precisely identical glasses. The singer produces as pure a tone as possible and shatters the first glass at a frequency of 808 Hz. She then sings a frequency of 838 Hz in the presence of the second glass. The second glass will likely: A. shatter after a longer amount of time because the applied frequency is higher. B. shatter after a shorter amount of time because the applied frequency is higher. C. not shatter because the applied frequency is not equal to the natural frequency of the glass. D. not shatter because higher-frequency sounds are associated with more attenuation.

Correct Answer: C Explanation: If these two glasses are perfectly identical, then the fact that the first glass shattered at 808 Hz tells us that this is very close (if not identical) to the natural (resonant) frequency of the glass. If she produces a frequency that is not equal (or very close) to the natural frequency, then the applied frequency will not cause the glass to resonate, and there will not be the increase in wave amplitude associated with resonating objects. Attenuation will increase with increased frequency because there is more motion over which nonconservative forces can damp the sound wave; however, even if sound level was matched to that which shattered the first glass when accounting for attenuation, the glass would still not shatter for the reasons described above, eliminating choice (D).

5 m3 of a gas are brought from an initial pressure of 1 kPa to a pressure of 3 kPa through an isochoric process. During this process, the work performed by the gas is: A. -10 kJ B. -10 J C. 0 J D. +10 kJ

Correct Answer: C Explanation: Isovolumetric/isochoric: Volume held constant and the work done by or on the system is 0 An isochoric process, by definition, is one in which the gas system undergoes no change in volume. If the gas neither expands nor is compressed, then no work is performed. Remember that work in a thermodynamic system is the area under a P-V curve; if the change in volume is 0, then the area under the curve is also 0.

A certain sound level is increased by 20 dB. By what factor does its intensity increase? A. 2 B. 20 C. 100 D. log 2

Correct Answer: C Explanation: Let Ii be the intensity before the increase and If be the intensity after the increase. Using the equation that relates sound level to intensity, obtain the ratio of Ii to If: Bf = Bi + 10 log (If/Ii) 20 dB = 10 log (If/Ii) 2 = log If/Ii 100 = If/Ii

Two parallel conducting plates are separated by a distance d. One plate carries a charge +Q and the other carries a charge -Q. The voltage between the plates is 12 V. If a +2 μC charge is released from rest at the positive plate, how much kinetic energy does it have when it reaches the negative plate? A. 2.4 × 10-6 J B. 4.8 × 10-6 J C. 2.4 × 10-5 J D. 4.8 × 10-5 J

Correct Answer: C Explanation: Recall that the change in potential energy, ΔU, and the change in potential, ΔV, are related by W = ΔU = qΔV. Therefore, ΔU = (2 × 10-6 C) × (-12 V) = -2.4 × 10-5 J. The positive charge is moving from the positive to the negative plate, and is therefore decreasing in potential energy; this is reflected by the fact that the voltage is -12 V rather than +12 V. The potential energy that is lost is converted into kinetic energy, so the charge must gain 2.4 × 10-5 J of kinetic energy.

A proton and an alpha particle (a helium nucleus) repel each other with a force of F while they are 20 nm apart. If each particle combines with three electrons, what is the magnitude of the new force between them? A. 9F B. 3F C. F

Correct Answer: C Explanation: The magnitude of the electrostatic force is given by the equation Fe = kq1q2/r^2 Because the distance does not change during the interaction in the question, the value of r is irrelevant to the answer. Currently, q1 and q2 are equal to +1e and +2e, respectively;the addition of three electrons (each of which carries a charge of ?e) will change the charges to ?2e and ?1e. Therefore, the product q1q2before the interaction is equal to the product q1q2 after the interaction (+2e2). Because k and r also remain constant in this system, the magnitude of the force does not change.

An experimenter is attempting to investigate the effect of a new antibiotic on E. coli. He plates cells and administers one milliliter of the antibiotic. Which of the following is an appropriate negative control in this experiment? A. A plate with no cells that was coated with one milliliter of antibiotic. B. A plate with E. coli and no additional treatment. C. A plate with E. coli and one milliliter of isotonic saline. D. A plate of epithelial cells treated with one milliliter of antibiotic.

Correct Answer: C Explanation: The purpose of a control is to keep the conditions of two experiments as close as possible to establish causality. In this case, the one milliliter volume addition might have impacted the growth of E. coli; thus, we must control for this by administering an equal volume of a theoretically inert compound to a plate of E. coli.

A nuclide undergoes two alpha decays, two positron decays, and two gamma decays. What is the difference between the atomic number of the parent nuclide and the atomic number of the daughter nuclide? A. 0 B. 2 C. 4 D. 6

Correct Answer: D Explanation: In alpha decay, an element loses two protons. In positron decay, a proton is converted into a neutron. Gamma decay has no impact on the atomic number of the nuclide. Therefore, two alpha decays and two positron decays will yield a daughter nuclide with six fewer protons than the parent nuclide.

What is the binding energy of the argon-40 isotope in MeV? (Note: mproton = 1.0073 amu, mneutron = 1.0087 amu, mAr-40 nucleus = 39.9132 amu, c^2 = 932 MeV/amu) A. 0.4096 MeV B. 40.3228 MeV C. 381.7 MeV D. 643.8 MeV

Correct Answer: C Explanation: To determine the binding energy, we must first determine the mass defect. The mass defect is simply the masses of each of the protons and neutrons in the unbound state added together minus the mass of the formed argon-40 nucleus (which contains 18 protons and 40 - 18 = 22 neutrons): Mass Defect = (18X1.0073) + (22X1.0087 amu) - 39.9132 amu =18.1314 + 22.1914 - 39.9132 =40.3228 - 39.9132 =0.4096 amu The binding energy can then be determined from this mass defect: E = mc^2 = 0.4096 amu X 932 MeV/ amu =0.4 X 900 = 360 MeV The closest answer is choice (C).

A dipole is placed in an electric field and is allowed to come to equilibrium. How would the dipole react if the direction of the electric field is suddenly reversed? A. It rotates to align with the new field. B. It accelerates linearly along the field lines. C. It experiences no rotational or linear movement. D. It both rotates to align with the new field and accelerates linearly along the field lines.

Correct Answer: C Explanation: Torque is a function of both force applied and the angle at which it is applied. A dipole placed in an electric field will experience a torque until it comes to rest oriented within the field, at which point the angle between the plane of the dipole and the electric field is 0°. Once this point is reached, inverting the electric field has no impact on the dipole because it will now have an angle of 180°, the sine of which is still 0.

A rock (m = 2 kg) is shot up vertically at the same time that a ball (m = 0.5 kg) is projected horizontally. If both start from the same height: A. the rock and ball will reach the ground at the same time. B. the rock will reach the ground first. C. the ball will reach the ground first. D. the rock and ball will collide in the air before reaching the ground.

Correct Answer: C Explanation: We only need to analyze the motion in the vertical dimension to answer this question. If both the rock and ball began with no vertical velocity, they would reach the ground at the same time. However, because the rock begins with an upward component of velocity, it will take time to reach a maximum height before falling back toward the ground. Functionally, the rock's free fall thus starts higher and later than the ball's. The rock will necessarily hit the ground after the ball.

Which of the following are able to produce a virtual image? I. Convex lens II. Concave lens III. Plane mirror A. I only B. III only C. II and III only D. I, II, and III

Correct Answer: D Explanation: All images produced by plane mirrors will be virtual, so statement III is true. The same goes for diverging species (convex mirrors and concave lenses), so statement II is true. Converging species (concave mirrors and convex lenses) can produce real or virtual images, depending on how far the object is from the species, so statement I is also true.

A 40 kg block is resting at a height of 5 m off the ground. If the block is released and falls to the ground, which of the following is closest to its total mechanical energy at a height of 2 m, assuming negligible air resistance? A. 0 J B. 400 J C. 800 J D. 2000 J

Correct Answer: D Explanation: Assuming negligible air resistance, conservation of energy states that the total mechanical energy of the block is constant as it falls. At the starting height of 5 m, the block only has potential energy equal to U = mgh = 40 * 10 * 5 = 2000 J Because the kinetic energy at this point is 0 J, the total mechanical energy is 2000 J at any point during the block's descent.

Which of the following relationships between measurement error and overall error is correct? A. Unreliable data leads to confounding. B. Invalid data leads to confounding. C. Unreliable data leads to bias. D. Invalid data leads to bias.

Correct Answer: D Explanation: Data that is off in a systematic way (reads at a value that is not the true value) will cause bias. This type of data error is an example of a lack of validity (or accuracy). Unreliable data suffers from random, not systematic, error. Confounding arises from errors in data analysis, not data collection.

Imagine that a beam of monochromatic light originates in air and is allowed to shine upon the flat surface of a piece of glass at an angle of 60° with the normal. The reflected and refracted beams are perpendicular to each other. What is the index of refraction of the glass? A. sqr rt 3/3 B. 1 C. 2 D. sqr rt 3

Correct Answer: D Explanation: Drawing a diagram is best here. Because the angle given is with respect to the normal, you know that the incident angle must equal 60°. You know that the reflected beam will have an angle of 60° relative to the normal. Therefore, the reflected beam will make an angle of 30° with the plane of the glass. If the reflected and refracted beams are perpendicular to each other, the refracted beam will make a 60° angle with the plane of the glass. θrefractedis therefore 30° relative to the normal. Using n1 sin θ1 = n2 sin θ2, we have 1 sin 60° = n2 sin 30° sqrrt 3/2 = n2 (1/2) sqrrt 3 = n2

A massless spring initially compressed by a displacement of two centimeters is now compressed by four centimeters. How has the potential energy of this system changed? A. The potential energy has not changed. B. The potential energy has doubled. C. The potential energy has increased by two joules. D. The potential energy has quadrupled.

Correct Answer: D Explanation: Elastic potential energy, like kinetic energy, is related to the square of another variable, as shown by the equation U = 1/2 kx^2 Increasing the displacement by a factor of 2 increases the potential energy by a factor of 22 = 4.

A new medication for heart failure is being developed and has had a statistically significant effect on contractility in clinical trials. Which of the following would NOT likely cause the drug to be held back from common use? A. The value of α used was 0.5. B. Similar compounds display toxicity. C. The effect size is clinically insignificant. D. The study had low power to detect a difference.

Correct Answer: D Explanation: If a study has low power, it is more difficult to get results that are statistically significant. Therefore, if the results are still statistically significant even with low power, then there is likely a large effect size that makes the effect clinically significant. If the value of α used in the study was 0.5, then statistically significant results do not mean much—traditionally, α = 0.05 or a smaller probability is used, eliminating choice (A). Concerns about toxicity should always limit the use of a drug, eliminating choice (B). A statistically significant result is only of interest if it also represents a clinically significant improvement, eliminating choice (C).

A child stands between two mirrors with his arms out, perpendicular to the mirrors. One plane mirror is 5 m away from his left hand and another plane mirror is 7 m away from his right hand. How far apart are the two images produced by the mirrors if the child has an arm span of 0.5 m? A. 2 m B. 12 m C. 12.5 m D. 24.5 m

Correct Answer: D Explanation: In plane mirrors, the image is as far away from the mirror as the object is. In other words, the image produced by the left mirror is 5 m away from the mirror because the child is standing 5 m away from the mirror. Similarly, the right mirror produces an image that is 7 m away from the center of the mirror. To calculate how far away the two images are, take into consideration not only the image distance but also the distance of the object (the child) from the mirrors and the child's arm span of 0.5 m. Therefore, the images are 5 + 5 + 0.5 + 7 + 7 = 24.5 m apart.

Ignoring attenuation, how does the intensity of a sound change as the distance from the source doubles? A. It is four times as intense. B. It is twice as intense. C. It is half as intense. D. It is one-quarter as intense.

Correct Answer: D Explanation: Intensity is equal to power divided by area. In this case, area refers to the surface area of concentric spheres emanating out from the source of the sound. This surface area is given by 4πr2, so as distance (r) doubles, the intensity will decrease by a factor of four.

Which of the following will not result in the splitting of white light into its component colors? A. Dispersion through a prism B. Diffraction through a grating C. Refraction within a thin film D. Reflection from an ideal convex mirror

Correct Answer: D Explanation: Light can be split into its component colors by dispersion, such as that through a prism, eliminating choice (A). Diffraction by a diffraction grating will also separate colors by their wavelengths, eliminating choice (B). The refraction of light within a thin film also leads to light dispersion as the different colors are refracted at slightly different angles in the film, eliminating choice (C). A mirror with significant aberration could lead to a separation of light into its component colors, but we are told that this is an ideal mirror. Thus, choice (D) is the correct answer.

Substances A and B have the same freezing and boiling points. If solid samples of both substances are heated in the exact same way, substance A boils before substance B. Which of the following would NOT explain this phenomenon? A. Substance B has a higher specific heat. B. Substance B has a higher heat of vaporization. C. Substance B has a higher heat of fusion. D. Substance B has a higher internal energy.

Correct Answer: D Explanation: Saying that substance B has a higher internal energy cannot explain the phenomenon because the internal energy is irrelevant; the heat involved in the process is related only to the specific heat, the heat of fusion, and the heat of vaporization. All of the other choices could explain the phenomenon. The heat required to melt the solid is determined by the heat of fusion, choice (C). The heat required to bring the liquid to its boiling point is determined by the specific heat, choice (A). The heat required to boil the liquid is determined by the heat of vaporization

Which of the following measures of distribution is most useful for determining probabilities? A. Range B. Average distance from mean C. Interquartile range D. Standard deviation

Correct Answer: D Explanation: Standard deviation is the most common measure of distribution. It is the most closely linked to the mean of a distribution and can be used to calculate p-values, which are probabilities (specifically, p-values are the probability that an observed difference between two populations is due to chance).

What is the angular frequency of the third harmonic in a pipe of length 0.6 m with one closed end? (Note: The speed of the sound is approximately 340 m/s) A. 213 radians per second B. 425π radians per second C. 425 radians per second D. 850π radians per second

Correct Answer: D Explanation: The angular frequency is related to the frequency of a wave through the formula ω = 2πf. Thus, our initial task is to calculate the frequency of the wave. Knowing its speed, we determine the frequency by first calculating its wavelength (ν = fλ). For the third harmonic of a standing wave in a pipe with one closed end, the wavelength is λ = 4L/n = 4*0.6 m / 3 = 0.8 m The frequency of the wave is therefore f = v/λ -> 340 m/s / 0.8 = 425 Hz Finally, obtain the angular frequency simply by multiplying the frequency of the wave by 2π: ω = 2πf = 850π radians per second

Which of the following will most likely increase the electric field between the plates of a parallel plate capacitor? A. Adding a resistor that is connected to the capacitor in series B. Adding a resistor that is connected to the capacitor in parallel C. Increasing the distance between the plates D. Adding an extra battery to the system

Correct Answer: D Explanation: The electric field between two plates of a parallel plate capacitor is related to the potential difference between the plates of the capacitor and the distance between the plates, as shown in the formula E = V/d The addition of another battery will increase the total voltage applied to the circuit, which, consequently, is likely to increase the electric field. The addition of a resistor in series will increase the resistance and decrease the voltage applied to the capacitor, eliminating choice (A). Adding a resistor in parallel will not change the voltage drop across the capacitor and should not change the electric field, eliminating choice (B). Increasing the distance between the plates, choice (C), would decrease the electric field, not increase it.

An electron is accelerated over a distance d by an electrical potential V. The electrical potential applied to this electron is then increased by a factor of 4 and the electron is accelerated over the same distance d. The speed of the electron at the end of the second trial will be larger than at the end of the first trial by a factor of: A. 16 B. 8 C. 4 D. 2

Correct Answer: D Explanation: The electrical potential (V) is equal to the amount of work done (W) divided by the test charge (q). This means that the potential is directly proportional to the amount of work done, which is equal to the amount of energy gained by the particle; therefore, the overall amount of energy increases by a factor of 4. Because energy is directly proportional to the square of the speed (according to 1/2 mv^2), the speed must increase by a factor of 2.

A submarine is inspecting the surface of the water with a laser that points from the submarine to the surface of the water and through the air. At what angle will the laser not penetrate the surface of the water but rather reflect entirely back into the water? (Assume nwater = 1.33 and nair = 1.) A. 19° B. 29° C. 39° D. 49°

Correct Answer: D Explanation: This question is testing our understanding of total internal reflection. As the laser beam travels from water to air—that is, from a higher to a lower index of refraction—the angle of refraction increases. At the critical angle (θc), the angle of refraction becomes 90°; at this point, the refracted ray is parallel to the surface of the water. When the angle of incidence is greater than the critical angle, all the light is reflected back into the water. The question is asking for the critical angle: θc = sin^-1 (n2/n1) = sin ^-1 (1/1.33) -> sin^-1 (1/4/3 = 3/4) We know that sin 45 degrees = sqr rt 2/2 = 0.707, so we know that the answer must be close to 45 The inverse sine of 0.75 must be slightly higher than 48.59° is the exact answer.

If the area of a capacitor's plates is doubled while the distance between them is halved, how will the final capacitance (Cf) compare to the original capacitance (Ci)? A. Cf = Ci B. C. Cf = 2Ci D. Cf = 4Ci

Correct Answer: D Explanation: This question should bring to mind the equation C = ε0 (A/d) where ε0 is the permittivity of free space, A is the area of the plates, and d is the distance between the plates. From this equation, we can infer that doubling the area will double the capacitance, and halving the distance will also double the capacitance. Therefore, the new capacitance is four times larger than the initial capacitance.

A voltaic cell provides a current of 0.5 A when in a circuit with a 3 Ω resistor. If the internal resistance of the cell is 0.1 Ω, what is the voltage across the terminals of the battery when there is no current flowing? A. 0.05 V B. 1.5 V C. 1.505 V D. 1.55 V

Correct Answer: D Explanation: This question tests our understanding of batteries in a circuit. The voltage across the terminals of the battery when there is no current flowing is referred to as the electromotive force (emf or ε of the battery). However, when a current is flowing through the circuit, the voltage across the terminals of the battery is decreased by an amount equal to the current multiplied by the internal resistance of the battery. Mathematically, this is given by the equation V = ε - irint To determine the emf of the battery, first calculate the voltage across the battery when the current is flowing. For this, we can use Ohm's law: V= IR = 0.5 A * 3 ohms = 1.5 V Because we know the internal resistance of the battery, the current, and the voltage, we can calculate the emf: E (epsilon) = V + i *r int = 1.5 V + .5 A * 0.1 ohms 1.5 + 0.05 = 1.55 V The answer makes sense in the context of a real battery because its internal resistance is supposed to be very small so that the voltage provided to the circuit is as close as possible to the emf of the cell when there is no current running.

Resistors in parallel

Current will divide to pass through resistors separately 1/Rp=1/R₁+1/R₂+1/R₃+... Overall reduction in equivalent resistance (total resistance will be less than smallest resistance in circuit) Rp decreases as more resistors are added Magnitude of current in each branch inversely proportional to resistance *So, if circuit has two branches in parallel, and one branch has twice the resistance (half the magnitude of current), then the other will have twice the current *Total resistance halved by wiring two identical resistors in parallel *If n is identical resistors wired in parallel, the total resistance = R/n (voltage and current are equal through cell so I total / n is current through each) Wired with common high potential and low potential terminal, but charge can flow through different paths (but the voltage drop experienced by each division of current is the same because all pathways originate and end at common point) *It doesn't matter how many steps each path takes, the change is the same in the end V=V₁=V₂=... Remember Kirchhoff's loop rule: if every resistor is in parallel, voltage drop across each pathway alone must be = to voltage from source *In series, the current stays the same but the voltage changes, in parallel, the current changes so the voltage stays the same Resistance in each pathway may differ -Electrons prefer path of least resistance, so smallest resistance will have largest current (inverse relationship)

Force on a current-carrying wire in a magnetic field

Current, like point charge, experiences magnetic force in magnetic field For a straight wire, the magnitude of the force (FB) = ILB sin θ where I = current, L = length of wire in field, B is magnitude of magnetic field, θ is angle between L and B CURRENT IS THE FLOW OF POSITIVE CHARGE (even though only negative charges are actually moving If the current is to the top of the page, and the uniform magnetic field (B) is into page, then sin θ = sin 90 = 1, and the force (direction of palm/middle finger) is going to the left

If the magnetic field a distance r away from a current-carrying wire is 10 T, what will be the net magnetic field at r if another wire is placed a distance 2r from the original wire and has a current twice as strong flowing in the opposite direction? A. 0 T B. 15 T C. 20 T D. 30 T

D. 30 T Notice right away that between the two wires, the direction of the magnetic field is the same: into the page. (use the second right hand rule, where thumb goes in direction of the current) Therefore, because the vector direction is the same, we can just focus on the magnitudes of the two magnetic fields. We know that B1 = 10 T at a distance r. Consider the relationships in the equation B = M0*I/ 2*pi*r Magnetic field and current are directly proportional, whereas magnetic field and distance are inversely proportional. Therefore, doubling the current will result in double the magnetic field as the first wire, or 20 T. The overall magnitude of the magnetic field is 10 T + 20 T = 30 T into the page.

Two resistors are wired in series and connected to a battery, if a third resistor is added in series, the voltage drop across of the first two resistors:

Decreases Voltage must be "used up" as current passes through New resistor in front of other causes total resistance to go up, currents goes down, and voltage dropped at each resistor to go down

Diamagnetic, paramagnetic, ferromagnetic

Diamagnetic materials: Atoms with no unpaired electrons (no magnetic field) -Slightly repelled by magnet / weakly antimagnetic -Wood, plastic, water, glass, skin Paramagnetic and ferromagnetic have unpaired electrons, so they have net magnetic dipole moment, but they are usually randomly oriented so they dont have net magnetic field Paramagnetic: Weakly magnetized, align magnetic dipoles with external field -Alluminum, copper, gold Ferromagnetic: Like paramagnetic (unpaired electrons and permanent atomic magnetic dipoles that are normally oriented randomly so material has no net magnetic dipole)< but these become strongly magnetized when exposed to external magnetic field at certain temperatures -Iron, nickel, cobalt -Field lines exit North Pole and enter south pole -Impossible to have monopole magnet because magnetic field lines are circular

Single Slit and Slit-lens system

Diffraction through single slit does not create characteristic fringes when projected onto screen, although the light does spread out (like a fan) When a lens is introduced into system, the additional refraction of light causes constructive and destructive interference, creating fringes

Dot Product vs Cross Product

Dot Product.: Vector a * vector b = vector b * vector a (direction does not matter) | vector a | | vector b |*cos theta =(Magnitude of a times magnitude of b times cosine theta) Scalar quantity Only forces parallel and antiparallel Cross Product: vector aXvector b = | vector a | | vector b |*sin theta Direction DOES matter Cross product uses right hand rule *looking for part perpendicular to a

Hypothesis Testing and Confidence Intervals If the P value is greater than alpha (0.05), than we __________ which means the data is................ If the P value is less than alpha (0.05), than we __________ which means the data is................

Draw conclusions about populations based on sample data -Interpreted in context of probabilities, and what we deem to be acceptable risk of error Hypothesis Testing: Begins with idea about what may be different *Null hypothesis: Always says two populations are equal, or single population can be described by parameter equal to given value *Alternative hypothesis may be nondirectional (not equal) or directional (mean of population A greater than mean of population B) -Z or t-tests -> rely on standard or t distribution *Test statistic determines likelihood that statistic was obtained by random chance (assuming null hypothesis was true) = p-value (compare p-value to significance level (alpha) which is usually = 0.05) If the P value is greater than alpha (0.05), than we fail to reject the null hypothesis, which means the data is not statistically significant (not much of a difference between the populations) If the P value is less than alpha (0.05), than we reject the null hypothesis, which means the data is statistically significant *Higher p-value = higher likelihood that the null hypothesis is true, so don't reject it *Alpha = level of risk we are willing to accept for incorrectly rejecting null hypothesis (type 1 error: likelihood that we report a difference when there isn't one) *Type 2 error (B): Incorrectly fail to reject the null hypothesis (there is a difference, but we didn't find it) *Power = 1-B: Correctly reject null hypothesis *Confidence = We did not find a difference, and there wasn't one, so we were correct Confidence Intervals: Determine range of values from sample mean and standard deviation *Usually 95% confidence level, use table to find z or t-score (multiply this by standard deviation int hen add and subtract from mean to get interval) *Wider interval = higher confidence level (95% is common)

Dynamics Free Body Diagrams: Three people are pulling on ropes tied to a tire with forces of 100N (North East), 125 N (North west), and 125N (straight down) as shown in image on next card. Find the magnitude and direction of resultant force sin30 = 0.5 cos 30 = 0.866 sin 37 =0.6 cos37 = 0.8

Dynamics: The study of forces and torques Fnet, x = sum of fx = 100cos30 - 125cos37 = 100(0.866) - 125(0.8) = -13.4 N Fnet, y = sum of fy = 100sin30 + 125sin37 -125 = 100(0.5) - 125(0.6) -125 = 50 + 75 -125 = 0 N So, the net force will be 13.4 N to the left

Photoelectric effect (Discovered by Hertz, but Einstein got the Nobel prize) and Threshold Frequency

Ejection of electron from surface of metal in response to light When light of a high frequency (usually blue light or UV light) is incident (An incident ray is a ray of light that strikes a surface) on a metal in a vacuum, metal atoms emit electrons -> these liberated electrons produce current (net charge flow per unit time (I=Q/t) *Magnitude of current is proportional to intensity * If light beams frequency is above the threshold frequency of metal, light beams of greater intensity produce more photons per unit time that fall on electrode producing more electrons liberated *Greater intensity = more electrons liberated *When light frequency is above threshold frequency, magnitude of resulting current is directly proportional to intensity and amplitude of light beam Threshold Frequency (fT): The minimum frequency of light that causes ejection of electrons -Depends on chemical composition / type of metal exposed to radiation -"All or nothing response": If frequency of photon less than fT (f<fT) then no electron is ejected, but if f> fT, then an electron will be ejected and maximum kinetic energy of ejected electron will be equal to work function (hfT - hf) *Einstein: Light beams consists of integral number of light quanta called photons. The energy of each photon is proportional to frequency of light: E = hf where E is energy of photon of light, h is Planck's constant (6.626 X10^-34 J*s), and f is frequency of light *We can use frequency to find wavelength using c = f*wavelength Waves with higher frequency have higher energy and shorter wavelengths (toward blue to violet end and UV end of spectrum) *Lower frequency = longer wavelengths and lower energy ( red to infrared end of spectrum) *ENERGY OF PHOTON INCREASES WITH INCREASING FREQUENCY *Only discuss electrons being ejected from metals *and not protons or neutrons is because of weak hold metals have on valence electrons (due to low ionization energy) *Example of energy transfer: Light energy causes increase in electrical potential energy in atom The photoelectric effect is strong support for particle theory of light, which states that light is not continuous wave but acts as discrete bundles of energy called photons. The speed of ejected electrons depends on COLOR of light, not intensity 1. Red light sends electrons flying off metal 2. Increasing brightness of red light ejects more electrons 3. Changing light to high intensity blue light results in much faster electrons (light can behave as continuous wave or bundle of energy (photons) -> blue photon (higher frequency's hotter wavelength) packs more energy than red, hitting electron harder -> greater intensity increases number of ejected electrons

Beta Decay

Emission of a Beta (B) particle (electron: Given by symbol e- or B-) *Even though electrons don't reside in nucleus, they are emitted by the nucleus when a neutron decays into a proton, a Beta particle and antineutrino (v with line over it) *Don't worry about neutrino and antineutrino for MCAT -Electron almost 2000 X lighter than proton, so beta radiation from radioactive decay is more penetrating than alpha radiation Induced decay (positron emission) -> positron released (has the mass of electron but carries positive charge)(e+ or B+). Neutrino (v) emitted here as well During B- decay (image shown), neutron converted into proton and B- particle (Z=-1, A = 0) -Atomic number of daughter nucleus will be one higher than parent nucleus, and mass number will not change *Remember, Z = atomic number = number of protons (Add one) *A = mass number = protons + neutrons (does not change) During B+ decay (image same but B+ instead of B- on far right and Z-1 instead of Z+1), proton converted into a neutron and a B+ particle (Z = +1, A=0) is emitted. Atomic number of daughter nucleus will be one lower and mass number won't change In both types of beta decay there needs to be conservation of charge. If negative charge (B-) is produced, a neutron needs to be converted to proton. If positive charge (B+) is produced, proton converted to neutron to maintain charge *NEGATIVE BETA DECAY PRODUCES NEGATIVE BETA PARTICLE AND POSITIVE BETA DECAY PRODUCES POSITIVE BETA PARTICLE

Alpha Decay

Emission of an alpha (a) particle, which is a (4 over 2) He nucleus thats has 2 protons, 2 neutrons, and no electrons -Alpha particles do not have any electrons, so they carry a charge of +2 -> they interact with matter very easily and do not penetrate shielding (like lead sheets) extensively -Very massive compared to beta particle and carries twice the charge -Emission of a particle means that the atomic number of the daughter nucleus will be two less than parent nucleus and the mass number will be four less

Kinetic Energy

Energy is the property of a system that enables it to do something or make something happen, including the capacity to do work. SI units are joules (J)(For all forms) Kinetic Energy: Energy of motion (any time an object has speed it has kinetic energy) *Kinetic energy is related to SPEED, not velocity (an object has the same kinetic energy regardless of the direction of its velocity vector ) K = 1/2 * mv^2 m is mass in kilograms, v is speed in meters/second, k is kinetic energy in joules (J)(kg*m^2/s^2) *Faster speed = more kinetic energy (as speed doubles, kinetic energy quadruples)

Electric field

Exerting forces on other charges that move into the space of a field -Produced by a source charge (Q) -When a test charge (q) (charge placed in the electric field) is placed in an electric field (E), it will experience an electrostatic force (Fe) = qE -Stationary source charge Q (Creates the electric field)(If Q and q have same charge, it is repulsive) -Magnitude of electric field (E) = Fe/q = kQ/r^2 where E is electric field magnitude (N/C), Fe is magnitude of force felt by q, k is electrostatic constant, Q is source charge magnitude, r is distance between charges -Divide Coulumbs law by magnitude of test charge (q) -> determine magnitude of e field at point around source charge (Q) -Use kQ/r^2 when no value for test charge is there -Electrostatic forces are directly related to charge and related to distance by inverse square relationship. -Source charge creates E field, not test charge , so we cant use E = Fe/q to determine relationship, so e filed is unrelated to test charge but it is still related to distance by inverse square With positive test charge: -If the source charge is positive, test charge experiences repulsive force and goes away from source (vectors radiate out) -If source charge is negative, test charge attracted (electric field vectors toward charge) *For a pair of charges, negative electrostatic forces go from one point to another (attractive), positive electrostatic force points from one charge away from the other (repulsive) Field lines represent electric field vectors (imaginary lines that represent how positive test charge would move)-> point away from positive, and towards negative -Denser field lines = stronger field -Lines never cross E field and electrostatic forces are vectors If test charge is positive, force in same direction as e filed vector of source charge If test charge (q) is negative, forces will be in opposite direction to field vector of Q

Error Sources

Experimental bias: Usually minimal, experimenter's personal opinions end result in faulty hypothesis from incomplete early data and research collection Instrument error may effect may effect accuracy, precision, or both Accuracy = Validity: Ability of an instrument to measure the true value (scale should say that a 170 lb person weighs 170 lbs) (can be wide range if average comes out to actual number, like 150 and 190 lbs) Precision = Reliability : Ability of instrument to read consistency, or within narrow range (129-131 lbs, narrow range, but not precise because the person actually weighs 170) Bias is a systematic error in data (only an inaccurate/ not valid tool will cause bias, but imprecise tool will still induce error) Random chance can introduce error Random error is hard to avoid, but can be limited with really large sample size

A block weighing 100N is pushed up a frictionless incline over a distance of 20 m to a height of 10 m Find: Minimum force required to push block Work done by the force Force required and the work done by the force if the block were lifted vertically 10 m

First draw free body diagram (in image shown) Gravity is always going straight down (Fg) and normal force is always perpendicular to surface (N). The block isn't floating, so I guess they equal eachother Then, you have the force of you pushing, with arrow going up the plane You are trying to push the block parallel to the incline plane, so the magnitude of applied force is equal to parallel component of gravity: F = mg* sin (theta) mg = weight, which is given in Newtons (100N) sin theta is opposite over hypotenuse, which = 10 / 20 here, so F = 100N * 10/20 = 50N Now, find the work You have distance, so use W = Fd cos theta W = 50N * 20m * cos (theta) theta here is 0 because there is no angle between you force and the surface (they are parallel), and cos (0) = 1 So, Work = 1000 J Now, if you just raised the block straight up, the amount of work it takes will still be 1000J BUT when you do W = Fd cos theta, you are lifting the object 10 meters straight up instead of 20 along an incline place (think of now having sin (90) = 1) so force = 100 N (You have to lift it all by yourself) W = Fd cos theta = 100N * 10m * 1 = 1000J still, but twice the force is needed to raise the block vertically compared to pushing it up the incline

An object is 15 cm to the left of a thin DIVERGING lens with a 45 cm focal length. Find where image is formed, if it is upright or inverted, real or virtual, radius of curvature (assuming lens is symmetrical and made of glass with non-negligible thickness and index of refraction = 1.50 )

First, it is diverging, so mirror or lens, you know focal length will be negative 45 -> -45 Now set up 1/f = 1/i+1/o 1/i = 1/-45 - 1/15 -> 1/-45 - 3/45 = -4/45 Now invert: -45/4 = -11.25 cm (image is negative = on same side, virtual, not inverted) (virtual images from single lens are never inverted) Radius of curvature: 1/f = (n-1)(1/r1 - 1/r2) Symmetrical = radii are = and opposite As light goes from left to right, r1 is concave (r1<0) and r2 is convex (r>0) 1/f = (n-1)(-2/r) r= -2f (n-1) r = -2 (-45) (1.5-1) = 45 cm

Strings

Fixed/ immobile at both ends = nodes where λ = wavelength of standing wave, L is length of string, n is positive nonzero integer called the harmonic = number of half-wavelength Remember: frequency (f) = v/λ, so f = nv/2L Only one antinode between the two nodes at the end, so the length of the sting = 1/2 the length of the wavelength of standing wave (wavelength = 2L, because a wavelength goes from peak to valley to peak, and there is only 1 peak here) If there are 2 antinodes in between the 2 nodes on the end, there must be a third node in between antinodes. Here, the length = wavelength Pattern: Length (L) of string = multiple of half-wavelengths (node to node with one antinode in between = half wavelength ) L = λ/2, 2λ/2, 3λ/2..... λ = 2L/n The lowest frequency (longest wavelength) is known as fundamental frequency (first harmonic) When n = 2 -> first overtone / second harmonic (1/2 the wavelength and twice the frequency as first harmonic) n=3 -> third harmonic = second overtone * Number of antinodes will tell you what harmonic it is *Harmonic given by number of half-wavelengths in a string All possible frequencies that sting can support make up the harmonic series *# of antinodes + 1 = # of nodes

Sign conventions for lenses

For both lenses and mirrors, positive m = upright image and -m = inverted image For both, positive image distance means image is real (located on real (R) side) whereas negative distance means the image is virtual The difference is, for mirrors and lenses, the "Real" sides (where light actually goes) are opposite -For mirrors, the real side is where light is reflected back, so its on the same side as the object (in front of mirror) -For lenses, they don't actually reflect light, so the real side is on the other side of the lens (light is reflected through) (virtual side is on the same side as the light source) BUT just because the object of a single lens is on the virtual side does not make it virtual (objects are real, with positive distance) For both mirrors and lenses, focal length and radii of curvature relationships are same Converging species have positive focal lengths have radii of curvature (Concave mirrors and convex lenses) Diverging species have both negative (Convex mirrors and concave lenses) *remember, lenses have to focal lengths and two radii of curvature *For thin lens, where thickness is negligible, the sign of focal length and radii of curvature are given based on first surface the light passes through

Pressure

Force per unit area P = F/A Pnet = Fnet/A where P=pressure, F = magnitude of normal force vector, and A is area Measured in pascal (Pa) = newton per square meter (a N/m^2) *If pressure decreases 1 percent and area does not change, the force will be decreased by 1 percent *You can also use millimeters of mercury (mmHg) or torr (which are each to each other) or atm 1.013X10^5 Pa = 760 mmHg = 760 torr = 1 atm Pressure is scalar quantity (magnitude but no direction)(scalar because pressure applied same to all points in container) *BUT when unequal pressures are exerted against objects, forces acting will add in vectors (force is a vector) , possibly result in acceleration (when gravity is present this also results in pressure differential)

Circular Motion

Forces cause an object to move in a circular pathway *after cycle, displacement = 0 *nonuniform circular motion (speed of object not constant) is possible, but MCAT focuses on uniform Uniform Circular motion: Instantaneous velocity vector is always tangent to circular path *Object moving in circle has tendency (inertia) to break out of its circular path a move in line *It is kept from doing so by centripetal force (always points radially inward) *Only force is centripetal force *In uniform circular motion, tangential force is zero because there is no change in speed of object

Electromagnetic Spectrum

From longest wavelength / lowest energy / Lowest frequency: Long radio waves, AM radio waves, FM radio waves, Microwaves, Infrared, Visible light spectrum (red to violet), ultraviolet, X-rays, gamma (y) rays Frequency goes from 300 kilohertz (smallest frequency = radio waves) to 3X10^21 Hz (biggest = gamma rays) If a light ray has a frequency of 5.0X10^14, wavelength = c/f = 3X10^8 / 5.0X10^14 = 6X10^-7 meters (600 nm), so its within visual light spectrum Visible light spectrum from 400-700 nm, full spectrum goes from about 10^-16 meters to 10^8 meters Can be measured in mm (10^-3 m), micrometers (10^-6), nm (10^-9) and A (angstrom, A with little circle over it = 10^-10 m) Violet has the shortest wavelength (around 400) and red has the highest (around 700) Lowest Energy/frequency = highest wavelength Light that contains all colors in equal intensity = white The color of an object that does not omit its own light is dependent on the color of light that it reflects Object that appears red is one that absorbs all colors except for red (it reflects red) -So, a red object under green illumination will appear black because it absorbs green light and has no red light to reflect Blackbody: ideal absorber of all wavelengths, which would appear completely black (if at lower temp than surroundings) *Ultraviolet light is more likely to induce a current in a metal than visible light. This is because photons of ultraviolet light have a higher energy

Nuclear Reactions

Fusion, fission radioactive decay Involve combining or splitting nuclei Binding energy greater for intermediate sized atoms because they are most stable When small atoms combine or large atoms split, greater amount of energy released *Binding energy is amount of energy needed to get protons and neutrons together (energy released when nucleus is formed)(stable), and also = energy released when we break up nucleus -> more stable state, it takes more energy to break them up "For heavy or massive nuclei, the positively charged nucelons (protons) on opposite sides of the nucleus are repelling each by electrostatic repulsion, and the strong nuclear force is very weak at these distances. So average binding is weak. Only for medium sized nuclei is each nucleon fully within range of all its fellow nucleons' strong force, and there are a lot of them. So average binding is strong for these nuclei" Isotopic Notation: mass number over atomic number before element Atomic number (Z) = number of protons in nucleus Mass number (A) = number of protons + neutrons

Exponents

If the base is the same, for addition, b^n + b^n = 2b^n -If they have different bases, don't try and add Multiplication and division with same base: X^A * X^B = X^(A+B) X^A / X^B = X^(A-B) For a number that is raised to an exponent and then raised to another, the two exponents are multiplied (X^A)^B = X^(A*B) When a fraction is raised to an exponent, both are raised (X/Y)^A = X^A / Y^A Negative exponents are inverse functions: X^-A = 1/ X^A For fractional exponents, numerator can be treated like exponent and denominator represents root of the number: X^A/B = Bsqrrt (X^A) sqrrt of 4.9X10^7 -> sqr rt of 49X10^8 = 7X10^4

Open Pipes

If the end of a pipe is open it will support antinode If the end of a pipe is closed, it will support node One need must be open for air, but if this end is covered by a musicians moth (for example), it becomes closed end Open pipes are open at both ends (flute), closed pipes are only open at one (like clarinet and brass) Open pipe has antinodes at both ends, one node in the middle, so Length = λ/2 (similar to string) For open pipes: Number of nodes tells what harmonic it is = number of half wavelengths Second harmonic (first overtone L = λ) -> 2 half wavelengths = one full wavelength Third harmonic (3 nodes)(3 half wavelength) = second overtone -> L = 3λ/2 Image shown is first, second, and third harmonics f = nv/2L where n = number of half wavelengths λ = 2L/n

Pressure and Volume (related to work)

Imagine contained cylinder with moveable piston When gas expands, it pushes piston, exerting force that moves piston up and increases volume (work done BY the gas, work is positive) When gas compressed, piston moves down on gas, exerting force that decreases volume (Work done ON the gas, work is negative) Work has been done when volume has changed due to applied pressure Pressure-Volume (P-V) curves: Work done determined by area enclosed on graph (image shown) *If volume stays constant, delta V = 0, then no work is done because there is no change in area (shown in image A): this is called Isovolumetric / isochoric process *If volume changes but pressure remains constant (Delta P = 0), then the area under curve is rectangle (image B): Isobaric processes Work can be calculated using: W = PΔV For C), neither pressure or volume held constant, so find area by saying area 1 (triangle) = 1/2 ΔVΔP and area 2 (rectangle) = PΔV, then add them up *Area of triangle + area of rectangle = Work D shows closed cycle where system returns to initial state (don't need to know how to calculate area) *Different path require different amounts of work

Infrared (IR) Spectroscopy and UV-Vis spectroscopy

Infrared (IR) Spectroscopy: Determine chemical structure because different bonds absorb different wavelengths of light UV-Vis spectroscopy : Looks at absorption of light in visible and UV range Absorption spectra: color bar with peal areas of absorption shown with black lines The sky is blue because blue light is least absorbed by atmospheric gases Changes in molecular structure shift absorption patterns We see colors that are NOT absorbed -Most indicators, like phenolphthalein, have different absorption patterns (appear different colors) at different protonation states (no color in acidic state, pink in basic state = absorbs all but longer wavelengths) Conjugated double bonds and Aromatic rings allow absorption in visible range The energy difference between ground-state e- and higher level e- orbits determines frequencies that material absorbs (absorption spectrum)

Dielectric Materials

Insulation Air, glass, plastic, ceramic, certain metal oxides When introduced between plates of capacitor, it increases capacitance by a factor of k (dielectric constant) Vacuum has k = 1, air slightly above 1, glass is 4.7, rubber is 7 C' = kC where C' is new capacitance with dielectric present and C is original capacitance -k can never be less than 1, and dielectric material can never decrease capacitance Add this into equation for parallel plate capacitance, and we get "CAKED" C = Akε0/d Dielectrics in isolated charged capacitors (disconnected from circuit): Voltage across capacitor decreases because dielectric shields opposite charges from each other (lowering voltage increase capacitance by k) *Introducing k increases C and decreases V (Because C = Q/V) Dielectrics in charged circuit capacitors (connected to voltage): Capacitor increases (increases amount of charge stored by k), voltage remains constant -Only useful if it is allowed to discharge Lightening: Very large amount of charge exceeds capacitance of surface and cloud (Cloud and ground serve as parallel plate capacitor)> Rapid discharge across plates = failure of capacitor, while creating current through wire would be normal function

Insulators and Conductors

Insulator will not easily distribute charge over its surface/ transfer charge -Electrons tend to be closely linked with nuclei -Most nonmetals -Serve as dielectric materials in capacitors or prevent grounding Conductor: Distributes charge evenly -> transfers and transports charge

Internal and External Validity (Generalizability)

Internal Validity: Support for causality -> tendency of the same experiment to produce the same results when repeated (supports causality) External validity = Generalizability (ability to take generated information and apply it to larger group) Low generalizability = narrow sample conditions, don't represent target population High generalizability = representative of target population

FINER Method Questions

Is it going to be feasible? Do other scientists find it interesting? Is this particular question novel? Would the study obey ethical principles? Is the question relevant outside the scientific community?

Water flows from a pipe of diameter 0.15 m into one of diameter 0.2 m. If the speed in the 0.15 m pipe is 8 m/s, what is the speed in the 0.2 m pipe?

It is known that water flows faster through a narrower pipe. The speed is inversely proportional to the cross-sectional area of the pipe because the same volume of water must pass by each point at each time interval. Let A be the 0.15 m pipe and B the 0.20 m pipe, and use the continuity equation: νA*AA = νB*AB where ν is the speed and A is the cross-sectional area of the pipe. Because ν is inversely proportional to the cross-sectional area, and the area is proportional to the square of the diameter A = pi*r^2 = pi*d^2 /4 we obtain the following: Vb = Va (dA / dB)^2 Vb = 8* (.15/.2)^2 = about 4.5 Choice (B) most closely matches our result and is thus the correct answer.

A moving negative charge placed in an external magnetic field circulates counterclockwise in the plane of the paper as shown. In which direction is the magnetic field pointing? A. Into the page B. Out of the page C. Toward the center of the circle D. Tangent to the circle

Left Hand: Thumb left, middle finger down, index finger out of page (towards you) Lets say we are looking at negative charge at 12 oclock. The tangent line at that point has velocity to the left (so thumb goes to left) If you use your right hand, thumb is left, back of hand is down (opposite of middle finger, because charge is negative, so back of hand represents force towards the center of the circle) -The magnetic force must always point radially toward the center of the circle. Index finger (magnetic field) pointing towards you now, out of page B. Out of page This problem is an application of the right-hand rule. The velocity vector v is always tangent to the circle. The magnetic force must always point radially toward the center of the circle. Use the point labeled in the diagram to set up the right-hand rule. Your thumb points up the page, tangent to the circle at this point. The back of your hand, which represents the force on a negative charge, points to the left, radially toward the center of the circle. Your fingers must point out of the page to get your hand into this position. Therefore, the direction of the magnetic field must be out of the page.

Lenses

Lenses refract light and mirrors reflect it Lenses: 2 surfaces that affect light path Light is refracted twice as it passes from air to lens and then from lens back to air MCAT lenses generally have negligible thickness Light can travel from either side of a lens Lens has two focal points, one on each side (can be measured in either direction from center) Thin spherical lens: -For a thin spherical lens, the focal lengths are equal, so we only talk about one For lenses (and also mirrors): 1/f = 1/i + 1/o magnification (m) = -i/o Image: A (top) = converging lenses Image B (bottom) = concave (diverging) lensesTo find where lens image is, find where the rays intersect (marks the tip of the image) -If they don't intersect, extend to other side (virtual image) -If ray is parallel to axis = refracts through focal point of front face of lens -If ray is through or toward focal point before reaching lens, it refracts parallel -If ray to center of lens, it continues straight with no refraction

Mass and Weight

Mass (m) is a measure of a body's inertia/the amount of matter in the object -Scalar quantity (magnitude only) -SI unit = kilogram (independent of gravity: 1kg on earth will have the same mass as 1 kg on the moon) -Weight (Fg): measure of gravitational force on an object mass (Force = vector quantity with units in newtons (N)) Fg = m*g where Fg = weight, m= mass, and g is acceleration due to gravity (9.8 m/s^2) -Applied to single point on object called center of mass/gravity (located at geometric center) (only actually located in center for object with homogenous body (symmetrical shape and uniform density) For a system in which particles are distributed in all three dimensions, the center of mass is defined by the three coordinates (x, y, z): x = m1x1 + m2x2 +m3x3..... / m1+m2+m3...... y = m1y1 + m2y2 +m3y3..... / m1+m2+m3...... z = m1z1 + m2z2 +m3z3..... / m1+m2+m3......

Conductivity (metallic and Electrolytic)

Metallic conductivity: Seen in metals and some salts -Metal have lowest ionization energies, so it is really easy for them to lose electrons. Because of this weak hold to electrons, the electrons are free to move around, conducting electrical charge -Relies on uniform movement of freee electrons Electrolytic conductivity: Seen in solutions, depends on strength of the solution (relies on ion concentration) -Measured by placing solution as resistor in a circuit and measuring changes in voltage across the solution -Concentration and conductivity are directly related -Conductivity in nonionic solution is ALWAYS lower than in ionic solution Conductance is the reciprocal of resistance (measured in Siemens (S), S/m (Siemens / meter) for conductivity

Meters: Ammeters, Voltmeters, and Ohmmeters

Meters: Devices that are used to measure circuit quantities in real world Ammeters: Measure current at pointing circuit (circuit must be on, or current = 0) -Must have low /0 resistance and no voltage drop or it will mess up circuit readings -Inserted into series Voltmeters: Use magnetic properties of current carrying wires, used to measure voltage (potential difference) drop across 2 points in a circuit (wired in parallel) (also requires circuit to be on) (Ideally has infinite resistance) Ohmmeters: Circuit doesn't need to be on, used to calculate resistance using ohmmeters voltage and circuits current -Ideally resistance is 0 -Placed at 2 points in series with circuit element of interest Voltmeters and ammeters are designed to have minimum impact on a circuit, so they can be used together Both ammeters and ohmmeters have negligible resistance Ideal voltmeters have infinite resistance, and ideal ammeters have no resistance.

Standard Deviation (σ)

Most informative measure of distribution Take the difference between each data point and the mean, squaring the value, dividing the sum of the squared values by the number of points in the data set -1, and then taking the square root of all that *Note: when calculating mean we use n in denominator, but for σ we use n-1 Can be used to determine outlier: If data point lies ore than 3 standard deviations away from mean, it is outlier (in normal distribution, 99% of data falls within 3 SD (68% within 1, 95% within 2) Range = 4 X σ (only use when you can't calculate σ)

Data Analysis (Experimental Approach)

Must account for variables outside of independent and dependent (including gender, age, lifestyle, BMI,.... = confounding variables) Variables used to create regression models: Binary: Yes/no questions, better/worse Continuous: amount of weight lost, % improvement.... Categorical: state of residence, socioeconomic status Regression analysis may demonstrate different mathematical relationships Research methods that generate non-numerical data are qualitative Research methods that generate numerical data are quantitative

Probability 10% of population has diabetes and 30% is obese. If 7% has both diabetes and is obese, are the events independent? If individual chosen at random, what is probability that patient having at least one of the two conditions ? In 10 births, what is the probability of having at least 1 boy?

Mutually exclusive outcomes cannot occur at the same time (The probability of 2 mutually exclusive events occurring together is 0) Exhaustive outcome: There are no other possible outcomes (flipping heads or tails = exhaustive outcome because there are only 2 options) For independent events, the probability of 2 or more events occurring at the same time is the product of their probabilities alone (Coin toss: Probability of getting head two times in a row is 1/2 X 1/2 = 0.25) Probability of at least one of two events occurring = symptoms of initial probabilities - the probability that both will occur When you see the term: And: multiply the probabilities Or: Add the probabilities (and subtract the probability of both happening together) Answer: If the events were independent, the likelihood of being obese and having diabetes would be 0.3X0.1 = 0.03, but it is actually 0.07, so the events are not independent *independent means they have no effect on each other Determine probability ("or" situation) 0.3+0.1 - 0.07 = 0.33 = 33% In 10 births, what is the probability of having at least 1 boy? (Mutually exclusive) Think of this as, what is the probability of not having all girls Having all girls = (0.5)^10, and probability of having at least 1 boy = 1- (0.5)^10 = 99.90%

Resonance

Natural frequencies = resonant frequencies If natural frequency is within frequency detection range of human ear, the sound is audible Quality of sound = timbre (determined by natural frequency/frequencies) Single frequency = pure tone Multiple frequencies have no relation to each other (noise, not music) BUT if you have multiple frequencies that are related by whole ratios (fundamental pitch / multiple overtones) we get a richer, more full tone (musical) 20-200 HZ are generally audible to humans, high frequency hearing declines with age You can easily change natural frequency Strings have infinite number of natural frequencies that depend on length, linear density, and tension Forced oscillation: Periodically varying force applied to system, and system will then be driven at frequency = to frequency of force If the frequency of the applied force is close to natural frequency, you will have a larger amplitude of oscillation (force frequency = natural frequency -> resonating (amplitude is at maximum) -If there was no friction, the amplitude would increase indefinitely BUT no system is completely frictionless, so you get damping or attenuation (decrease in amplitude caused by applied or nonconservative force -Maximum amplitude can be bad -> glass shattering

Motion with constant acceleration

Object can undergo two types of motion: Constant (no acceleration) or changing velocity (with acceleration) Acceleration can be constant or changing, but MCAT focusing on constant Linear motion: -Falling objects exhibit linear motion with constant acceleration -Velocity and acceleration vectors are parallel or antiparallel Equations: v= v0 + at x = v0t + at^2/2 v^2 = v0^2 + 2ax x = v(with line over it)*t where x v and a are displacement (when motion is vertical use y instead), velocity, and acceleration vectors v0 is initial velocity v with line over it = average time With free fall problems, air resistance is assumed negligible so object falls with constant acceleration of gravity (9.8 m/s^2) (Will not reach terminal velocity) -This is called free fall *The only force acting on both free fall and projectile motion is gravity If air resistance is NOT negligible , it opposes motion of object (increases as speed of object increases) -Object in free fall experiences growing drag force as magnitude of velocity increases, eventually = in magnitude to weight of object, and then object falls with constant velocity (first law) = terminal velocity

Displacement

Object in motion may experience change in position in space (displacement = x or d) -Vector Quantity: Magnitude and direction Connects initial position to final position (shows net change, not actual path taken) (Distance (d) consider the path taken and is a scalar quantity) If they end up in the same place they started, displacement is 0

In a double slit experiment, what is the linear distance (y) between the 6th and 8th minima on the screen? Wavelength = 550 nm Slits serrated by 0.14 mm (=d), and screen = 70 cm (=D) from slit

Position of dark fringe (minimum) = d sin θ = (n+1/2) * wavelength We don't know sin ,θ but for small angles sin θ is about = to tan θ because the hypotenuse and adjacent side are close in length. Tan θ = y / D (70 cm) d (y/D) = (n+1/2) * wavelength y =( (n+1/2) * wavelength* D )/ d n = 8-6 =2 y8-y6 = ( (n8+1/2) * wavelength* D )/ d - ( (n6+1/2) * wavelength* D )/ d 1/2 subtracts out Δy = Δn * wavelength * D / d 2*(550X10^-9m) (0.7 m)/ 0.14X10^-3 m = 5.5 mm

Potential Energy (U)

Potential Energy: Associated with object's position in space (intrinsic qualities) *Can be chemical, electrical, etc *Potential energy dissipated as movement: Gravitational and elastic potential energy Gravitational Potential Energy: *Depends on objects position with respect to datum (Zero potential energy position or "ground", usually chosen for you) U = mgh where U is potential energy in joules, m is mass in kilograms, g is the acceleration due to gravity, h is height above datum *Direct relationship to all variable (3X height causes increase in gravitational potential energy by actor of 3) Elastic Potential Energy: *Think of springs: when it is stretched or compressed from equilibrium length is has elastic potential energy U = 1/2 kx^2 where k is spring constant (measure of stiffness) and x is magnitude of displacement from equilibrium *nearly conservative Electrical potential energy exists between charged particles Chemical potential energy is the energy stored in the bonds of compounds

Measuring Power

Power is the rate the energy is transferred/transformed -Measured as ratio of work (energy expenditure) to time P = W/t = ΔE/t -Energy supplied by cell that houses a spontaneous oxidation-reduction reaction which generates flow of electrons when switch is closed -Current delivers energy to various resistors The rate at which energy is dissipated from resistor: P= IV = I^2R = V^2/R (All related to Ohm's Law V= IR *High voltage power lines carry smaller current, so less energy is lost from system (High current = high energy loss)

Measurements of Distribution

Range: An absolute measure of the spread of a data set, while interquartile range and standard deviation provide more information about the distance that data falls from one of the measures of central tendency -Use to determine if something is an outlier -Range: Difference between its largest and smallest values Range = x max - x min -Heavily effected by outliers, but number of data points don't matter -When you can't calculate standard deviation, 1/4 of the range can be used as estimate Interquartile range: Related to median (2nd quartile), and 1st and 3rd quartiles -Divide data sets into 4 parts with each having 1/4 of entire set To find 1st quartile range: Sort in ascending order, multiply n by 1/4 (if this is a whole number, then Q1 = mean of this number and next number up) -If it is a decimal, round UP to the next whole number To find 3rd Quartile range, multiply n by 3/4 and repeat Interquartile range (IQR) = Q3 - Q1 Can be used to find outliers: any value more than 1.5X interquartile range above or below = outlier *1.5 X IQR below Q1 or 1.5X IQR above Q3

Pulleys

Reduces necessary force at the cost of increased distance to achieve given value of work/energy transference Applying a smaller force over a greater distance If a block is hanging in translational equilibrium from 2 ropes, the tension in each rope is equal to half the weight of the block Each rope supports 1/2 of blocks weight (load), so only 1/2 the force (effort) is required to lift crate -But, mechanical advantage comes at the expense of distance. To lift object certain height in air (load distance), must pull through a length of rope (effort distance) equal to twice that displacement -If you want to lift something 3m, both sides of supporting rope must shorten by 3 meters, so you actually have to pull 6 meters of rope *LOAD AND EFFORT ARE BOTH FORCES. The load determines the necessary output force. From the output force and mechanical advantage, we can find input force We approximate simple machines to be conservative systems by ignoring small amount of energy lost due to external forces like friction Real pulleys dont achieve 100% efficiency (idealized pulleys have no mass or friction, and work that goes in = work that comes out) Work Input = product of effort and effort distance Work output = product of load and load distance Efficiency = Work output / Work input = (load*load distance)/(effort*effort distance) Efficiency of a machine gives the amount of useful work generated by machine for a given amount of work put into system *Percent of work put in that becomes unusable is due to nonconservative or external forces For each additional pair of pulleys added, effort is reduced *If effort is divided among 6 lengths of rope (6 pulleys), effort required is 1/6 of total load (increasing number fo pulleys decreases the tension in each segment of rope = increase in mechanical advantage), but we would need to pull the length of rope 6X the desired displacement, and efficiency will decrease due to added weight of each pulley and frictional forces

Geometrical Optics: Reflection

Reflection is the rebounding of incident light waves at the boundary of a medium Reflected light waves are not absorbed into the second medium, they bounce off and go back through the first medium Image is reflection on a plane mirror The Law of reflection: The incident angle will equal the angle of reflection as measured from normal θ1 = θ2 where θ1 is the incident angle and θ2 is the reflected angle (both measured from normal) Normal line drawn perpendicular to boundary of medium (all angles measured from normal, not from surface) Images from mirrors can be real (light actually converges at the position of image) or virtual (light only appears to come from the position of the image but does not actually converge there) *Real images can be projected onto screen

Reflection VS Refraction VS Diffraction

Reflection: angle of incoming light is same as angle of reflected light, allows us to see objects (mirrors) Refraction: the bending/change of speed when light encounters a different medium (lenses) Diffraction: light passes through slit and bends slightly around the edges

Snell's Law Light will bend ____________ normal when going from low n to high n Light will bend ______________ normal when going from high n to low n

Related to refraction, n=c/v, so n₁sinθ₁=n₂sinθ₂, where n is index of refraction, c is speed of light, and v is speed of light in vacuum, and n1 and θ₁ refer to medium from which light is coming and n2 and θ2 refer to medium light is going in to. θ measured with respect to normal When light enters a medium with a higher index of refraction, it bends towards the normal (sinθ2 < sinθ₁, so θ2<θ₁) (going from air into water bends towards normal) When light enters medium with lower index of refraction, it bends away from normal Light will bend toward normal when going from low n to high n Light will bend _away from normal when going from high n to low n If incident angle is large than critical angle, total internal reflection will occur *When changing mediums, frequency stays the same, but wavelength changes. Going into higher index of refraction, wavelength slows

Populations and Parameters VS Samples and Statistics

Research uses sample rather than entire population: Population: Complete group of every individual that satisfies attributes of interest Information that is calculated using every person in population = parameter Generalizations about population based on sample data Sample: Any group taken from population that does not include all individuals in population -> should be representative of population -Use random samples -information from sample called statistic -> can be used to estimate parameters

Belmont Report (1979): 3 pillars of research ethics *Inspired by Tuskegee Experiment RJB

Respect,Justice, Beneficence Respect for persons: Honesty between subject and researcher -Informed consent -No coercive influence (Children, pregnant women, and prisoners are considered especially at risk for coercion) -Ability to cease participation -Institutional review boards put in place systematic protections against unethical studies -Confidentiality Justice: Applies to selection of topic and execution of research -Morally relevant differences: Not everyone should be treated exactly the same (age) -Not morally relevant: Race, ethnicity, sexual orientation, financial status (you should not treat people differently because of these) -Justice increases external validity through increasing diversity -Violation of justice: Choosing study participants that are not part of target population More inclusive version of beneficence Maximize good, minimize bad: do things int he least painful way possible -Equipoise: One can't approach research with knowledge that one treatment is superior to another -> providing an inferior treatment= harm

Absorption and Emission of Light

Review: Bohr model says that electron energy levels are stable and discrete, corresponding to specific orbits -Electron can jump from low to higher energy orbit by absorbing photon at frequency to match energy difference between orbits (E = hf) -If photon does not carry enough energy, it does not jump -When electron falls, photon of light is emitted with energy = energy difference between two orbits -> process of atomic absorption and emission

Rotational Equilibrium

Rotational motion = forces applied against object that cause it to rate around fixed point (pivot) called the fulcrum *Applying force some distance from the fulcrum generates torque (t)(Moment of force) -Torque (measured in N*m) generates rotational motion (primary motivator for rotational movement that combines force, lever arm, and angle between), depends on the force and length of the lever arm and angle at which force is applied T = r X F = rFsin(theta) where r is length of lever arm, F is magnitude of force, and theta is angle between the lever arm and force vectors *Occurs in the absence of net torques *Constant angular velocity (usually 0 on MCAT) sin90 =1 , so torque is greatest when force is applied 90 degrees (Perpendicular) to lever arm sin0 = 0 so there is no torque when force applied parallel to lever arm Rotational Equilibrium exists only when vector sum of all torques = 0 (second condition of equilibrium) Torque clockwise = negative, counterclockwise = positive *either the object is not moving at all (more common) or object rotating with constant angular velocity

Sinusoidal transverse and longitudinal waves

Sinusoidal waves have individual particles that oscillate back and froth with a displacement that follows a sinusoidal pattern Transverse waves: direction of particle oscillation is perpendicular to propagation (movement) of wave -Electromagnetic waves (x-rays, microwaves, visible light) -Energy is delivered in the direction of wave travel, so for transverse wave, the particles are oscillating perpendicular to the direction of energy transfer -Longitudinal waves have particle oscillation parallel to the direction of propagation and energy transfer -Sound waves -Oscillates through cycles of compression and rarefaction (decompression)

Attenuation (Damping)

Sound is not transmitted undiminished. Even after taking decrease in intensity associated with distance into account, real world measurements of sound are always lower than calculations predict This is because oscillations still are moving and still impacted by nonconservative forces, like friction and resistance Causes decrease in amplitude during each oscillation = gradual loss in sound Does not effect frequency, so pitch doesn't change This is why its harder to hear in cluttered space (friction from surfaces) Usually negligible in short distance

Shock Wave

Special case of Doppler effect Object producing sound while going above speed of sound allows wave fronts to built on top of eachotehr at the front of object Creates much larger amplitude (related to degree of compression of media = large pressure differential/pressure gradient) Highly condensed wave front = shock wave -Very high pressure followed by very low pressure = sonic boom -Can be heard ANY time object going faster than speed of sound, not just at the point when the speed of sound is passed (Mach 1) Shock waves have the greatest impact when the source is traveling exactly at the speed of sound. Shock waves are the buildup of wave fronts as the distance between those wave fronts decreases. This occurs maximally when an object is traveling at exactly the same speed as the wave is traveling (the speed of sound). Once an object moves faster than the speed of sound, some of the effects of the shock wave are mitigated because all of the wave fronts will trail behind the object, destructively interfering with each other.

Spherical Aberration (errors)

Spherical mirrors and lenses are never perfect Blurring of the periphery of an image from inadequate reflection of parallel beams at the edge of a mirror -Parallel rays aren't perfectly reflected or refracted through the focal point, leading to blurriness at periphery Chromatic aberration is predominately seen in spherical mirrors: dispersive effect (leads to rainbow halo at the edge of image) Dispersion: When various wavelengths of light separate from each other (splitting white light into colors using prism) -Violet light = smallest wavelength, so it is bent more (greatest amount of refraction = on the bottom). Red light experiences least refraction because it has longest wavelength As light enters a medium with different angle of refraction, the wavelength changes but the frequency of the light does not Dispersion is the tendency for different wavelengths of light to experience different degrees of refraction, leading to separation of light into visible spectrum Aberration (spherical or chromatic) is the the alteration or distortion of image as result of an imperfection in the optical system

Zeroth Law of Thermodynamics

States the transitive property of thermal systems: if a=b and b=c then a=c Id a is in thermal equilibrium with b, and b with c, then a and c are also in thermal equilibrium -> so when brought into thermal contact, no net heat will flow between objects -The systems A, B, and C are at the same temperature. -Does not imply physical contact necessarily systems that are in thermal equilibrium exist at the same temperature. Systems are in thermal equilibrium if they do not transfer heat, even though they are in a position to do so, based on other factors. For example, food that's been in the refrigerator overnight is in thermal equilibrium with the air in the refrigerator: heat no longer flows from one source (the food) to the other source (the air) or back. What the Zeroth Law of Thermodynamics means is that temperature is something worth measuring, because it indicates whether heat will move between objects. This will be true regardless of how the objects interact. Even if two objects don't touch, heat may still flow between them, such as by radiation (as from a heat lamp). However, according to the Zeroth Law of Thermodynamics, if the systems are in thermal equilibrium, no heat flow will take place. *So, heat DOES flow between objects NOT in thermal equilibrium

Statistical Significance vs. Clinical Effect

Statistical significance- are results due to random chance? -Refers to low likelihood of experimental findings being due to chance Clinical significance- are results clinically meaningful? Was there a notable or worthwhile change in health status as a result of our intervention Statistical significance does not imply clinical meaningfulness -Refers to usefulness or importance of experimental findings to patient care of patient outcomes

Fluorescence

Step-wise photon emission (each energy transition releases photon of light (Smaller energy transitions than initial energy absorbed = materials can release photons in visible range If you excite fluorescent substance (ruby, gems, phosphors in fluorescent lights) with UV radiation, it glows with visible light Photons of UV light have high frequency (short wavelengths) -After being excited to higher energy state by UV radiation, electron in fluorescent substance returns to original state in 2 or more steps (each step involves less energy, photon emitted with lower frequency/longer wavelength than absorbed UV photon. -If wavelength of emitted photon is within visible range, it will be seen as particular color -Multi-step emission plectra of different fluorescent materials = different color lights

Electron Capture

The atomic number becomes one less than the original, but the mass number remains the same. Electron capture is a relatively rare process -equation is similar to that of β+ decay but not identical because a particle is absorbed, not emitted. some unstable radionuclides (generic term for any radioactive isotope) can capture an inner (K or L shell) electron that can combine with a proton to form a neutron; releasing neutrino (reverse of B- decay) -Atomic number now one less, and mass number remains same -Rare process

Hydrostatics

The branch of science that treats of the pressure and equilibrium of fluids at rest. The study of fluids at rest and the forces and pressures associated with standing fluids Fluids: Characterized by ability to flow and conform to container shape (Both gases and liquids) Both fluids and solids can exert large forces perpendicular to their surface, but only solids can withstand shear (tangential) forces (parallel force between object and surface of object)

How do the following concepts relate to one another: Venturi effect, Bernoulli's equation, and continuity equation? What relationship does each describe?

The continuity equation describes the relationship of flow and cross-sectional areas in a tube, while Bernoulli's equation describes the relationship between height, pressure and flow. The Venturi effect is the direct relationship between cross-sectional area and pressure, and results from the combined relationships of the Bernoulli and continuity equations.

An electron with a speed of 3x10^5 cm/s moves in a northerly direction through a region of space containing a uniform electric field of strength 100 V/m, directed towards the east. Which of the following best describes the effect of the field on the motion of the electron?

The electron is deflected to the west and experiences an increase in speed. Negative charge in electric field feels force in opposite direction of field (Field points east, force towards west) -Think of the electric field as being positive Newton's second law: net force applied to body = body undergoes accretion in the same direction as the net force Acceleration associated with electric force will increase velocity in westward direction. Since electron did not already have a component of velocity in either west or east direction, this will have the effect of increasing total speed of electron

Mechanical Advantage (Simple Machines)

The factor by which a simple machine multiplies the input force to accomplish work Sloping inclines make things easier by distributing required work over larger distance, decreasing required force Something that allows smaller required input force = mechanical advantage : Ratio of magnitudes of force exerted on object by simple machine (F out) to the force applied on the simple machine (F in) *Mechanical advantage = F out / F in *Ratio, so it is dimensionless 6 simple machines designed to provide mechanical advantage: -Inclined plane -Wedge (2 merged incline planes) -Wheel and axle -Lever -Pulley -Screw (rotating inclined plane) *Distance through which smaller force is applied to do work must be increased *Because displacement is path independent, actual distance doesn't matter (assuming all forces are conservative) *So, applying a lesser force over a greater distance to achieve the same change in position (displacement) accomplishes the same amount of work

At a place where g= 9.8 m/s^2, an object is thrown vertically downward with a speed of 5 m/s while a different object is thrown vertically upward with a speed of 10 m/s Which object undergoes a greater change in speed in a time of 2 s?

The first object has a greater change in speed. Each object acceleration = 9.8 m/s^2, so object's velocity changes by 9.8 m/s each second 2 second period = 9.8X2 = 19.6 m/s change in velocity But we are looking at speed Object 1 has initial velocity of -5 m/s and ends with -24.6 m/s magnitude (absolute value) of |-24.6 |- |-5| = 19.6 m/s Second object starts with velocity of +10 m/s and ends with -9.6 m/s Taking magnitude (absolute value), we get |-9.6| - |10| = -0.4 m/s Therefore, the second object has a much smaller change in speed than the first. This is because the force acting on the object was the opposite direction from the object's motion in the initial conditions.

Single slit and double slit diffraction and interference

The image formed during double-slit diffraction contains fringes because light rays constructively and destructively interfere. -Both double slit and single slit use the equation d sin theta = (n+1/2)*wavelength (lambda) -sometimes seen as d sin theta = m*wavelength (lambda) For small angle values, sin theta = d * y/L = (n+1/2)*wavelength m can equal 0,1,2,3.... y is proportional to m -All of the bright fringes are about the same size initially (spots of fringes have same intensity/brightness) -Slits are a lot closer together because the bigger the d, the smaller the y (closer the fringes are together because y is difference from screen) *m= n+1/2 from MCAT equation? -So we get a set of even waves from the two slits, and then we get the pattern from each of the single slits interacting with each other A single slit forms an image of a wide band of light, spread out from original beam -We dark fringes when m is 1,2,3,4.... but not 0. At 0, we have the large bright fringe in the middle (central maxima that is twice as wide and a lot brighter) -Doens't have little slits/dots that are present from double slit

Nuclear binding energy and mass defect

The mass of the nucleus is actually slightly smaller (excluding hydrogen) than the mass of protons + neutrons -> the difference in mass is called mass defect Explained by Einstein's E = mc^2 where E is energy, m is mass, and c is speed of light Mass defect is result of matter that has been converted to energy during nuclear fusion -Apparent loss of mass when nucleons come together as some of the mass is converted into binding energy -Very small amount of mass will yield VERY large amount of energy (1 gram of mass will yield 89.9X1012 J or 21.5 kilocalories of energy) Protons and neutrons (nucleons) come together to form nucleus -> attracted to each other through strong nuclear force (stronger than repulsive electromagnetic force between protons)(Strongest of the 4 fundamental forces (Strong and weak nuclear forces, electrostatic forces, and gravitation), but acts only over really short distances) -Unbonded = more energy = more mass -Bonded system is at lower energy level than unbounded constituents (difference in energy must be radiated away in form of heat, light, electromagnetic radiation, etc) before mass defect becomes apparent -This BINDING ENEGRY allows nucleons (protons and neutrons) to bind together in nucleus -Amount of mass transformed into energy is tiny fraction of initial total mass Binding energy per nucleon peaks at iron (iron contains most stable nucleus) *intermediate sized nuclei more stable than really large or really small Weak nuclear force contributes to stability of nuclear (only 1 millionth as strong as strong nuclear force)

At what angle of launch is projectile going to have the greatest horizontal displacement? What angle will result in the greatest vertical displacement, assuming level surface?

The product of sine and cosine is max at 45 deg angle Because horizontal displacement relies on both measurements, the max horizontal displacement will be achieved at this angle (45 degrees). Vertical displacement will always be 0 as the object returns to the starting point (objects launched vertically will experience the greatest vertical distance) *90 degrees or the highest angle will result in the greatest maximum height reached and the greatest time in the air.

Sound Level

The softest sound human can hear= 1X10^-12 W/m^2 VERY little mechanical disturbance (1 billionth of a centimeter) Intensity of sound at pain threshold = 10 W/m^2 1X10^4 W/m^2 causes instant perforation of eardrum Large range, so we use logarithmic scale, called the sound level (B) measured in decibels (dB) B = 10 log (I/I0) where I = intensity and I0 = threshold for hearing (1X10^-12 W/m^2)(used as reference intensity) When intensity of sound is changed by some factor, calculate new sound level using: Bf = Bi + 10 log (If/Ii) where If/Ii = ratio of final intensity to initial intensity Mostly deal with base-10 logarithms, like log 1000 = 3 because 10^3 = 1000 log 1 = 0 because 10^0 = 1

Electrostatics

The study of stationary charges and the forces that are created by and act on those charges -Gravity is always attractive force, but electrostatic forces can be attractive or repulsive depending on charge -Even stuff that is usually neutral can become charged via friction -Ground = means of returning charge to earth -More static electricity in drier air /lower humidity because charges can separate easier SI unit for charge = Coulomb (C) Fundamental unit if charge = e = 1.60X10^-19 C -Proton and electron both have this amount of charge (same magnitude), but proton has positive charge and electron has negative , and the proton has much larger mass

Vector Addition If V = 10m/s and theta = 30°, what are X and Y? What is the magnitude of the vector with X= 3 m/s and Y = 4 m/s?

The sum or difference is called the resultant of the vectors Add tip to tail (length of arrows must be proportional to the magnitudes of the vectors -The sum is the line going from tail of A to tip of B (or tip of last letter, may be C or D) Another method for finding resultant = breaking vectors into perpendicular components (x and y components) -Image shown X= V cos theta Y = V sin theta If V = 10m/s and theta = 30°, X = 10 * √3/2 = 5√3 m/s Y= 10* 1/2 = 5 m/s V = √x^2 + y^2 or V^2 = X^2 + Y^2 Angle of resultant vector can be found by theta = tan^-1 (Y/X) What is the magnitude of the vector with X= 3 m/s and Y = 4 m/s? = √3^2 + 4^2 = √25 = 5 m/s

A BASE jumper runs off a cliff with a speed of 3 m/s Which of the following is closest to his speed after 0.5 seconds?

This is a projectile motion question. The horizontal component of the jumper's velocity will remain 3 m/s throughout the jump. The vertical component of his velocity starts at 0 After 0.5 seconds, it will be: Vy = V0 + at Vy = (-9.8 m/s^2)(0.5s) = -4.9 m/s To get the overall velocity, consider the horizontal and vertical velocities using vector analysis and find the resultant. Doing so = sqr rt of 3^2 + 4.9^2 = sqr rt of 34 This magnitude (speed) is just a bit under 6

Observational Approach (three types of studies)

Three types: Cohort: Form of longitudinal study (follows the same subject over time) -> subjects sorted into different groups based on exposures and then followed to see if they end up with the outcome (following equal number of smokers and non-smokers for 20 years to see who develops more lung cancer) (better when exposure is rare) Cross-sectional: Single point in time: exposure and outcome ascertained together Case-control: Working backwards: start with outcome, work back to see if they had exposure (better when outcome is rare) Often look for connections between exposure and outcome -> but CANNOT demonstrate causality (but tendency toward casualty can be shown with Hill criteria)

Right Hand Rule

Thumb: Velocity (indicates direction of movement) Fingers/index finger: Field lines Palm/middle finger: Force on positive charge (back of hand = negative charge, or use left hand) -The magnetic force must always point radially toward the center of the circle

Half-life (T1/2)

Time it takes for half of the sample to decay Each half life: 1/2 of remaining sample decays so that remaining amount asymptomatically approaches 0 N(t) = N0 (1/2)^ (t/(T 1/2) N(t)= quantity of the substance remaining N0= initial quantity of the substance t= time elapsed T 1/2 = half life of the substance Portion remaining will never actually reach 0, but its usually considered decayed after 7 or 8 half lives

What are the requirements to have a nonzero electric field? A nonzero magnetic field? A nonzero magnetic force?

To create an electric field, you need a charge To create a magnetic field, you need a moving charge To create a magnetic force, you need an external electric field acting on a charge moving any direction except for parallel or antiparallel to the external field

Multiplying vectors by other vectors

To generate a scalar quantity like work, we Multiply magnitudes of 2 vectors (force and displacement) and cosine of angle between them (Called dot product: A*B) A*B = |A| |B| cos theta When generating third vector like torque, determine both magnitude and direction *Multiply magnitudes (force and lever arm) and the sin of the angle between *Then, use right hand tule to determine direction (called cross product) AXB = |A| |B| sin theta *Cross product always perpendicular to the plane created by vectors (Vector usually going into or out of page) Right Hand Rule: C = AXB 1. Hold hand flat and straight. Point thumb in direction of vector A 2. Extend fingers in direction of vector B 3. Palm of hand represents plane between the 2 vectors. Direction of palm = direction of resultant C OR: With your right-hand, point your index finger along vector a, and point your middle finger along vector b: the cross product goes in the direction of your thumb. *For cross products, order matter (unlike scalar multiplication, which is commutative, meaning 3X4 = 4X3)

A long straight wire carries a current directed towards the top of the page. A proton moves with velocity 2 x 10^4 cm/s towards the bottom of the page and to the left of the wire. The magnetic force on the proton is:

Towards the left Right hand rule: Curl right hand around wire, thumb points up (direction of current), fingers (field lines) come out of page to left of wire and go into page to the right of wire Magnetic force of proton: thumb points down, fingers point in direction of magnetic field Palm should face direction of force (which we found to be towards the left)

Translational Equilibrium

Translation: Motion through space without equilibrium Translational Equilibrium *If the vector sum of all forces on an object cancels out, the object experiences no acceleration Occurs when forces cause an object to move without any rotation *May be linear or parabolic *Can be solved using free body diagram and Newton's 3 laws *Occurs in absence of any net forces acting on an object. *Has constant velocity and may or may not also be in rotational equilibrium Equilibrium Conditions: Translational Equilibrium only exists when the vector sum of all of the forces acting on object is 0 (First condition of equilibrium (reiteration of Newtons 1st law) -> Resultant force is 0 = no acceleration (this could mean the object is stationary or at constant velocity) *If there is no acceleration, then there is no net force on the object. This means that any object with a constant velocity has no net force acting on it. However, just because net force = 0 does not mean velocity does *So, object experiencing translational equilibrium will have constant velocity; both a constant speed (0 or nonzero value) and constant direction A moving object can either be in translation or rotational equilibrium or both. Translation equilibrium only requires the net force = 0, the velocity is constant though. In rotational equilibrium the net torque is 0, and angular velocity is constant

Traveling and Standing Waves

Traveling (moving) Wave: string fixed at one end, wave will travel (propagate) toward the fixed end -When it reaches the fixed end, it is inverted and reflected back (the 2 waves (one going towards fixed end and one reflected back) interfere with each other Standing Wave: Both ends are fixed and traveling waves are excited in the string -> reflected waves match up and waveform appears to be stationary (only apparent string movement is fluctuation of amplitude at fixed points along string)(image shown) -Waves are still moving but they are reflected back and cancel each other out -Points where the waves is constantly 0 = nodes -Points midway between nodes where fluctuation is with maximum amplitudes = antinodes Pipes and strings can support standing waves

Heat of Transformation

When a substance is undergoing phase change, like solid to liquid, the heat added/removed doesn't cause change in temp (phase change occurs at constant temperature) *During a phase change, heat energy causes changes in particles potential energy and energy distribution (entropy) but not kinetic energy = no change in temperature *Temp won't change into all of the substance has been converted from one phase to another (No matter how much heat you add to ice, it won't raise temp from 0 deg C until all ice has melted) Adding heat raises temp by increasing average kinetic energy = more freedom to move But, phase change related to potential energy, no kinetic -Breaking hydrogen bonds = greater degrees of freedom of movement = greater number of MICROSTATES = increases potential energy (average kinetic energy is same as solid water at same temp) When heat energy is added or removed from system in phase change, use: q = mL where q = amount of heat gained or lost, m is mass, L is heat of transformation or latent heat of substance because you cant calculate temp change (there is none)

Estimating Logarithms Estimate log 7,426,135,420

When estimating the logarithm of a number, use scientific notation. If the value is written in proper scientific notation, it will be in the form of: n x 10^m. log (nX10^m) = log (n) + log (10^m) = m + log (n) Because n is a number between 1 and 10, its logarithm will be a decimal between 0 and 1 because (log 1 = 0 and log 10 =1). The closer n is to 1, the closer log n will be to 0. The closer n is to 10, the closer it will be to 1. TO estimate, just move the decimal of n so that: log (nX10^m) = log (n) + log (10^m) = m + log (n) = m + 0.n This is similar to calculating negative logarithms and negative exponents for pH -log ( n X 10^-m) = m - 0.n Estimate log 7,426,135,420 log (7.5 X 10^9) (count everything but the number in front of the decimal) log (7.5) + 9 -> 0.75 + 9 = about 9.75

A light ray of wavelength 600nm enters a piece of glass with index of refraction 1.5. Which of the following best describes the path of the emerging ray.

When light enters a medium with higher index of refraction it bends towards normal so that theta 2 < theta 1 Air: 1 and glass: 1.5, so light bends towards normal when entering glass If index of refraction were smaller, light will bend away from normal as light exits glass

Multiple Slits (diffraction)

When waves interact, displacements add together (interference)(occurs in light and sound waves) Thomas Young: double slit experiment -> light is a wave Regions of constructive interference between 2 light waves appear as bright fringes (maxima), regions where light waves interfere destructively -> dark fringes (minima) appear *Fringes result from constructive and destructive interference between light rays Maxima and minima alternate in a diffraction pattern. A maximum is equidistant between to minima, and a minimum is equidistant between two maxima Position of dark fringes = d sin θ = (n+1/2)*wavelength (incident wave) where d= distance between slits, θ is angle between line drawn from midpoint between slits to dark fringe and normal n is integer indicating number of the fringe *Bright fringes halfway between dark fringes

Pascal's Principle

for fluids to be incompressible (fluids w/ volumes that can't be reduced through application of force), a change in pressure will be transmitted undiminished to every portion of the fluid and to the walls of the container Hydraulic system: Generates mechanical advantage-> output force generated by magnifying input force by a factor = to the ratio of the cross-sectional area of the larger piston to that of the smaller piston (but the volume displaced is the same) -Operator applies force to side with smaller area because pressure same on both sides of lift, and P = F/A, so smaller force can be applied to smaller area to generate same pressure P= F1/A1 =F2/A2 F2 = F1 (A2/A1) Volume (V) = A1d1 = A2d2 where A is area and d is distance / displacement Combining equations for pressure and volume, we get equation for work as the product of constant pressure and volume change (isobaric process because no pressure change) W = PΔV = F1/A1 (A1d1) = F2/A2 (A2d2) W = F1d1 = F2d2 Pressure = F1/A1 = F2/A2 Work = magnitude of force * displacement (times the angle of cosine, which in most cases is 0) *This shows that no additional work is done/unaccounted for (greater the the force, smaller the distance, and only a little force over small area (creates a lot of distance) needed to generate a lot of force over larger area (smaller distance moved though)) *THE LARGER THE AREA, THE LARGER THE FORCE (although the force will be exerted through a smaller distance) Note: When air pressure changes above large body of water, water rises or falls to re-establish pressure equilibrium (low pressure air system creates hill, high pressure creates valley of water)

Independent and dependent variables

independent variable- the experimental factor that is manipulated; the variable whose effect is being studied. dependent variable- the outcome factor; the variable that may change in response to manipulations of the independent variable. Independent variable should go on X-axiz of graph, dependent variable goes on Y axis

Multiple Lens Systems

lenses in contact are a series of lenses with negligible distances between them Behave as single lens with equivalent focal length given by 1/f = 1/f1 + 1/f2 + 1/f3..... Equivalent Power (P) = P1+P2+ Think of corrective lenses: Cornea of eye (converging lens) in contact with contact lens (either converging (for farsighted people) or diverging (for nearsighted people) For lenses not in contact, the image of one lens becomes the object of another (image from last lens = image of the system) -Microscopes and telescopes Magnification (m) = m1 x m2 ...

Which is NOT equivalent to log (XY/WZ)? log(X) + log(Y) - log(W) - log(Z) log(X) + log(Y) + log(1/W) - log(Z) log(Y)-(logWZ)+log(x)) log(X) - (log(W) + log(Z) - log(Y))

log(Y)-(logWZ)+log(x)) This would be log (Y/WZX) log (1/x) - -log (x) log(xy) = log(x) + log(y)

Rules of Logarithms

loga(1) = 0 * Lowercase a means it is the base log a(A) = 1 log (A X B) = log A + Log B log (A / B) = log A - Log B log (A^B) = B *log A log (1/A) = - log A "p" is shorthand for -log, so pH is -log [H+] and pKa is -log (Ka) The most common bases used are base 10 (common logarithm) or base e (natural logarithm) e = Euler's number = 2.7183 log e = ln Converting common Logs to natural logs: log x = ln x / 2. 303

Standing Waves

produced by the constructive and destructive interference of two waves (traveling wave and its reflected wave) Standing wave forms whenever 2 waves of same frequency in opposite directions interfere with one another Appear to not be moving and only fluctuate in amplitude Alternated points of maximum displacement (amplitude) = antinodes Places with no displacement (amplitude = 0 ) = nodes But not every frequency of traveling wave will result in standing wave: Length of medium dictates frequency and wavelength that can establish standing wave Have to have boundaries at both ends: closed boundaries do not allow oscillations (correspond to nodes) and open boundaries allow maximal oscillation (correspond to antinodes) (open end of pipe and free end of flag)

Spherical Mirrors

two kinds: concave and convex Implies that mirror is pat of a much larger sphere shaped mirror spherical mirrors have centers of curvature (C) and radius of curvature (r) -> C= point on optical axis at equal distance to r from vertex of the mirror (The center of curvature would he the center of the spherical shaped mirror if it were a sphere) Convex: Passenger side mirror: Diverging, everything appears smaller and farther away) Concave Mirrors: Make-up mirror: everything appears bigger and closer (Converging) -Can produce real, inverted images or virtual, upright images depending on where object is relative to focal point ConCAVE: like looking into cave because it curves inward (thinnest in middle) = Converging (light rays converge after they reflect) -If we were to look at a sphere from the outside, we would see convex (diverging) surface (from the inside = concave) -Concave: C and r located in front of mirror -Convex: C and r located behind the mirror Focal length (f) is the distance between focal point (F) and mirror All spherical mirrors: f = r/2 where the radius of the curvature (r) is distance between C and the mirror Distance between object and mirror = o Distance between image and mirror = i f = r/2 1/f = 1/o + 1/i = 2/r All values have the same units If the image has a positive distance (i> 0) it is a real image (in front of mirror) If the image has a negative distance ( i<0) it is virtual and located behind the mirror plane mirrors can be thought of as spherical mirrors with indefinitely long focal distances (f) Magnification (m) is dimensionless -> ratio of image distance to object distance: m = -i/o negative magnification = inverted image m<0 Positive magnification = upright image Absolute value of m tells you if image is smaller or larger than object | m | > 1 means image is bigger than object | m | = 1 means image = size of object

Propagation speed of a wave (v)

v = fλ The distance from one maximum (crest) to the next is called the wavelength (λ) f= frequency = number of wavelengths passing a fixed point per second (measured in hertz (Hz) or cycles per second (cps) The inverse of frequency (cycles per second) is period (T) (seconds per cycle) T = 1/f Also: Period (T) = λ/v Angular frequency (w) is measured in radians per second (often used with simple harmonic motion in springs and strings (pendula) w = 2pi*f = 2 pi / T *The magnitude of the angular frequency is larger than the magnitude of the frequency. Waves oscillate about central point called equilibrium position Displacement (x) describes how far point is from equilibrium position (expressed as vector quantity) Amplitude (A): Maximum magnitude of displacement from equilibrium in a wave (Not the total height (which would be 2X amplitude), just from central point up or down)

What is the final temperature of a 5 kg silver pendant that is left in front of an electric heater, absorbing heat energy at a rate of 100 W for 10 minutes? Assume the pendant is initially at 20°C and that the specific heat of silver is 233 J/kg*K

watts are equal to joules per second; in other words, power is energy transfer over time. In 10 minutes, the pendant absorbs the following amount of energy: E = P*t = 100W*600 seconds = 6X10^4 J Now we can find the final temperature from this equation: q = mcΔt 6X10^4 J = 5*233*Δt 60X10^3 / 5 = 233 * Δt 12000/233 = about 50 The final temperature is thus 20 + 52 = 72°C. Or you could just plug and chug if you answer choices....

Sigmodial curve

what kind of curve does allosteric regulation of hemoglobin have?