MCAT : Physics

How does one calculate the interquartile range (IQR)?

(Remember how we find Q₃,Q₁?)

Ray diagrams for convex lenses

(Top pictures) 1. Rays that hit the lens parallel to the axis will converge inward toward the focal point 2. Rays passing first through the focal point will run parallel to the axis after hitting the lens

(X¹)² =

(X¹)² = X¹*²

Conversion factor between units of heat Calorie calorie joule BTU

1 Cal = 1000cal = 4184J = 4BTU

Specific heat values of water

1cal/g*K = 4.184 J/g*K

Equation for the thermal expansion of solids

A change in the temperature of most solids results in a change in their length according to the equation shown -α is the coefficient of linear expansion, which characterizes how a specific metal's length changes as temperature changes

Distinguish between positive and negative image distances

A positive image distance means that it is a real image (located in front of the mirror), while a negative distance means it is a virtual image (located behind the mirror) Remember that for lenses, the real image will be located on the opposite (virtual) side

Positively-skewed distribution

A positively-skewed distribution has a tail on the right side --the mean of such distributions will be higher than the median --also known as right-skewed or right-tailed

By convention, current is considered the flow of __________ charge

By convention, current is considered the flow of positive charge --the direction of current is thus opposite to the direction of actual electron flow

Electric field lines

By convention, the direction of the electric field vector is given as the direction that a positive test charge would move in the presence of a source charge --where the field lines are closer together, the field is stronger, and weaker where they are further apart --because electric field and electrostatic force are both vector quantities, it is important to remember the conventions for their direction

Rules for capacitors in parallel

Capacitors in parallel look like resistors in parallel 1. Add up capacitance as you would resistors in series 2. For capacitors in parallel, the voltage across each is the same and equal to the emf 3. Q can be found for each by using the source voltage and individual capacitances

Atmospheric pressure

Changes with altitude -impacts a number of processes including hemoglobin's affinity for oxygen and the boiling of liquids

Cohesion -what kind of menisci are seen associated?

Cohesion is the attractive force that a molecule of liquid feels toward other molecules of the same liquid -convex/backward menisci occur when these forces are greater than adhesive forces

Concave mirrors are ___________ mirrors, while convex mirrors are ___________

Concave mirrors are converging mirrors because they cause parallel incident light rays to converge after reflection Convex mirrors are diverging mirrors because they cause parallel incident light rays to diverge after reflection *The reverse is true for lenses!*

Confounding

Confounding is a data analysis error that results in the characterization of an incorrect relationship, usually the result of a variable not taken into account during the study For example, the assertion that data shows that having natural red hair leads to decreased pain tolerance --according to current research, there is no likely causality, but a third variable, such as a gene mutation could potentially cause both natural red hair and decreased pain tolerance --this is an example of a confounding variable

Two methods of determining whether a force is conservative

Conservative forces are those that are path independent and do not dissipate energy 1. Have the object in question return to its starting position after initially undergoing a displacement -if the net change in energy is zero regardless of path taken, the forces acting on the object are conservative 2. Have the object in question undergo a displacement -if the energy change is equal regardless of path taken, then the forces acting on the object are conservative forces

√3 =

√(3 ≈ 1.7

√2 =

√2 ≈ 1.4

Gravitational potential energy

Depends on an object's position with respect to ground or some zero potential energy position

Mass defect

Describes the difference between the sum of the masses of the protons and neutrons within the nucleus and the actual mass of that nucleus, which is somewhat smaller --the result of the strong nuclear force that allows the nucleus to stay together

Dielectric materials

Dielectrics, insulating materials placed between the plates of a capacitor, cause the electric field inside the capacitor to be reduced for the same amount of charge on the plates -molecules of the dielectric material get polarized in the field, and they align themselves in a way that sets up another field inside the dielectric opposite to the field from the capacitor plates -according to the equation V=Ed, a decrease in the electric field will decrease the voltage across the capacitor, increasing its capacitance

Diffraction

Diffraction refers to the spreading out of light as it passes through a narrow opening

How to distinguish between linear, semilog and log-log graphs?

Distinguish between these three by the spacing 1. Linear (linear, parabolic, exponential, logarithmic) --traditional unit spacing for both axes 2. Semi log --one axis maintains the traditional unit spacing while the other assigns spacing based on a ratio 3. Log-log graphs --both axes use a constant ratio

Four equations for linear motion at constant acceleration

Free fall questions involve linear motion with constant acceleration

Fusion phase change -when does it occur?

Fusion is another term for melting and occurs at the melting point

Intensity of sound equation

I = P/A P = power (W) A = area (m²) With regard to the bottom equation pictured, know that intensity is inversely proportional to the square of the distance from the source

X-ray diffraction

Method of using diffraction during protein analysis that is often combined with protein crystallography

Kinetic energy

Note its related to speed, particularly in the context of the linear motion equations -KE is the same regardless of the direction an object is traveling, and so is not related to velocity

Torque equation for a dipole in an electric field

Remember the equation for the dipole moment (p) = qd, which may sometimes be used this equation

Current equation

The current is the amount of charge (q) passing through a conductor per unit time

Power of a resistor -define -3 equations

The power of a resistor is the name given to the rate at which energy is dissipated by a resistor

logA1 =

logA1 = 0

logAA =

logAA = 1

log(A^B)

logA^B = B*logA

Free body diagrams

Free body diagrams are useful in finding net forces on objects on which many forces are acting -find x and y components of each force and add them all together

Write out the doppler effect equation

If memorized in this form, the upper sign should be used when the detector (upper) or source (lower) is moving toward the other, while the lower sign should be used when either the detector or the source is moving away from the other

Radiation in terms of thermodynamics

In terms of thermodynamics, radiation is the transfer of energy by electromagnetic waves -how the sun is able to warm the earth -

Describe "beneficence" in terms of research

It must be our intent to cause a net positive change for both the study and general populations, and we must do our best to minimize any potential harms

Convert from Celsius to Kelvin?

K = C + 273

What are "morally relevant differences" in terms of scientific research?

Morally relevant differences are defined as those between individuals that are considered an appropriate reason to treat them differently --for example, all else being equal, a transplant that is as likely to benefit a young child or an elderly adult may be given to the child with a longer life expectancy --contributes to our notions of justice in scientific research

Deriving the equation for electric potential at some point P near an electrical dipole

1. For a collection of charges, the electrical potential is the scalar sum of the potentials due to each charge at that point, as shown 2. Assuming the point is very far from the dipole relative to the distance between the charges, we can make two approximations: -(r⁺)(r⁻) = r² -(r⁻)-(r⁺) = dcosθ 3. Using these along with the equation for the dipole moment, we have the final equation for electric potential at some point P near an electrical dipole

Density values for water -three to know

1g/cm³ = 1000kg/m³ = 1000g/L

Observation bias

Also called the Hawthorne effect, observation bias posits that behavior of study participants is altered simply because they recognize that they are being studied --for example, patients in a study for a given weight loss drug may begin exercising more frequently, or may make healthier diet choices, artificially increasing the perceived effect of the drug

Kirchhoff's junction rule

At any junction in a circuit, the sum of currents directed into that point equals the sum of currents directed away from that point --conservation of electrical charge

Do instruments introduce bias when they are inaccurate, or imprecise?

Because bias is a systematic error in data, only an inaccurate tool will introduce bias, though an imprecise tool will still introduce error

Convex lenses are _________ lenses, while concave lenses are __________ lenses

Convex lenses are converging lenses, while concave lenses are diverging lenses This is the opposite of convex/concave mirrors

Coulumb's law

Coulomb's law quantifies the magnitude of the electrostatic force between two charges at a distance r from one another

Critical speed -definition -equation

Critical speed is the speed of a fluid at which turbulence can arise -Reynolds number is a constant that relates the size, shape and surface roughness of any objects within the fluid -η is the viscosity of the fluid

Force experienced when a test charge is placed in an electric field

Electric fields are produced by source charges, and this measures the force on a test charged placed at some point within the electric field

Calculating electrical potential at some distance from a source charge

Electrical potential is a scalar quantity!

Relationship between pressure/volume and work

For isobaric processes (those in which pressure remains constant), work is defined as the change in volume a system experiences multiplied by the pressure

Ohm's law

Ohm's law helps explain voltage drops between any two points in a circuit

Instantaneous acceleration

On a velocity vs time graph, the slope of the graph at any particular moment indicates average acceleration -if the slope is positive, the acceleration is in the direction of velocity - if the slope is negative, this is deceleration, acceleration in the direction opposite that of velocity -this should be contrasted with average acceleration, given by ∆v/∆t

Wave sources traveling above the speed of sound

Once an aircraft attains a speed above that of sound, the region of constructive interference changes from one location at the aircraft, to a shockwave cone that is 3D -wave crests meet at this cone (think a wake on water 2D) - the faster the speed above that of sound, the narrower the cone

Continuity equation for fluids

Q = v₁A₁ = v₂A₂ Do not confuse flow rate (Q), which is constant at any cross-sectional area, to linear speed (v), which is not!

Three rules for drawing ray diagrams for convex mirrors

Remember that for convex mirrors, the center of curvature (C) and the focal point (F) lie behind the mirror 1. Rays traveling parallel to the axis before striking the mirror reflect in such a manner that its extension will pass through the focal point 2. Rays striking the convex mirror such that its extension will pass through the focal point reflect parallel to the principal axis 3. Rays striking the convex mirror such that its extension will pass through the center of curvature reflect back along the same path

What is the equation for the electric field at any point along the perpendicular bisector of a dipole?

Remember that the perpendicular bisector is found at the midpoint between the two charges in the dipole --the electric field vectors will point in the direction opposite p (dipole moment)

Describe "respect for persons" in terms of research

Respect for persons includes the need for honesty between subject and researcher, which usually prohibits deception and includes the process of informed consent and a commitment to autonomy

How is standard deviation calculated?

Standard deviation is calculated using the following steps: 1. Add up how far each data point is from the mean and square each value 2. Add the resulting values together 3. Divide this by the number of data points minus one 4. Take the square root of this value

Decay constant and half-life

The decay constant is equal to ln(2) over the half life

How are x- and y-components of a vector determined given only its magnitude and angle (θ)?

Vx = Vcosθ Vy = Vsinθ

log(1/A) =

log(1/A) = -logA

log(A*B) =

log(A*B) = logA + logB

Speed of sound equation

v = √(B/ρ) B = bulk modulus, a measure of the medium's resistance to compression ρ = density of the medium

Ray diagrams for concave lenses

(Bottom pictures) 1. Rays that hit the lens parallel to the axis will refract outward, at an angle equal to the focal point in front of the image as shown 2. Rays moving at an angle toward the focal point behind the mirror will refract parallel to the axis

What are the three most common causes of outliers?

1. A true statistical anomaly --a person who is over seven feet tall 2. A measurement error --reading the cm side of the tape measure instead of inches --should be excluded from analysis 3. A distribution that is not approximated by the normal distribution --skewed distribution with a long tail, i.e.

Ammeter 1. What does it measure? 2. How is it placed? 3. What is its ideal resistance?

1. Ammeters measures current at some point within a circuit --requires that the circuit be on, or the current will = 0 2. Ammeters are inserted in series --current remains the same across all parts of a series circuit 3. Ideally, they will not impact V=IR, and must have resistances close to 0

Rules for object placement and concave mirror ray diagrams: - An object placed between C and F will produce what kind of image? - An object placed at F will produce what kind of image? - An object placed between F and the mirror will produce what kind of image?

1. An object placed between C and F will produce a real, inverted, magnified image 2. An object placed at F will form no image 3. An object placed between F and the mirror will produce a virtual, upright, magnified image

Rules for linear motion at constant acceleration

1. An object's velocity at its maximum height is zero 2. The time it takes an object to reach its maximum height equals the time it takes to return to its starting height -as long as the object ends up at the height at which it started, total time in flight equals the time necessary to get to the maximum height (final velocity = 0) multiplied by two 3. You should always use up as the positive direction

Steps in the scientific method

1. Generate a testable question 2. Gather data and resources 3. Form a hypothesis --proposed explanation or answer to the testable question 4. Collect new data --experimentation involves manipulating and controlling variables of interest --observation often involve no changes in the subject's environment 5. Analyze the data 6. Interpret the data and existing hypothesis --if the data is inconsistent with the original hypothesis, consider alternate hypotheses 7. Publish for peer review 8. Verify results under new conditions

Distinctions between static and kinetic friction

1. Kinetic friction is constant, and independent of how much sufrace area is in contact or the velocity of movement 2. The value of µs will always be higher than µk, and therefore the maximum static friction value will always be greater than the constant kinetic friction value

What three factors can increase the power of an experiment?

1. Large difference in means between the populations being compared 2. Less scatter of data/more precise measurements 3. Increased sample size --more samples = more confidence in the difference or lack of difference found between populations --this is the only one of the three that we have control over

Ohmmeter 1. What does it measure? 2. How is it placed? 3. What is its ideal resistance?

1. Ohmmeters measure resistance through supplying its own voltage to any two points in series --does not require the circuit to be on 2. It is placed in series 3. Since it is measuring resistance, its ideal resistance is zero

Right hand rule for direction of magnetic force on a moving charge

1. Place your thumb in the direction of the velocity vector of the moving charge 2. Put your fingers in the direction of the magnetic field 3. Your palm will point in the direction of the magnetic force on the positive charge, while the back of your hand will point in the direction of the force on a negative charge

Straight, current-carrying wires and the right-hand rule

1. Point thumb in the direction of the current and wrap fingers of the right hand around the wire 2. Fingers mimic the circular field lines, curling around the wire

Write out the the table for the four possible outcomes of hypothesis testing

1. Power (1-β) --the chance of detecting a difference between the two populations 2. α --the chance of seeing a difference between the two populations that is not there 3. β --the chance of missing a difference between the two populations that is there 4. Null hypothesis correct --no difference between the two populations

Steps for finding V,I, and R at individual as well as combined resistors in series

1. Sets of resistors in series can be thought of as a single, large resistor, that equals the sum of the individual resistances 2. Using the total resistance, use V = IR to find the current through the single, big resistor, and this will be constant across individual resistors 3. Use resistance and current values to find the voltage drop across each individual resistor

How are the following determined for spherical mirrors? 1. Center of curvature 2. Radius of curvature 3. Focal point 4. Focal length 5. Image distance 6. Object distance

1. The center of curvature is would be the center of the spherically-shaped mirror it it were a complete sphere 2. The radius of curvature is the distance from the vertex of the mirror to its center of curvature 3. The focal point is always half of the radius of curvature 4. The focal length is the distance from the focal point to the mirror 5. Image distance is the distance between the image and the mirror 6. Object distance is the distance between the object and the mirror

Steps for finding V,I, and R at individual as well as combined resistors in parallel

1. The voltage drop across resistors in parallel will be the same at each one because all pathways originate from and end at a common pathway -can think of it as one resistor does not affect the other resistors because each is a different path, so the voltage drop will be the same at each -Vs = V₁ = V₂, etc 2. As a general rule, resistors in parallel are added according to (1/R₁) + 1/R₂......) 3. Use the resistance and voltage values to find the current at each individual resistor

Voltmeter 1. What does it measure? 2. How is it placed? 3. What is its ideal resistance?

1. Voltmeters measure the voltage drop across a circuit element --requires that the circuit be on, or the current will = 0 2. Voltmeters are inserted in parallel --if hooked up in series, current will not flow through that part of the circuit because of the high resistance 3. Ideally, a voltmeter has infinite resistance --want a big resistance so that all the current will go through the circuit element that we are measuring the voltage drop across

Rules for projectile motion

1. the equations for linear motion can be used to analyze the two dimensions of motion separately 2. objects will experience the force of gravity in the y direction, but horizontal velocity will be constant because air resistance is usually negligible

What are the boundaries of the visible region of the electromagnetic spectrum?

400nm - 700nm

Capacitance equation

= Q/V ε₀ = permittivity of free space A = area of overlap of the two plates d = distance between the plates

Define a directional alternative hypothesis and give an example

A directional alternative hypothesis states that the null hypothesis is wrong, and also specifies whether the true value of the parameter is greater than or less than the reference value specified in null hypothesis --the advantage of using a directional hypothesis is increased power to detect the specific effect you are interested in --the disadvantage is that there is no power to detect an effect in the opposite direction A researcher has exam results for a sample of students who took a training course for a national exam. The researcher wants to know if trained students score above the national average of 850. A directional alternative hypothesis can be used because the researcher is specifically hypothesizing that scores for trained students are greater than the national average. (H₀: μ = 850 vs. H₁: μ > 850)

Negatively-skewed distribution

A negatively-skewed distribution has a tail on the left side --the mean of such distributions will be lower than the median --also known as left-skewed or left-tailed

Define a nondirectional alternative hypothesis

A nondirectional alternative hypothesis states that the null hypothesis is wrong but does not predict whether the parameter of interest is larger or smaller than the reference value specified in the null hypothesis. A researcher has results for a sample of students who took a national exam at a high school. The researcher wants to know if the scores at that school differ from the national average of 850. A nondirectional alternative hypothesis is appropriate because the researcher is interested in determining whether the scores are either less than or greater than the national average. (H₀: μ = 850 vs. H₁: μ≠ 850)

Period definition

A period is the number of cycles per second (s⁻¹) and is the inverse of the frequency (1/f)

What does it mean for a thermodynamic process to be adiabatic?

A thermodynamic process is adiabatic when no heat exchange occurs -thus, ∆U = -W for these processes

What does it mean for a thermodynamic process to be isobaric?

A thermodynamic process is isobaric when there is no change in pressure during the process -thus, the work done during this process will equal P∆V

What does it mean for a thermodynamic process to be isochoric?

A thermodynamic process is isochoric (isovolumetric) when there is no change in volume during the process, and thus no work done -thus, ∆U = Q for such these processes

What does it mean for a thermodynamic process to be isothermal?

A thermodynamic process is isothermal when temperature is held constant, resulting in no change in its internal energy -thus, Q = W for these processes

Absolute/hydrostatic pressure equation

Absolute/hydrostatic pressure refers to the pressure exerted by a fluid on a submerged object at depth h --Po = ambient pressure (pressure at the surface) Remember that Po will not always equal Patm -in other fluid systems, the surface pressure may be higher or lower than atmospheric pressure

Adhesion --what kind of menisci are seen associated?

Adhesion is the attractive force that a molecule of liquid feels toward the molecules of some other substance, such as the container it is in -concave menisci occur when these forces are greater than cohesive forces

Equipotential lines

An equipotential line is one on which the potential is the same at every point, and thus no work is done when moving a test charge from one point on an equipotential line to another -moving a charge between equipotential lines is proportional to the potential difference between them and the magnitude of the test charge according to the equation for electrical potential, but will be independent of the path taken to get there -note that for a positive test charge such as that pictured, potential decreases as lines move further and further from the positive source charge, while the opposite is true if this source charge is negative

Distinguish between real and virtual images

An image is said to be real if light actually converges at the position of the image, while a virtual image is one in which light only appears to be coming form the position of the image but does not actually converge there Plane mirrors create the appearance of light rays originating behind the mirrored surface --the distances between the real and virtual image and the plane mirror are always the same

Newton's second law

An object of mass m will accelerate when the vector sum of the forces results in some nonzero resultant force vector -note that net force and acceleration vectors point in the same direction

Any number to the zeroth power =

Any number to the zeroth power = 1

Equation for the volume expansion

Applies to both liquids and solids but is usually applied only to liquids, whose only appreciable parameter of thermal expansion is volume -recall the thermal expansion equation for solids - β is the coefficient of volumetric expansion that characterizes how a specific material's volume changes as the temperature changes and is equal to three times the coefficient of linear expansion (β = 3α)

Archimedes' principle --write out the equation

Archimedes' principle states that a body either wholly or partially immersed in a fluid will be buoyed upwards by a force equal to the weight of the fluid it displaces -remember to always use the density of the fluid itself!

Kirchhoff's loop rule

Around any closed circuit loop, the sum of voltage sources will always be equal to the sum of voltage (potential) drops -all the electrical energy supplied by a source gets fully used up by the other elements within that loop

Pulleys and mechanical advantage

As we saw with the heavy create, each additional pulley lessens the effort needed by each individual pulley, but lengths the effort distance required to lift the object the desired distance (load distance) -in the first example, the load is divided between the two pullets, so the effort is only 1/3(w) in each -we need to pull through a length of rope that is twice the load distance In the third example, the load is divided amongst the four pulleys, but we need to pull through a length of rope that is four times the load distance

Mechanism of the mechanical advantage of pulleys

Assuming that the heavy crate is momentarily being held stationary in midair, the system is in equilibrium -the weight (load) is balanced by the total tension in the ropes -the tensions in the two vertical ropes are equal, and thus each supports half of the crate's total weight -thus, only half of the force (effort) is required to lift the crate This advantage comes at the expense of distance - to lift an object a certain distance (load distance), one must pull a length of rope equal to twice the displacement (effort distance)

Strong nuclear force

Attraction felt between protons and neutrons that holds them together in the nucleus --the bound system is at a lower energy level than the unbound constituents, and the difference in energy must be radiated away in the form of heat, light or other electromagnetic radiation that results in mass defect --the weak nuclear force also contributes to the stability of the nucleus, but is about one-millionth the strength of the strong nuclear force

Describe the purpose of blinding in experimental research

Because many of the measures in biomedical research are subjective, the perception of the subject and the investigator may be biased by knowing which group the subject is in --to combat this, subjects and or investigators are not given information about which group a subject is in - this is known as blinding

Distinguish bias and confounding

Bias is a result of flaws in the data collection phase of an experimental or observational study, while confounding is an error in analysis

Bimodal distribution

Bimodal distributions contains two peaks with a valley in between --if there is sufficient separation of the two peaks, or a sufficiently small amount of data within the valley region, bimodal distributions can often be analyzed as two separate distributions However, they do not have to be analyzed as two separate distributions - the same measures of central tendency (mean, median, mode) can be applied to them as well

Electron capture

Can be considered the reverse of beta decay --a proton is converted to a neutron, resulting in an atomic number decrease while mass number remains unchanged

Rules for capacitors in series

Capacitors in series look like resistors in series 1. Add capacitance as you would resistors in parallel 2. The Q across each capacitor will be the same (just as the current through parallel resistors is the same), and can be found by using the sum of the capacitors' capacitance and the total voltage applied, just as you would for resistors in series 3. Can then use Q and C for each capacitor to find the individual voltage drops across each

Case-control study

Case-control studies are a type of observational study that identifies the number of subjects with or without a particular outcome, and then looks backwards to assess how many subjects in each group had exposure to a particular risk factor --for example, a study in which 100 patients with lung cancer and 100 patients without lung cancer are assessed for their smoking history

Chromatic abberation

Chromatic aberration occurs because lenses refractive indices decreases with increasing wavelength in degrees unique to each wavelengths of light --manifests as "fringes" of color along boundaries that separate dark and bright parts of the image, because each color in the optical spectrum cannot be focused at a single common point. Since the focal length f of a lens is dependent on the refractive index n, different wavelengths of light will be focused on different positions.

Circular polarization

Circularly polarized light has a uniform amplitude but continuously changing direction, which causes a helical orientation in the propagating wave --like other waves, the helix has average electric and magnetic field vectors that are perpendicular

Rules for closed pipes

Closed pipes are those with on fixed end and one open end -unlike strings or pipes, the harmonic in a closed pipe is equal to the number of quarter-wavelengths There can only be odd harmonics for closed pipes because these are measured in quarter-wavelengths, rather than half-wavelengths in strings and open pipes -the first harmonic (n=1) is known as the fundamental frequency -the third harmonic (n=3) is known as the first overtone -the fifth harmonic (n=5) is known as the second over tone

Cohort study

Cohort studies are a type of observational study in which subjects are sorted into two groups based on differences in risk factors (exposures) and then assessed at various intervals to determine how many subjects in each group had a certain outcome --for example, a study in which 100 smokers and 100 nonsmokers are followed for 20 years while counting the number of subjects who develop lung cancer in each group

Relationship between common logarithms and natural logarithms=

Common logarithms are base-ten logarithms (log₁₀), while natural logarithms are based on Euler's number (loge or ln) and are related by the following equation logx ≈ (lnx)/2.3

What are confidence intervals used for and how are they calculated?

Confidence intervals are used to estimate population means from a sample data set --how sure are we that a mean value represents a more general mean? For instance, an author's study determines that the mean glucose reading of subjects in their study is 120mg/dl ± 5mg/dl --this means that if we were to repeat their study, that 95% of the time, the mean that we find for our subjects under similar experimental conditions to their's would fall between 115-125mg/dl Calculation: CI₉₅ = Mean ± 1.96*SEM --standard error of mean = SD/square root of the number of samples

Cross products and vectors -how are they determined? -when are they useful?

Cross products are determined through multiplying the magnitudes of the two vectors of interest and the sin of the angle between them, as shown below: AxB = |A||B|sinθ Once the magnitude of the resultant vector is determined, the right-hand rule can be used to determine its direction -point index finger in the direction of the first vector and the middle finger in the direction of the second: the direction the thumb is pointing is the direction of the vector

Cross-sectional study

Cross-sectional studies are a type of observational study that attempt to categorize patients into different groups at a single point in time --for example, a study to determine the prevalence of lung cancer in smokers and nonsmokers at a given point in time

Damping

Damping is a decrease in the amplitude of a wave caused by an applied or nonconservative force -if an oscillating system were frictionless, a periodically-varying force with a frequency equal to the natural frequnency of the system would continually add energy to the system, and the amplitude would increase indefinitely -however, because no system is completely frictionless, there is always damping, which affects amplitude but not frequency (pitch) of oscillation!

Differences in standard deviation

Data sets with smaller standard deviations are more tightly-oriented (taller, narrow distributions), while those with larger standard deviations are more spread out (shorter, wider distributions)

Detection bias

Detection bias occurs when there appears to be a trend in data that is instead caused by methods in detecting the data --higher rates of cancer being the product of prevalence of cancer increasing, rather than in an increase in our ability to detect what is already there

Are distance and displacement scalar or vector quantities? -how do they relate to speed and velocity, respectively?

Distance is a scalar quantity Displacement is a vector quantity Speed is distance/time and accounts for path taken Velocity is displacement/time and does not account for path taken

Rule for convex (diverging) mirror ray diagrams

Diverging mirrors produce only virtual, upright, reduced images regardless of the position of the object --the further the object from the mirror, the smaller the virtual image

Doppler ultrasound

Doppler ultrasound combines standard ultrasound with a doppler mode that is used to determine the flow of blood within the body by detecting frequency shifts associated with movement toward or away from the receiver

Dot products and vectors -how are they determined? -when are they useful?

Dot products are used to generate scalar quantities like work -results in a scalar number -found through multiplying individual vectors that have the same dimensions

Electric dipoles

Electric dipoles result from two equal and opposite charges being separated by a small distance, and can be either transient or permanent -most often, we are asked to calculate the electrical potential at some point P near the dipole

Electrical potential

Electric potential is the amount of electric potential energy that a unitary point charge would have if located at any point in space -equal to the work done by an external agent in carrying a unit of positive charge from the arbitrarily chosen reference point (usually infinity) to that point without any acceleration

Positron emission

Emission of a positron, which has the mass of an electron but carries a positive charge (denoted e⁺ or β⁺) --during B⁺ decay, a proton is converted into a neutron, hence the atomic number will decrease by one, while the mass number will remain the same

Beta decay -shielding?

Emission of a β-particle, which is an electron --during beta decay, a neutron is converted into a proton, and thus the atomic number will go up by one, while the mass number remains the same -β-particles are singly-charged and very small, and thus more likely to penetrate shielding than alpha particles

Alpha decay -shielding?

Emission of an α-particle that consists of two protons, two neutrons and two electrons -alpha particles are relatively large and react with matter easily, and thus do not penetrate shielding (like lead sheets) extensively

Gamma decay

Emission of γ-rays, high-energy photons that carry no charge and simply lower the energy of the parent nucleus without changing the mass/atomic numbers --high-energy state of the parent nucleus may be represented by an asterisk

Entropy definition and equation

Entropy is a measure of how widely spread out energy becomes in a process -Qrev = heat gained or lost in a reversible manner -when energy is distributed into a system at a given temperature (+Q), its entropy increases (+ΔS), and when energy is distributed out of a system at a given temperature (-Q), its entropy decreases (-ΔS )

Convert from Celsius to Fahrenheit

F = (9/5)C + 32

Newton's first law

F = ma = 0 -a body at rest or in motion at a constant velocity will remain that way unless a net force acts upon it -law of inertia

Universal circular motion and centripetal force

Fc = mv²/r

Atomic fission

Fission is a process by which a large nucleus splits into smaller nuclei --results in the release of energy

Fluoresence

Fluorescent substances can be excited using UV radiation, whose photons have relatively high frequencies --after being excited to a higher energy state, the electron in the fluorescent substances returns to its original state in two or more steps --by doing so, each step involves less energy and thus the photon is emitted with a lower frequency than the absorbed ultraviolet photon --if the wavelength of this emitted photon is within the visible range of the electromagnetic spectrum, it will be seen as light of the particular color corresponding to that wavelength

Therapeutic ultrasound

Focusing sound waves from an ultrasound machine using a parabolic mirror causes constructive interference at the focal point of the mirror, creating a high-energy wave exactly at that point that can be used in lithotripsy or ablating small tumors

P-value use in directional and nondirectional tests

For a directional test, if the p-value is less than α, we reject the null hypothesis and state that there is a statistically significant difference between the two groups For a nondirectional test, if the p-value is less than α/2, we reject the null hypothesis and state that there is a statistically significant difference between the two groups

Newton's third law

For every force exerted by object A on object B, there is an equal but opposite force exerted by object B on object A -applies to physical contact as well as forces like gravitation and electromagnetism

Multiple lens systems not in contact

For lenses not in contact, the image of one lens becomes the object of another lens given by the following equation --telescope, microscopes are good examples

Lensmaker equation

For real lenses (lenses for which thickness cannot be neglected), the focal length is related to the curvature of the lens surfaces and the index of refraction by the lensmakers equation

Atomic fusion

Fusion occurs when small nuclei combine to form a larger nucleus --results in the release of energy

Gauge pressure --definition --equation

Gauge pressure is the amount of pressure in a closed space above and beyond atmospheric pressure -it is good to know how to relate this to absolute/hydrostatic pressure

What is a null hypothesis?

General statement or default position that there is no relationship between two measured phenomena, or no association among groups Rejecting or disproving the null hypothesis—and thus concluding that there are grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science, and gives a precise criterion for rejecting a hypothesis.

List and describe the nine Hill's criteria

Hill's criteria describe the components of an observed relationship that increase the likelihood of causality in the relationship. --the more criteria that are satisfied by a relationship, the likelier it is that the relationship is causal 1. Temporality --the independent variable (the variable being manipulated) must occur before the dependent variable (the variable being observed) --THIS IS THE ONLY ONE THAT IS UNIFORMLY NECESSARY FOR CAUSATION 2. Strength --as more variability in the outcome variable is explained by variability in the independent variable, the relationship is more likely to be causal 3. Dose-response relationship --as the independent variable increases, there is a proportional increase in the response --the more consistent the relationship, the more likely it is causal 4. Consistency --the relationship is found to be similar in multiple settings 5. Plausibility --There is a reasonable mechanism for the independent variable to impact the dependent variable supported by existing literature 6. Consideration of alternate explanations --If all other plausible explanations have been eliminated, the remaining explanation is more likely 7. Experiment --If an experiment can be performed, a causal relationship can be determined conclusively 8. Specificity --The change in the dependent variable is only produced by an associated change in the independent variable 9. Coherence --The new data and hypothesis are consistent with the current state of scientific knowledge

Define hypothesis testing and list the three factors to take into account

Hypothesis testing involves mathematically calculating probabilities that two means are truly different and not just the result of random chance These probabilities are dependent on three factors: --difference between the means --the scatter of the data --number of subjects tested

Finding outliers using standard deviation

If a data point falls more than three standard deviations from the mean, it is considered an outlier

Describe forced oscillation

If a frequency of the applied force is close to that of the natural frequency of the system, the amplitude of oscillation becomes much larger --pushing a child on a swing --the amplitude is increasing because the force frequency is nearly identical to the swing's natural frequency

Slit-lens system --bright and dark fringes

If a lens is placed between a narrow slit and a screen, a pattern is observed consisting of a bright central fringe, with alternating dark and bright fringes on each side of this --the central maximum is twice as wide as the bright fringes on the sides, and widens more as the slit is narrowed

Forced oscillation

If a periodically-varying force is applied to a system, the system will be drive at a frequency equal to the frequency of the force, known as forced oscillation -if the frequency of the applied force is close to that of the natural frequency of the system, the amplitude of oscillation becomes much larger because the force frequency is nearly identical to the natural frequency -pushing a child on a swing

How do we determine causality between the independent and dependent variables?

If the change in the independent variable (the variable being manipulated) always precedes the change in the dependent variable, (the variable being observed) and the change in the dependent variable does not occur in the absence of the experimental intervention, the relationship is said to be causal

What is the significance of mean and median values that are either close together or far apart?

If the mean and median are far from each other, this implies the presence of outliers or a skewed distribution --if the mean and median are very close, this implies a symmetrical distribution

What is true of two objects placed in a fluid that displace the same volume of that fluid?

If two objects placed in a fluid displace the same volume of fluid, they will experience the same buoyant force even if the objects have different masses

Convert between the following units of pressure: atm mmhg Pa torr

Ignore bar/psi

Describe "justice" in terms of research

In a world where all individuals and all questions are ethically the same, the only way to determine the selection of a research question to maintain justice is through random chance --thus, justice in research applies to both the selection of a research topic and the execution of the research (such as seeking a diverse group for a study)

Dielectrics in circuit capacitors

In charged capacitors within a circuit connected to a voltage source, dielectric materials increase capacitance by a factor of k while the voltage remains constant because it is coming from a voltage source --the increase in capacitance in this case is due to an increased in stored charge

Distinguish between single-blind and double-blind experiments

In single-blind experiments, either only the patient or only the assessor is blinded, while in double-blind experiments, the investigator, subject and assessor all do not know the subject's group

Equipose

In studies comparing two potential treatment options, one cannot approach the research with the knowledge that treatment is superior to the other --if it becomes evident that one treatment option is clearly superior before the study is scheduled to finish, the trial must be stopped because providing an inferior treatment is a net harm

Define confidence in terms of hypothesis testing

In terms of hypothesis testing, confidence refers to the probability of correctly failing to reject a true null hypothesis

Conduction in terms of thermodynamics

In terms of thermodynamics, conduction is the direct transfer of energy from molecule to molecule through collisions -think of burning your fingers on a hot stove Metals are the best heat conductors because metallic bonds contain a density of atoms embedded in a sea of electrons which facilitate rapid energy transfer -gases tend to be the poorest heat conductors because there is so much space between individual molecules that energy-transferring collisions occur infrequently

Convection in terms of thermodynamics

In terms of thermodynamics, convection is the transfer of heat by the physical motion of a fluid over a material -because this involves flow, only liquids and gases can transfer heat by this means

Normal distribution

In the normal distribution, the mean, median mode are the same --~68% of the distribution is within one standard deviation of the mean, 95% within two, and 99% within three --remember that the percentages outside 1,2, or 3 standard deviations is split up on either side of the graph

Component method of adding/subtracting vectors

In this method, each vector is broken down into its x- and y-components, which are then added or subtracted as desired. These components are found using the equations below -conversely , if we know the components, we can find the magnitude of the vector using the pythagorean theorem Vx = Vcosθ Vy = Vsinθ

Distinguish between independent and dependent events in terms of probability

Independent events have nothing to do with each other --rolling die Dependent events do have an impact on one another --selecting a red ball from a container of red and blue balls

Relationship between sound intensity, amplitude, and distance from the source

Intensity is equal to the square of the amplitude of the sound wave Intensity of also inversely proportional to the square of the distance from the source -think of sound waves emanating in all directions from a source

Intensity of sound definition and units

Intensity is the average rate of energy transfer per area across a surface that is perpendicular to the wave and is given in W/m² -while the loudness/volume of sound is subjective depending on brain function and factors such as stiffening of ossicles, the intensity of sound is objectively measurable

Thin film interference

Interference patterns occur as light waves reflecting off the external surface of the film interfere with light waves reflecting off of the internal surface of the film

First law of thermodynamics and sign conventions

Internal energy (∆U) -positive value indicates increasing temperature -negative value indicates decreasing temperature Heat (Q) -positive value indicates heat is flowing into the system -negative value indicates heat is flowing out of the system Work (W) -positive value indicates work is being done by the system (expansion) -negative value indicates work is being done on the system (compression)

Distinguish between internal and external validity

Internal validity is the tendency of the same experiment to produce the same results, while external validity have samples that are representative of the target population --internal validity is negatively impacted by a confounding variable

Define the following: Isolated systems Closed systems Open systems

Isolated systems can exchange neither energy nor matter with their surroundings Closed systems can exchange energy, but not matter with their surroundings Open systems can exchange both matter and energy with the environment

Kinetic friction --definition --equation

Kinetic friction exists between a sliding object and the surface over which it slides -note that unlike static friction, kinetic friction will have a constant value --begins to slide on ice (not rolling on pavement)

Multiple lens systems in contact

Lenses in contact are a series of lenses with negligible distances between them and behave as a single lens --contact lenses sitting right on the eye is a good example

Rectilinear propagation

Light that is traveling through a homogeneous medium will travel in a straight line --direction will change at an interface between two media

Ferromagnetic materials and magnetic fields

Like paramagnetic materials, these have unpaired electrons that are randomly-oriented Unlike paramagnetic materials, these will be become strongly magnetized when exposed to a magnetic field -what we think of as magnets

Longitudinal waves

Longitudinal waves are those in which the particles of the wave oscillate parallel to the direction of propagation through compression and rarefaction -sound waves

centripetal magnetic

Magnetic forces can cause charged particles to move in circular or spiral paths -in this case, we can set the magnetic force equal to the centripetal force equations: mv²/r = qvBsinθ To determine the direction of the magnetic field, use the right-hand rule - the force of the magnetic field will always point toward the center of the circle -place thumb in the direction of the velocity vector, and fingers toward the center -for positive charges, the direction of the magnetic field is the direction of the palm, while for negative charges, it is in the direction of the back of the hand

Distinguish between insulators and conductors in terms of resistance

Materials that offer almost no resistance are called conductors, while materials that offer very high resistance are called insulators --those found in between are knowns as resistors

Measures of central tendency

Measures of central tendency are those that describe the middle of a sample --mean, median values are examples

Measures of distribution/dispersion

Measures of distribution describe the spread of data --range, IQ ranges are examples

mechanical advantage

Mechanical advantage is the ratio of magnitudes of the force exerted on an object BY a simple machine to the force applied ON the simple machine -it is the force accomplished by using a tool, including simple machines like wedges, wheel and axles, levers, and pulleys

Box plot

Median = Q₂ Whiskers can either correspond to the maximum and minimum value of the data set (as shown), or to the largest and smallest values within 1.5xIQR of the median, with outliers presented as individual points

Metallic conductivity

Metal atoms can easily lose one or more of their outer electrons, which are then free to move around in the larger collection of metal atoms, making most metals good electrical and thermal conductors

People who are myopic require _________ lenses, while those who are hyperopic need ____________ lenses

Myopia is another name for nearsightedness and is corrected with a diverging (concave) lens Hyperopia is another name for farsightedness and is corrected with a converging (convex) lens

Weight of any volume of a given substance with a known density

Normally applied to liquids and is also known as the buoyant force

Magnetic force on a charge moving through a magnetic field

Note that the magnetic force is a function of the sine of the angle between the moving charge and magnetic field vectors -this means that the charge must have a perpendicular component of velocity in order to experience a magnetic force -sin0 and sin180 = 0

Law of reflection

Note that the normal line is drawn perpendicular to the boundary of the medium, and all angles in optics are measured from the normal, not the surface of the medium

Write out Bernoulli's equation

Nothing more than a statement of energy conservation -more energy dedicated toward fluid movement means less energy dedicated to static fluid pressure, and vice vversa

Objects more dense than the fluid they are in will __________, while those that are less dense will _____________

Objects more dense than the fluid they are in will sink to the bottom, while those that are less dense (or have equal density) than the fluid they are in will stop sinking and float once the volume of displaced fluid exerts a force equal to the weight of the object *The specific gravity of the object gives how much of the floating object will sit below the surface* -a specific gravity of 1 indicates that 100% of the object will submerge, but the object will not sink

Explain observation studies and list the three types

Observation studies are used to study certain causal associations for which an experiment cannot be performed for ethical or practical reasons --these do not demonstrate causality, although the tendency toward casualty may be demonstrated using Hill's criteria --the three types of observational studies are cohort, cross-sectional and case-control studies

Of the three measures of central tendency, which is least likely to be affected by outliers?

Of the mean, median and mode, the mode is least likely to be affected by outliers because these are unlikely to change the most common number in the data set

Laminar flow

Often modeled as layers of fluid that flow parallel to each other -layers closest to the wall of the pipe flows more slowly than the more interior layers of fluid

Angular frequency definition and units

Often used to describe simple harmonic motion in things like springs and pendula -measured in radians/sec

Perpendicular bisector of a dipole

One very important equipotential line is that which lies halfway between +q and -q in a dipole (imagine as the charges being the 'half's in the picture) -because the angle between this place and the dipole axis is 90°, the electric potential along this plane is 0 (cos90 = 0) -we are often asked to calculate the magnitude of the electric field on the this bisector

Rules for open pipes

Open pipes support antinodes at both ends -rules are similar to those of strings -what are the equations for wavelength and frequency that are also true for strings? -the distance between antinodes is always half of a wavelength -the number of nodes will always be equal to the harmonic -there will always be one more antinode than node -the first harmonic (n=1) is known as the fundamental frequency -the second harmonic (n=2) is known as the first overtone, which continues according to this pattern

Power in terms optics

Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light and is inversely related to the focal length -it has the same sign as f, and is positive for converging lens and negative for diverging lens

Distinguish between paramagnetic and diamagnetic in terms of magnetic fields

Paramagnetic materials have unpaired electrons that are randomly oriented and so will not create a magnetic field itself --will become weakly magnetized in the presence of an external magnetic field and align with the external field, but become randomly oriented once the external field is removed Diamagnetic materials have no unpaired electrons, and thus create no magnetic field --wood, water, glass

What is pitch?

Pitch is our perception of the frequency of sound -for our purposes, sound frequencies are usually within the normal range of human hearing (20-20,000Hz) -sound waves with frequencies below 20 Hz are called infrasonic waves, while those with frequencies above 20,000 Hz are called ultrasonic waves

Plane-polarized light and optical activity

Plane-polarized light is that in which the electric firleds of all the waves are oriented in the same direction (parallel) -the optical activity of a compound, the result of the presence of chiral centers, causes plane-polarized light to rotate clockwise or counterclockwise by a given number of degrees related to its concentration (specific rotation) Thus, enantiomers will have opposite specific rotations

Distinguish between positive and negative controls

Positive controls are those that ensure a change in the dependent variable when it is expected, while negative controls ensure no change in the dependent variable when no change is expected --in the development of a new assay for detection of HIV, administering the test to a group of blood samples known to contain HIV would be an example of a positive control, while administering the test to a group of samples known not to contain HIV could constitute a negative control --negative controls are often used to assess for placebo effect

Define power in terms of hypothesis testing

Power is the probability of correctly reporting a difference between two populations when one actually exists --correctly rejecting a false null hypothesis --equal to 1-β

Power definition and equation

Power refers to the rate at which energy is transferred from one system to another -measured in Watts (J/s)

isochoric curve

Pressure-volume curves help us determine the work done on or by a system undergoing a thermodynamic process -if pressure remains constant as volume changes, then the area under the curve is the volume change and thus the work done, according to W=P∆V -remember that the area of a right triangle is 1/2(base)(height), should it be necessary

Describe the purpose of randomization in experimental research on human subjects

Randomization is the method used to control for differences between subject groups in experimental research --once each individual is assigned to either a treatment or control group by an appropriate algorithm, the intervention is performed and the results measured

Average acceleration --definition --equation

Recall that acceleration is the rate of change in velocity that an object experiences as a result of some applied force -average acceleration is the change in velocity over the change in time

Dielectric material

Recall that dielectrics are insulating materials placed between the plates of a capacitor, causing the electric field inside the capacitor to be reduced for the same amount of charge on the plates -according to the equation V=Ed, a decrease in the electric field will decrease the voltage across the capacitor, increasing its capacitance -the higher the dielectric constant, the more the Electric field (and thus voltage) is decreased and the more charge can be stored in the capacitor

Distinguish between instantaneous speed/velocity and average speed/velocity

Recall that speed is distance/time and accounts for path taken, while velocity is displacement/time and does not account for path taken -instantaneous speed will always be equal to the magnitude of an object's instantaneous velocity Average speed is the ratio of the total distance travelled over the change in time and is scalar, while average velocity is the ratio of displacement over the change in time and is a vector

Relationship between static and kinetic friction

Recall the equations for static and kinetic friction -the maximum value for static friction will always be greater than the constant value for kinetic friction --the value of µs is always larger than µk

Reliability in terms of basic science research

Reliability (precision) is the ability of the instrument to read consistently, or within a narrow range and contributes to the validity of the instrument --more precise tests have smaller standard deviations (taller, narrow distributions) compared to less precise ones (shorter, wider distributions)

Four rules for drawing ray diagrams for concave mirrors

Remember that for concave mirrors, the center of curvature (C) and the focal point (F) lie in front of the mirror 1. Rays traveling parallel to the axis before striking the mirror are reflected back through the focal point 2. Rays passing through the focal point before hitting the mirror are reflected back parallel to the axis 3. Rays striking the mirror at the point of intersection with the axis are reflected back with the same angle measured from normal (not shown) 4. Rays passing through the center of curvature before striking the mirror are reflected back along the same path

Amount of work needed to move a charge between two points on the same equipotential line and between two different equipotential line

Remember that in terms of electrostatics, work is equal to the potential difference multiplied by the magnitude of the test charge that is being moved between those two points --within an equipotential line, no work is needed --between equipotential line, the amount of work needed is proportional to the potential difference between them and the magnitude of the test charge, but independent of path

Electric potential at some point P near an electrical dipole

Remember the equation for the dipole moment (p) = qd, which may sometimes be used this equation

Resonant frequency

Resonant (natural) frequency is the frequency at which a solid object vibrates when struck -if this natural frequency is within the frequency detection range of the human ear (20-20,000Hz) the sound will be audible -the quality of sound (timbre) is determined by the natural frequency, which may produce pure tones that sound musical, or more random tones that don't

Rotational equilibrium

Rotational equilibrium exists only when the vector sum of all the torques acting on an object is zero -torques that generate clockwise rotation are considered negative, while those that generate counterclockwise rotation are positive -thus, in rotational equilibrium, all of the positive torques must cancel out the negative ones

Selection bias

Selection bias occurs when the group being studied differs from the general population in ways other than exposure --this can be the result of people who volunteer being significant different from people who don't, or differences in age or gender profiles This is a more general term --if groups differ specifically by one factor (i.e. smoking) that affects the outcome, this is known as confounding

Semilog and log-log graph

Semilog graphs are specialized representations of a logarithmic data set in which the otherwise curved nature of the logarithmic data is made linear by a change in the axis ratio (one axis maintains the traditional unit spacing while the other assigns spacing based on a ratio) --log-log graphs are those in which both axes use a constant ratio from point to point

Electrolytic conductivity

Similar to metallic conductivity, but remember that electrolytic conductivity depends on the strength of the solution --distilled, deionized water has such a low ion concentration that it may be considered an insulator, while sea water is an excellent conductor

What are the sound intensity values for the threshold of hearing and threshold for pain?

Soft sound that the average human ear can hear = 1 x 10⁻¹² W/m² Intensity of sound at the threshold of pain = 10 W/m²

Solidification phase change -when does it occur?

Solidification is another name for freezing and occurs at the melting point

Damping/attenuation of sound

Sound and other forms of oscillation are subject to damping/attenuation over time due to the nonconservative forces such as friction, air resistance and viscous drag --note that these forces do not impact frequency, and thus the pitch, of sound

Specific gravity

Specific gravity is the comparison of a fluid's density to that of water at 1atm and 4°C -recall that the density of water = 1g/cm³ = 1000kg/m³ = 1000g/L *Any object with a specific gravity <1 will float, >1 will sink*

Spherical abberation

Spherical abberation is the blurring of the periphery of an image resulting from inadequate reflection of either parallel beams at the edge of a mirror, or inadequate refraction of parallel beams at the edge of a lens

Distinguish between state and process functions

State functions are thermodynamic properties that are a function only of the current equilibrium state -TVPHUGS D Process functions describe the path taken to get from one state to another -heat, work

Static friction --definition --equation

Static friction exists between a stationary object and the surface on which it rests -µs is unitless and dependent on the two materials in contact -N = normal force between two objects that is perpendicular to the plane of contact -static friction ranges from 0 when an object is resting on a surface with no applied forces, to the maximum at which the object begins to move -tire rolling on a road, maintaining a constant point of static contact

Distinguish between statistically and clinically significant

Statistically significant results are those that are not the result of random chance, while clinical significance is a notable or worthwhile change in health status as the result of an intervention --for example a decrease in systolic blood pressure of 1mm of mercury could be statistically significant, but it is not likely to change patient outcomes

Rules for waves produced by strings fixed at either end (5)

Strings are secured at both ends -the distance between nodes is always half of a wavelength -the number of antinodes will always be equal to the harmonic -there will always be one more node than antinode -the first harmonic (n=1) is known as the fundamental frequency -the second harmonic (n=2) is known as the first overtone, which continues according to this pattern

Convex/concave surfaces in spherical mirrors

The 'spherical' in spherical mirror implies that the mirror can be considered a spherical cap or dome taken from a much larger spherically-shaped mirror --if we were to look from the inside of a sphere to its surface, we would see a concave surface, while looking from the outside, we would see a convex surface --for a concave surface, the center of curvature and the radius of curvature are located in front of the mirror, while for a convex surface, the center of curvature and the radius of curvature are behind the mirror

Define the FINER method and list each letter

The FINER method is used to determine whether the answer to one's question will add to the body of scientific knowledge in a practical way, within a reasonable time period Feasible --is the necessary research study feasible? Interesting --do other scientists find this question interesting? Novel --Is the particular question novel? Ethical --Would the study obey ethical principles? Relevant --Is the question relevant outside of the scientific community?

Finding outliers using IQR

The IQR can be used to determine outliers --any value that falls more than 1.5 interquartile ranges below the first quartile or above the third quartile is considered an outlier

Pressure equation and units

The SI unit of pressure is the Pascal --1Pa = 1N/m² --remember that pressure is a scalar quantity

Bulk modulus and its effect on sound

The bulk modulus increases disproportionally more than density as one goes from gas to liquid to solid --therefore, sound travels fastest through solid and slowest through a gas

How does one calculate the position of the third quartile (Q₃)?

The calculate the position of the third quartile, multiply n by 0.75 --if this is a whole number, take the mean of this number and the next --if it is a decimal, round up to the next whole number and take that as the quartile position

Capacitance

The capacitance of a capacitor is defined as the magnitude of charge stored on one plate (+Q on the positive plate and -Q on the the negative plate) over the potential difference across the capacitor

Description and equation for the critical angle

The critical angle is the incidence angle at which the refracted angle is equal to 90° from normal, and the refracted light ray passes along the interface between the two media

Calculating the electric field produced by a capacitor

The direction of the electric field at any point between the plates is form the positive plate toward the negative plate -recall that electric fields always point in the direction a force would be exerted on a positive charge

Direction of the electric field between parallel plates in a capacitor

The direction of the electric field at any point between the plates is from the positive to the negative plate --direction positive charge would move

Wavelength and frequency definitions for a transverse wave

The distance from one wave maximum to the next is called the wavelength, while the frequency is the number of wavelengths passing a fixed point per second

Doppler effect wave souces

The doppler effect assumes wave sources are at rest or moving at speeds slower than the speed of the sound -note that in front of the wave source, crests of sound waves are compressed together, causing an increase in frequency (pitch), while behind the wave source, crests of sound waves are stretched apart, decreasing their frequency

Efficiency of a simple machine

The efficiency of a machine gives a measure of the amount of useful work generated by the machine for a given amount of work put into the system -this is in Newtons! In the case of pulleys, for each additional pulley added, the load is divided among more pulleys, so the effort required decreases proportionally -remember that we would need to pull through a length of rope equal to the load distance times the number of pulleys present -note that efficiency will decrease with each additional pulley added due to the added weight of each pulley and the additional friction forces

Electromotive force

The electromotive force is the potential difference between the two terminals of a galvanic (voltaic) cell when no charge is moving between them

Potential energy stored in a capacitor

The function of capacitors is to store an amount of energy in the form of charge separation, which we can think of as potential energy

Distinguish between the independent and dependent variables

The independent variable is the one that the experimenter is manipulating, while the dependent variable is the one being observed

How are mean values calculated and when are they most useful?

The mean is calculated by adding up all of the individual values within the data set and dividing the result by the number of values --mean values are a good indicator of central tendency when all of the values tend to be close to one another, while outliers can shift the mean toward one end of the range

How are median values calculated?

The median value for a set of data is its midpoint, where half of data points are greater than the median value, and half are smaller --in data sets with an even number of values, the median wll be the mean of the two central data points [(n+1)/2] --in data sets with an odd number of values, the median will be on of the data points --the median tends to be the less susceptible to outliers, but may not be useful for data sets with very large ranges

Threshold frequency and the photoelectric effect

The minimum frequency of light that causes ejection of electrons is known as the threshold frequency (fT), and depends on the type of metal being exposed to radiation --all-or-nothing effect that results in an ejection of an electron with a kinetic energy equal to the difference between hf and hfT (W)

How are mode values calculated and when are they most useful?

The mode is the number that appears the most often in a set of data --the mode is not typically used as a measure of central tendency for a set of data, but the number of modes and their distance from one another is often informative For instance, if a data set has two modes with a small number of values between them, it may be useful to analyze these portions separately or to look for confounding variables that may be responsible for dividing the distribution into two parts

The most common type of error in basic science research is _____________

The most common type of error in basic science research is measurement error

Explain the p-value

The p-value represents the chance that the null hypothesis is correct --calculated from the collected data and compared to the α error determined from the study design --a p-value less than 0.05 means that there is less than a 5% chance that there is not a statistically significant difference between the two groups, and thus we reject the null hypothesis and state that the difference in means is statistically significant

Write out how to calculate probability for independent events occurring simultaneously or indepedently

The probability of two or more such events occuring at the same time is product of their probabilities alone The probability of at least one of two events occurring is equal to the sum of their initial probabilities, minus the probability that they will both occur

How are range values calculated and when are they most useful?

The range of a data set is the difference between its largest and smallest values --range value are heavily affected by outliers because they do not consider the number of items of the data set, nor the placement of any measures of central tendency

Exponential decay constant

The rate at which the nuclei in a sample decay (Δn/Δt) is proportional to the number that remain (n) by the following equation: (Δn/Δt) = -λn --where λ is the decay constatnt

Standard error of mean

The standard error mean is a measure of how precisely one knows the true population and is calculated by dividing the standard deviation by the square root of the number of samples --larger standard deviations will require more samples to generate an acceptable standard error of the mean, while lower standard deviations will not require as many samples

Total mechanical energy

The sum of an object's potential and kinetic energies is its total mechanical energy -in the absence of nonconservative forces such as friction, the sum of the kinetic and potential energies will be constant

Lorentz force

The sum of the electrostatic and magnetic forces that may be acting on charges at the same time

Work-energy theorem

The work-energy theorem offers a direct relationship between the work done by all the forces acting on an object and the change in kinetic energy the object experiences as a result

Electric field magnitude at a point in space some distance from a source charge

This does not require the presence of other (test) charges

How does one calculate the position of the first quartile (Q₁)?

To calculate the position of the first quartile in a set of data sorted in ascending order, multiply the number of values in the data set by 0.25 --if this is a whole number, the quartile is the mean of the value at this position and the next highest positions --if this is a decimal, round up the next whole number, and take that as a quartile position

Sign conventions for single lenses What does a positive or negative value indicate for the following symbols? o i r f m

To identify the real side of a lens, remember that it is where light actually goes AFTER interacting with the lens or mirror -for mirrors, light is reflected and real object are on the real side, while for lenses, the light travels through the lens and the real object is on the virtual side

Finding resultant vectors using the tip-to-tail method

To subtract vectors using this method, simply invert the negative vector -for instance, if it were A-B, A would stay the same, while B would be flipped so that it is pointing in the opposite direction

Torque equation

Torque = r x F = rFsinθ -r is the length of the lever arm -F is the magnitude of the force From what we known about sin angles, no torque is experienced when the force is applied parallel to the lever arm, and the torque is maximal when the force is applied perpendicular to the lever arm

Total internal reflection

Total internal reflection occurs when all light incident on a boundary is reflected back into the original material --this occurs when moving from a medium with a higher refractive index to one with a lower refractive index (n₁ > n₂) at any angle of incidence above the critical angle

Translational equilibrium

Translational equilibrium exists only when the vector sum of all the forces acting on an object is zero -when the resultant force on an object is zero, it could be stationary, or moving at a constant velocity (and constant direction) -think of the blocks in the kaplan book - these can be solved using free body diagrams and Newton's laws

Transverse waves

Transverse waves are those in which the direction of particle oscillation is perpendicular to the propagation -visible light, micro- and x-rays -string attached to a fixed point is another example

Describe type I error in hypothesis testing

Type I (α) error occurs when we report a difference between two populations when one does not actually exist --rejecting the null hypothesis (H₀) when we shouldn't have --null hypothesis is not generally rejected unless α error < 0.05

Describe type II error in hypothesis testing

Type II (β) error when we report no difference between two populations when one actually exists --accepting the null hypothesis (H₀) when we shouldn't have Having too few patients can result in type II error

Ultrasound

Ultrasounds use high-frequency sound waves outside the range of human hearing to compare the relative densities of tissues in the body -an ultrasound machine consists of a transmitter that generates a pressure gradient which also functions as a receiver that processes the reflected sound -because the speed of the wave and travel time is known, the machine can generate a graphical representation of borders and edges within the body by calculating the traversed distance -relies on reflection, and thus an interface between two objects is necessary to visualize anything

Magnetic force that a current-carrying wire experiences when placed in a magnetic field

Use the same right hand rule used for moving charges to find the direction of the force --Thumb points in the direction of L, finger points in the direction of B --Force is in the direction of palm for positive charges, back of hand for negative charges

Poiseuille's law

Used to calculate the flow rate of a fluid with laminar flow through a pipe -η is the viscosity of the fluid -usually focus on the pressure gradient and radius

Venturi flow meter

Used to demonstrate Bernoulli's equation -as the cross-sectional area decreases from point 1 to point 2, the linear speed must increase according to the continuity equation -as the dynamic pressure increases, the absolute pressure must decrease at point 2 -with a lower absolute pressure comes less fluid in the column

Actual voltage supplied from a source conductor

V = Ecell - ir -Ecell is the emf of the cell, and r is the internal resistance of the thing we are talking about Most voltage sources (batteries) and conductive materials have some internal resistance that reduces the voltage supplied to a circuit by some measurable amount -if the cell is not driving any current (like when the circuit is open), the internal resistance is zero, and the voltage of the cell is equal to the emf

Validity in terms of scientific research and instrument error

Validity (accuracy) is the ability of an instrument to measure a true value

Draw out the four inclined plane components

W = Fg

Maximum kinetic energy of an ejected electron

W = h*fT --known as the work function

Phase differences between waves

Waves are in phase if their troughs and peaks coincide, while waves in which the peak of one coincides with the trough of another are 180° out of phase In addition to degrees, the phase difference can be expressed in terms of wavelength 360° difference = 1λ 180° difference = λ/2 etc

Equilibrium position of a wave

Waves oscillate about a central point called the equilibrium position -maximum displacement from the equilibrium position is called the amplitude

Electrical potential energy work

We define electrical potential energy for a charge at a point in space in an electric field as the amount of work necessary to bring the charge from infinitely far away to that point ΔU = W = Fdcosθ = Fr*1 = [kQq/r²][r] = kQq/r --in the equation for work, we define d as the distance r that separates the two charges, and assume the force and displacement vectors to be parallel

Dielectrics in isolated, charged capacitors

When a dielectric material is placed in an isolated (disconnected from any circuit), charged capacitor, the voltage across the capacitor decreases -this is the result of the dielectric material shielding the opposing charges from each other -by lowering the voltage across a charged capacitor, the dielectric has increased the capacitance of the capacitor by a factor of the dielectric constant

Write out Pascal's principle in terms of the following: -pressure -work

When a piston with the cross-sectional area A₁ is pushed down the left column, it exerts a force with a magnitude equal to F₁ and generates a pressure equal to P₁ (P=F/A) while displacing a volume of liquid equal to A₁d₁ -remember that W=P∆V

Elastic potential energy

When a spring is stretched or compressed from its equilibrium length, the spring has elastic potential energy -k is the spring constant that is intrinsic to a particular spring -x is the magnitude of displacement from equilibrium

Wave sources traveling at the speed of sound

When a wave source travels at the same speed as the wave, all of the wave crests meet at the wave source, producing very strong constructive interference at the source location -in the case of an aircraft, these are high-pressure sound waves

Changes in electrical potential and potential energy for positive and negative charges

When allowed, charges will move spontaneously in whatever direction results in a decrease in electrical potential energy -for a positive test charge, this means moving from a position of higher electrical potential to a position of lower electrical potential according to the equation -negative test charges will spontaneously move from a position of lower electrical potential to a position of higher electrical potential (again, because its q value is negative) In both cases however, their electrical potential energy is decreasing!

Nuclear equations and atomic/mass numbers

When balancing nuclear equations, it is important to balance the number of nucleons on both sides by balancing the atomic and mass numbers

What is the difference between insulators and conductors?

When given a charge, conductors are able to distribute it evenly over their surface, while this charge will not distribute evenly across the surface of an insulator

Photoelectric effect

When light of a sufficiently high frequency is incident on a metal in a vacuum, the metal atoms emit electrons -when the light's frequency is above the threshold frequency, the magnitude of the resulting current is directly proportional to the intensity and amplitude of the light beam

Dispersion and light

When light travels through a medium, different wavelengths travel at the same wavelength but different speeds --this implies that the index of refraction of a medium affects the wavelength of light passing through the medium according to n = c/v Like wave speed (v), wavelength is also affected when passing into different media according to λ = (λ₀/n) where λ₀ is the wavelength in a vacuum --thus, violet's smaller wavelength relative to red's means that it will be more affected by changes in media, resulting in its bending more *Frequency is not affected by the refractive index

Young's double-slit experiment

When monochromatic light (light at one specific wavelength) passes through the double slits, an interference pattern is observed on a screen behind the slits --regions of constructive interference between the two light waves appear as bright fringes (maxima) and regions where the light waves interfered destructively resulted in dark fringes (minima) The experiment contributed mightily to our understanding of light as waves that interact with one another

Nonconservative forces and work

When nonconservative forces are present, the total mechanical energy is not conserved -the difference in energy before and after is equal to the work done by the nonconservative forces -unlike conservative forces, nonconservative forces are path dependent - the longer the distance traveled, the larger the amount of energy dissipated -nonconservative forces include friction, air resistance, and viscous drag

torque dipole

When the electric dipole is placed in a uniform external electric field, the equal and opposite charges experience forces exerted on them individually by the field -the torque in each direction is equal to (d/2)Fesinθ, with the positive charge moving with the field and the negative charge moving in the direction opposite the field -the two values can be added to find the net torque, equal to dFesinθ = d(qE)sinθ = pEsinθ

Calculating decibel values after changes in sound level

When the intensity of a sound is changed by some factor, one can calculate the new sound level using this equation

When two electrically neutral metal plates are connected to a voltage source, positive charge builds up on the _______ potential terminal and negative charge builds up on the _______ potential terminal

When two electrically neutral metal plates are connected to a voltage source, positive charge builds up on the higher potential terminal and negative charge builds up on the lower potential terminal

Constructive interference

When waves are perfectly in phase, the displacements are equal to the sum of the amplitude of the two waves -partial constructive interference can occur when waves are not perfectly in phase, resulting in a displacement that is not quite equal to the sum of the wave amplitudes

Destructive interference

When waves are perfectly out of phase, the displacements are equal to the difference in the amplitude of the two waves -partial destructive interference can occur when waves are not perfectly out of phase, resulting in a displacement that is not quite equal to the difference between the wave amplitudes

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

Sound level equation and examples

Where Io is the threshold of hearing = 1 x 10⁻¹² W/m² for reference 1 x 10⁻¹² W/m² = 0 dB 1 x 10⁻¹¹ W/m² = 10 dB 1 x 10⁻⁵ W/m² = 70 dB

Speed of light equation

Where c is the speed of light in a vacuum --all electromagnetic waves travel at this speed in a vacuum

What is the relationship between focal length, image distance and the object distance?

Where d₀ is the distance between the object and the mirror, di is the distance between the image and the mirror, and f is the focal length and is equal to the distance from the focal point to the mirror --true for lenses as well *Remember that the focal length is equal to half the radius of curvature*

Magnification equation for mirrors

Where i = image distance, o = object distance --if |m| < 1, the image is smaller than the object --if |m| > 1, the image is larger than the object

Distinguish infrared spectroscopy and UV-vis spectroscopy with respect to visualizing molecular structure

While IR spectroscopy is used to determine chemical structure through a bond's absorption of different wavelengths of light, UV-vis goes one step further, looking at the absorption of light in the visible and ultraviolet range

Distinction between 95% confidence interval and standard deviations

While both the 95% confidence interval and two standard deviations describe values that fall in the 95% range, standard deviations describe a specific data set, while the confidence interval does not describe the data set but is predictive of the true mean for the entire population --when you see 95%, look at what they are asking for!

Changes in kinetic and potential energy of water during a phase change

While liquid water may have a greater number of microstates due increased freedom of movement, its average kinetic energy is the same as solid water at the same temperature, though the average potential energy increases during a phase change

Electromagnetic spectrum --relate frequency and wavelength with energy

While wavelength increases from left to right on the electromagnetic spectrum, energy is proportional to frequency and increases right to left

Relate frequency and wavelength with energy on the electromagnetic spectrum

While wavelength increases from left to right on the electromagnetic spectrum, energy is proportional to frequency and increases right to left

Work definition and equation

Work is a process by which nonconservative forces transfer energy from one system to another

Center of mass equation

X, Y, and Z are coordinates at any particular point in an objects path through the air -m₁, m₂, m₃ are three sample masses (three point in flight) -only for a homogenous body with symmetrical shape and uniform density should one expect the center of gravity to be located at its geometric center

X¹ × X² =

X¹ × X² = X¹⁺²

X¹ ÷ X² =

X¹ ÷ X² = X¹⁻²

X¹/Y¹ =

X¹/Y¹ = (X/Y)¹

X⁻¹ =

X⁻¹ = 1/X¹

Z score

Z = 0 --> mean Z = +1 --> 1SD above mean Z = -1 --> 1SD below mean If your test score is two standard deviations above the mean, your z score would be 2

Equation to determine speed of light in a medium

c = speed of light v = speed of light in another medium These give the index of refraction, which differ by material but are always greater than 1, indicating that the speed of light in any medium other than a vacuum will be less than c

log(A/B) =

log(A/B) = logA - logB

log(mx10ⁿ) =

log(m x10ⁿ) ≈ n +0.m log(m x10ⁿ) = log(m) + log(10ⁿ) = n log(5x10¹⁰) = log(5) + log(10¹⁰) = log(5) + 10

Write out the equations for wavelength and frequency for waves produced by a string fixed at either end

n is equal to the harmonic -these equations are also true for open pipes, but not for closed pipes

Write out the equations for wavelength and frequency open pipes

n is equal to the harmonic -these equations are also true for strings fixed at both ends, but not for closed pipes

Closed pipe equations for frequency and wavelength

n is equal to the harmonic -these equations are distinct from those for open pipes and strings

Snell's law

n₁sinθ₁ = n₂sinθ₂ -when light enters a medium with a higher index of refraction, it bends toward the normal, and when it enters one with a lower index of refraction, it bends away from the normal *Remember that θ is measured from the normal line, drawn perpendicular to the boundary of the medium, not the surface of the medium*

Heat gained or lost during phase change

q=mL --m is the mass of the substance L is the heat of transformation of the substance -heat of fusion is used for melting/freezing phase changes -heat of vaporization is used for boiling/condensation phase changes

What are the sin and cos values for θ=0°?

sin0 = 0 cos0 = 1 tan0 = 0

What are the sin and cos values for θ=90°?

sin0 = 1 cos0 = 0 tan0 = undefined (y/0)

What are the sin and cos values for θ=180°?

sin180 = 0 cos180 = -1 tan0 = 0

Equation used to locate dark fringes for a slit-lens system

sinθ = nλ/w --where a is the width of the slit --θ is the angle between the line drawn from the center of the lens to the dark fringe in question, and the axis of the lens --n indicates the number of the fringe in question (note that bright fringes are found halfway between dark fringes)

How to find dark fringes on a screen following passage through double slits

sinθ =[n+(1/2)*λ]/d d = distance between the two slits θ = angle between the line drawn from the midpoint between two slits to the dark fringe and the normal n = indicates the number of the fringe λ = wavelength of the incident light wave (note that bright fringes are found halfway between dark fringes)

Exponential decay

where n₀ = the number of undecayed nuclei at t = 0

Resistance equation

ρ = resistivity --some materials are intrinsically better conductors of electricity than others --function of temperature as well - most conductors have greater resistance at higher temperatures