Physics 2

Systems NOT in Equilibrium

"translational acceleration problems") Any problem where the object in question has a non-zero acceleration, or net force, is a non- equilibrium problem (constant force causes acceleration) Solve these problems in the same way you would an equilibrium problem, but add "ma" to the losing side. This is preferred over the "Sum of Forces" method because it allows you to ignore signs. Since there is an acceleration we know that the net forces acting from either side are not equal. That combined net force is what causes the object to accelerate. -By adding ma to the weaker side we are making them equal again.

(-) Charge = _________, (+) Charge = _________

(-) Charge = extra electrons ; (+) Charge = relatively fewer electrons, *positive charge is always a lack of electrons!*

Current

*Current flows opposite to the direction of electron flow.* I = ∆q/∆t -It is more intuitive to think of current as the amount of charge (i.e., electrons) that flows past a fixed point per unit time. -Current flows from positive (+) to negative (-) -Electrons flow from negative (-) to positive (+

Energy

*Energy = the capacity to do work *

Electric Field

*Field = An invisible influence that can exert a force on a mass or charge.*

Alternating Current (AC)

*Household wiring* utilizes AC current. Alternating current is also about what it sounds like—both the polarity of the voltage and the direction of the current periodically reverse. -A graph of current versus time for an AC current creates a sine wave.

Electromagnetic Waves

*No medium required*; capable of propagating in a vacuum; *transfer energy and momentum* through space -this is why we can see light from different planets -TRANSVERSE ONLY *(e.g., visible light, microwaves, radio waves, etc.)*

Adding Capacitors

*OPPOSITE PATTERN OF RESISTANCE* Capacitors in Series: add the inverse of the capacitance for each capacitor, then take the inverse of that sum 1/Ctotal = 1/C1 + 1/C2 + 1/C3... Capacitors in parallel: add the capacitance of each capacitor directly Ctotal =C1+C2+C3...

Voltage

*The amount of potential energy a system is capable of storing per unit charge (V = PE/q). * -The amount of work necessary to move a charge against an electric field

Conservation of Charge

*The universe always has zero net charge.* Charge is created by separation. If you separate one electron from a neutral atom you have created one independent unit of negative charge (the electron), but you have simultaneously created one independent unit of positive charge (the cation).

Wires in a Circuit

*The wires between any two elements in a circuit are assumed to be perfect conductors* resistance here = zero; all resistance occurs at the resistors

Converging Lenses (a.k.a., convex, positive)

*Usually* produces a positive, real, inverted image. -*When the object is inside the focal point it produces a negative, virtual, upright image.*

Describe the work done when a force, applied at an angle of 45 degrees to the horizontal, is used to push a box across the floor. Describe the work done when a box is moved at a constant velocity across a frictionless table. Describe the work done by the string when a ball on a string is swung in a circular motion.

*When the force is not in the same direction as the displacement, only that component of the force that is aligned with the displacement does work.* -Thus the work done is Fdcos(45). If the angle between force and displacement vectors is 90°, then no work can be done by that force. -If a box is moved at constant velocity horizontally, on a frictionless table, no work is done because there was no net pushing/pulling force, no friction force, and the energy of the box was the same before and after the motion (ignoring some net force necessary to get the box moving). -For a ball on a string no work is done by the centripetal force created by the string because this force is exactly 90° to the tangential displacement vector at any instant.

Snell's Law

*smaller index of refraction = larger angle to the normal because smaller indices of refraction have faster mediums*

Virtual vs. Real Image

-*Virtual*: There is no actual light emanating from or reaching the image (e.g., *the image formed behind a plane mirror*) -*Real*: There is actual light at the image (e.g., an image formed on your retina)

Derived Equations for Force in an Electric Field

-For gravity near earth: F = mg *For constant E-field: F = qE* -For real gravity: F = Gmm/r2 *For point charge E-field* F = Kqq/r2 (Coulomb's Law)*

Derived Equations for Electrical Potential Energy

-For gravity near earth: PE = mgh *For constant E-field: PE = qEd* -For real gravity: PE = -Gmm/r *For point charge E-field: PE = Kqq/r* *(attractive if it involves opposite charges, and repulsive if it involves like charges)*

Derived Equations for Electrical Voltage

-For gravity near earth: V = gh *For constant E-field: V = Ed (d measured against E)* -For real gravity: V = -Gm/r *For point charge E-field: V = Kq/r*

Derived Equations for Strength of the Electric Field

-For gravity near earth: g = F/m (from F = mg) *For constant E-field: E = F/q (or E = V/d)* -For real gravity: g = Gm/r2 *For point charge E-field: E = Kq/r2*

Variables that Affect Capacitance

-Increasing plate area increases capacitance because there is more room available on the inside surface of the plate to store electrons. -Electrons do not line up on the sides or back of the plate, so increasing plate thickness will have no effect on capacitance -Increasing the distance between the plates increases voltage for a given Q on the plates, which decreases capacitance according to C = Q/V. - Increasing the strength of the dielectric increases capacitance because it lowers the electric field between plates (because the field from the aligned dipoles partially cancels out the main field from the plates) allowing for a lower voltage for the same amount of charge. -Increased voltage, increases the charge stored but does not increase capacitance, which is the charge stored per voltage.

When you see the following, THINK WORK!

1) Change in velocity (change in KE = work; this is the most common example) 2) Change in height (change in gravitational PE = work) 3) Change in position of masses/planets/etc. in space (change in gravitational PE = work) 4) Change in position of a charge (change in electrical PE = work) 5) Compression of a spring (change in elastic PE = work) 6) Friction (change in internal energy = work) 7) Air Resistance (change in internal energy = work)

When is work negative? Two Conventions

1) If force and displacement are in opposite directions we say work is negative (e.g., lowering a barbell) 2) If it is done by the system it is negative.

When is work positive? Two Conventions

1) If the force and the displacement are in the same direction, work is positive (e.g., pushing a barbell up) 2) If work is done on the system it is positive (Gaining energy)

The Four Lens/Mirror Rules:For single-lens systems only!

1) Object distances (do) are ALWAYS (+) 2) Image distances (di) or focal point distances (f) are (+) if they are on the same side as the observer, and (-) if they are on the opposite side from the observer. diverging/concave lens = -f converging/convex lens = +f 3) The observer and the object are on the same side for a mirror, and on opposite sides for a lens (You have to be behind your glasses to see through them!) 4) PRI / NVU: "Positive, Real, Inverted" and "Negative, Virtual, Upright" These two trios of image descriptors always stick together. As long as you can confidently establish that the image has one of those three characteristics, you automatically know the other two! positive image= same side of the observer negative image = opposite side of observer

Ways to Think About Voltage

1) Voltage = potential energy/charge or mass (V = PE/q) 2) Voltage =an entity you can multiply by mass or charge to get PE (gh*m = mgh = PEgravitational ; Ed*q = PEelectrical = V*q)

Thin Lens Equation (Can Use for thin Mirrors too)

1/f = 1/di + 1/do di = image distance do = object distance

Intensity in Decibels Equation

10*log(I/I0); log (n * 10^m) = m + 0.n -I is the intensity of the sound wave in W/m^2 -I0 is the threshold of human hearing (I0 = 1 x 10-12 W/m2; which is usually given).

Conductor

A conductor is a material that allows the flow of electrons through it relatively unimpeded. This being said, even the best conductors do exhibit some small degree of resistance to the flow of electrons (superconductors being the possible exception).

Constant Electric Field/Uniform Electric Field (equate to "assumed" gravity or gravity near earth)

A constant electric field, as the name implies, is constant and its strength does not vary with distance - Be aware that the MCAT tends to use the variable d for distance when discussing constant electric fields (a.k.a., uniform electric fields) -A constant electric field exists between the two plates of a parallel plate capacitor. -Notice in the diagram above that *although the electric field is constant* at any point between the plates (recall that closer lines represent a stronger field), *voltage is NOT constant* -The equipotential lines show that voltage is constant if you move parallel to the plates, but not if you move perpendicular to the plates..

Electric Dipoles

A dipole is a separation of positive and negative charges of equal magnitude. When the MCAT discusses dipoles they will either be: 1) two opposite charges of equal magnitude very near one another in space, or 2)any object/molecule with a charge separation—wherein one side bears a full or partial positive charge and another side bears a full or partial negative charge (i.e., a polar bond). When a dipole is exposed to an electric field it will tend to align itself with that field.

Longitudinal Waves

A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. (Electromagnetic waves) -Longitudinal waves cause disturbances parallel to their direction of travel http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html

What lens type is found in a magnifying glass?

A magnifying glass is also a converging lens. -Note that in a magnifying glass we see an upright image—even though converging lenses are said to normally create positive, real, INVERTED images. This is an example of the caveat given in bold in the lesson: When the object is inside the focal point it produces a negative, virtual, upright image. This is the case with a magnifying glass. In order to see the magnified image the object must be inside the focal point of the lens.

Point Charge Electric Fields (equate to "real" gravity or gravity in space)

A point charge field is an electric field created by a point charge. The strength of the electric field varies with the distance r from the point charge -Be aware that the MCAT tends to use the variable r for distance when discussing point charges

Resistor

A resistor is a material that tends to impede the flow of electrons. All resistors do conduct electrons to some small degree.

Semi-conductor

A semiconductor is a material thought to be right in the middle of an insulator and a conductor (in terms of conductivity vs. resistivity)

Superconductor

A superconductor is a material that *under very precise conditions is thought to exhibit zero resistance to electron flow.*

Transverse Waves

A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. -Transverse waves cause disturbances perpendicular to their direction of travel

A 5 kg mass is accelerating down a 60 inclined plane at 5 m/s2. What is the force experienced by the box due to friction?

A; This is another non-equilibrium problem. Set the forces up the plane equal to the forces down the plane and add ma to the losing side, which in this case is the side of the upward forces. This should give you ma + Fup = Fdown. Note that ma is the mass times the actual acceleration of 5, not times gravity; that Fup is the frictional force we're looking for; and that Fdown is equal to mgsin(60). Solving should give you answer A, 20 N.

Near-Sighted

Able to focus clearly on close objects, but not on distant objects -The image is formed *on the front of the retina* - lens has too much focusing power (the focal length is too small). This causes the light to bend more than it should, and the image is formed closer to the lens than it should. -In normally-sighted individuals, images coming into the eye are focused directly on the retina -nearsightedness (myopia): either an elongation of the eye or severe curvature of the cornea such that the image tends to focus too early (results in people having more difficulty seeing things at a distance) corrected by concave lens longer eye needs less curvature

Far-Sighted

Able to focus clearly on distant objects, but not close objects -The image is formed *behind the retina* -For a far-sighted person, the lens has too little focusing power (the focal length is too large). This causes the light to bend less than it should, and the image is formed farther from the lens than it should. -Farsightedness (hyperopia): an eye that is too short or a cornea that doesn't curve enough. (people have more difficulty seeing things that are relatively close) corrected by convex lens (shorter eye needs more curvature to shorten focal point

Truck engine A has twice the power of truck engine B. True or False? a) Truck A can accelerate the same trailer from zero to 50m/s in half the time, b) Truck A can accelerate a trailer to a velocity v, in a time t, that is twice as massive as the trailer Truck B can accelerate to the same velocity in the same time period, c) Truck A can accelerate the same trailer to twice the velocity in the same amount of time. (Note: Assume the mass of the truck is negligible compared to the mass of the trailer.)

Accelerating the same trailer from 0 to 50 m/s would represent the same amount of work. Doing so in half the time would represent twice the power. Truck A does have twice the power of Truck B, so this is true. b) According to KE = 1/2mv2, twice as much energy would be required to accelerate at trailer twice as massive to the same speed. If this is accomplished in the same period of time, twice the power will be required. Truck A does have twice the power, so this statement is also true. c) Accelerating a trailer to twice the velocity will actually require four times the energy due to the square on velocity in the KE equation. Therefore, Truck A cannot accomplish this task and this answer is false.

What will be the effect of each of the following on the force experienced by a charged particle in a magnetic field? a) velocity slows to zero, b) the particle moves at an angle of 90 degrees with respect to the magnetic field vector, c) the particle moves at an angle of 180 degrees with respect to the magnetic field vector, and d) the particle moves in the same direction as the magnetic field vector.

According to F = qvBsin, if velocity is zero there is no force. The charged particles must move within the magnetic field for any force to be created; b) This same equation shows that force is at a maximum when = 90; c) and d) Once again, this same equation shows that when = 0 or 180 the force will be zero (because the sin of both angles is zero).

Sound Resonance

All objects have one or more natural frequencies at which they will vibrate when disturbed. Some objects produce a random array of different vibrational frequencies. Other objects (e.g., musical instruments) vibrate at non-random natural frequencies which are integer multiples of a number (e.g., 200Hz, 400Hz, 600Hz, 800Hz) -These orderly frequencies are called harmonics. When one object is vibrating near another object it can cause the neighboring object to begin vibrating at that same frequency. -*If the exact frequency at which the second object is caused to vibrate happens to be one of its natural frequencies (e.g., harmonics) the two objects are said to be in resonance.* -*Via constructive interference, two such instruments can produce a much louder sound.* -If the first object causes a vibration in the second object that is NOT a match to one of its natural frequencies, resonance does not occur.

Which form of light has the greatest velocity in a vacuum?

All of the waves on the electromagnetic spectrum travel at the same speed in a vacuum, the speed of light. For the MCAT use: *c = 3.0 x 10^8 m/s.* This value will not be given to you.

Know the Order and Relative Energy of Each Class of Electromagnetic Radiation

All of these waves are light!!! NOT JUST THE VISIBLE LIGHT SPECTRUM -*Longer wavelength = lower frequency = less energy; Shorter wavelength = higher frequency = more energy* *R*ich *M*en *I*n *V*egas *U*se *X*pensive *G*adgets

Diverging Lense (a.k.a., concave, negative)

Always produces a negative, virtual, upright image.

Insulator

An insulator is a material with a *very, very high resistivity.* -There is no perfect ideal insulator that allows zero current flow under all conditions. However, materials like glass and Teflon allow negligible current flow up to extremely high voltages.

Bar magnets

Bar magnets are usually made of nickel, iron, or an associated alloy. -Normally, the electrons in a metal are approximately split between spin states, and thus the tiny magnetic fields they create cancel each other out. In a bar magnet they are partially aligned, creating a net magnetic field.

Adding Batteries

Batteries in series: add the voltage of each battery directly; however, *current (Amps) and capacity [amp-hours, (Ah)] will remain the same* Vtotal =V1+V2+V3... Batteries in parallel: add the current (Amps) or capacity (Ah) ratings for each battery directly, but *voltage will remain the same.* For example, if you wire two 12 V batteries with a 50 Ah capacity together in SERIES, you will get the equivalent of one 24V battery with a 50 Ah capacity. If you wire the same two 12 V batteries together in PARALLEL, you will get the equivalent of one 12 V batter with twice the capacity: 100 Ah.

RIGHT HAND RULE for direction of the force

Be sure you can use this tool, the MCAT likes this one!

Light Traveling from Slow to Fast Medium?

Bent AWAY from the normal

Light Traveling from a Fast to Slow Medium?

Bent TOWARDS the normal

Equilibrium on an Inclined Plane:

Call all forces acting down the plane "down forces," and all forces acting up the plane "up forces." -The force down the plane due to gravity is always given by F = mgsinθ. -The force of friction is always parallel to the plane, but opposite the direction of the sliding motion. There will never be an acceleration perpendicular to the plane, so you can ignore these forces. -After you have accounted for all possible forces, set the sum of the "down forces" equal to the sum of the "up forces"

Capacitors

Capacitors store energy and charge by holding electrons on plates separated by a very small distance. Symbol: Two vertical lines of equal length C=Q/V

Relationship Between Magnetic Fields and Electric Fields

Changing electric fields create magnetic fields, and changing magnetic fields create electric fields.

Describe the energy transformations that take place as a rocket ignites, combusts its rocket fuel, launches into the air, rises to its maximum height, then falls back to earth and strikes the ground.

Chemical energy stored in the bonds of the rocket fuel is transferred into kinetic and gravitational potential energy as the rocket rises. If air resistance is taken into account some energy will also be dissipated as heat due to drag. Gravitational PE reaches a max at the max height and is then transferred back into kinetic energy (and heat if considering air resistance) as the rocket falls back to earth. When the rocket strikes the ground its kinetic energy is transferred into heat energy.

Name the type of energy possessed or created by each of the following: an explosion, a chemical reaction, a collision, any moving object, any object with height, a spring, a battery, two positive charges, and a water in a tank.

Chemical energy turns into heat energy and the kinetic energy of any flying debris; In a chemical reaction chemical energy is transferred between reactants and products—in an exothermic reaction heat is released; in a collision the KE of the objects before the collision is transferred into heat energy and is also used to do work on the object, creating damage/deformity/etc.; any moving object has kinetic energy; any object with height has gravitational potential energy; a spring stores elastic potential energy; a battery stores chemical energy; two separated charges contain electrical potential energy; water in a tank has gravitational potential energy and kinetic energy of the molecules.

Concave Mirrors

Concave Mirrors = Follow the same rules as converging lenses. POSITIVE REAL INVERTED IMAGE THINK SPOON!

Convex Mirrors

Convex Mirrors = Follow the same rules as diverging lenses. NEGATIVE, VIRTUAL, UPRIGHT THINK OF THE SPOON

Current Flow Through Parallel Resistors

Current flow through parallel resistors is always apportioned inversely based upon resistance. For example, if one resistor has twice the resistance, it will receive only half the current.

The Doppler Effect

Describes the difference between the actual frequency of a sound and its perceived frequency when the source of the sound and the sound detector are moving relative to one another v = *relative velocity*, not the velocity of either object c= the speed of the wave, either 3 x 10^8 m/s for light or *340 m/s for sound* moving away from each other ...vsource-vobserver

Diffraction

Diffraction is the bending of a wave around a corner or obstacle.

Diffraction

Diffraction is the tendency of light to spread out as it goes around a corner or through a slit. -Without diffraction the characteristic interference patterns would not be formed.

Direct Current (DC)

Direct current is about what it sounds like, the direct flow of current through a circuit from positive to negative (or in terms of electron flow from negative to positive). -DC current is the kind of power used in automobiles because it comes directly from the battery. -In fact, if something uses a battery you would be perfectly safe on the MCAT to assume that it must be an example of DC current. -This would therefore include all automobile electronics, anything you plug into the cigarette lighter (unless it is an inverter of course), your cell phone (battery), etc.

Dispersion

Dispersion is a change in index of refraction based on the frequency (or wavelength) of a wave. -*In a material with dispersion, different frequencies (or wavelengths) will be refracted to different angles, for the same incident angle.* - The classic example of dispersion is white light passing through a prism. For visible light traveling through glass longer wavelengths have smaller indices of refraction and therefore bend less than smaller wavelengths. This means red light bends the least, and violet light bends the most. This difference in refraction separates the white light into its colored components and produces a rainbow.

Energy of a Photon

E = hf h = Planck's constant, which is always given.

How will increasing each of the following change the distance between the fringes? a) wavelength, b) distance between the two slits, c) distance between the second and third screen.

Each answer is easily obtained by manipulation of the equation given: x = L/d. This is a simplified version of an equation relating to Young's experiment called "the small angle approximation." a) increasing wavelength will increase the distance between fringes (x); b) increasing the distance between slits (d) will decrease the distance between fringes (x); c) increasing the distance between the second and third screen (L) will increase the distance between fringes.

Velocity of Sound Waves in a Solid

Elastic property = " spring back" very strong Intertial Property = density of solids (much higher) -sound waves will increase speed when traveling through a solid compared to a gas (because of the higher bulk modulus of the solid).

Velocity of Sound Waves in Gas

Elastic property = bulk modulus Inertial Property = density Also Teperature dependent so: v ~ sqrt(T)

Electron Flow

Electron flow, however, goes from a high concentration of electrons (negative charge) to a low concentration of electrons (positive charge -Closer lines represent a stronger field; Lines further apart represent a weaker field.

Heat Transfer on the MCAT

Energy change in a system could be due to heat transfer as well. However, we have never seen the MCAT introduce this kind of heat on physics work and/or energy problems. -They will expect you to know that non-conservative forces such as friction dissipate some energy as "heat," leaving less energy available to do work (e.g., the velocity of a ball at the bottom of an inclined plane is less with friction than without. -This is because the energy dissipated to "heat" was not available to increase the KE of the ball). -However, this use of the word "heat" refers to an increase in the internal energy of molecules, not the "heat transfer" (Q) included in the 1st Law of Thermodynamics (∆E = W + Q). We'll cover these topics in more detail in the chemistry chapters.

Heat Energy

Energy dissipated as heat. -*On the MCAT, this is usually heat dissipated from a collision, or from a current-carrying wire.* The terms "heat energy" and "internal energy" are used almost interchangeably.

Equation for Force Exerted on a Charged Particle Moving in a *Magnetic Field*

F = qvBsinθ ; where θ is the angle between v and B. B= magnetic field v = velocity UNITS of B = N*s/C*m or Kg/A*s2 = tesla (T)

Field Lines

Field lines should always be drawn with their tails toward the positive charge and their heads toward the negative charge. *Current is said to flow from positive to negative*, so it could be compared to the orientation of field lines. CURRENT AND ELECTRIC FIELD = POSITIVE->NEGATIVE

Fluorescent light has to be of __________ energy (________ wavelength) than the source light used to cause the excitation.

Fluorescent light has to be of lower energy (longer wavelength) than the source light used to cause the excitation. -In most cases, the emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation.

Levers

Fm = mg(L1/L2) L1 = Lever arm for the mass L2 = Lever arm for the applied force

Ramps

Fm = mg(h/d) h = height of the ramp and d = is the distance along its hypotenuse. Fm refers to the force necessary to do the work with the machine; which will be less than doing it without the machine. -*Remember that the work with or without the machine will always be the same!* Also note that when the MCAT states a ramp is "5 meters long" or calls it a "5 meter ramp" this means the hypotenuse of the ramp is 5m.

Hydraulic Lifts

Fm = mg(h1/h2) h1= distance traveled by the large plunger and h2 = distance traveled by the small plunger or Fm = mg(A2/A1) A1 = cross-sectional area of the large plunger A2 = cross-sectional area of the small plunger

Pulleys

Fm = mg/(# of vertical ropes directly lifting the mass) *CAUTION*: Not every rope that is vertically oriented should be counted and entered into the above pulley equation. To be counted, a vertical section of rope must lift the mass directly, either by being attached to the mass, or by lifting a pulley that is attached to the mass. To test this, imagine isolating a single segment of rope and pulling upward on that segment only. Would that segment lift the mass? If not, it should not be included in the calculation.

The force necessary to lift a mass without a machine (at constant velocity)

Fnecessary = mg

A factory employee is attempting to move a 100 kg crate from the floor to a table 2 m off the floor. The maximum pushing, lifting, or pulling force of which he is capable is 200 N. If he were to construct a ramp to assist him, what is the minimum ramp length that will allow him to accomplish the task?

For any of these type of questions where you are asked to figure out how long a ramp must be, how long a fulcrum must be, etc. or to figure out how much a given person could actually lift using the aide of a machine, figure out first either 1) how much the object would take to lift without the machine or 2) how much the person can lift without the machine. Then you should be able to see the factor that is needed to make up the difference. In this case, the crate requires 1,000 N of force, but the worker is only capable of 200 N. So he must magnify the distance by a factor of 5 to keep the work the same. This means the hypotenuse of the ramp must be 5 times longer than the height, which is 2 meters. The ramp must therefore be 10 meters long.

Temperature and Resistivity

For good conductors (i.e., metals), it is generally true that resistivity increases linearly with temperature. -The resistivity of semiconductors actually decreases with temperature.

Total Internal Reflection

For light crossing a boundary from a slower to a faster medium (like from glass or water into air), if the angle of refraction would be 90° or more, the incident light does not enter the second medium at all—100% of the light is reflected off the boundary and back into the first medium. -*For total internal reflection to occur, the light must be passing from a higher-index medium to a lower-index medium.*

Converging Lenses Far vs. Near

For objects that are far away, assume the light rays hitting the lens are all parallel. -Considering converging lenses now, the rays will be focused to the focal point a distance f away from the lens. -As the object approaches the lens, however, the image will no longer be exactly at the focal point f.

Plane Mirrors

For plane mirrors only, the image and the object will always be equal distances on either side of the mirror.

Critical Angle

For waves passing from higher index mediums into lower index mediums, the critical angle is the angle of incidence for which the angle of refraction will be 90°. -If this angle is exceeded, refraction ceases and all waves are reflected back into the more dense medium—a phenomenon called "total internal reflection." -Snell's Law can be used to solve for the critical angle by plugging in 90° for θ2 n1sinθ2 = n2sin(90) If the two indices of refraction are know, the unknown variable θ1 would be the critical angle

Wave Frequency

Frequency of the wave is the number of times the wave cycle repeats in a given time period, usually each second (units = 1/s or s-1 or Hertz [Hz])

Pitch

Higher pitch sounds have higher frequencies, and -lower pitch sounds have lower frequencies

The Work-Energy Theorem

If a net force does work on a rigid object, the work done on that object is equal to the change in the kinetic energy of the object. W = KEfinal - KEinitial

Second Step to Solving An Ohm's Law Problem

If the above steps don't work apply Kirchoff's Rules -Kirchoff's 1st Rule: *total current into a node = total current out of a node* -Kirchoff's 2nd Rule: in any closed loop circuit, the sum of the voltages equals zero (i.e., *the sum of the voltage drops across each resistor equals the total voltage of the battery*) -Kirchoff's rules will often provide you with the missing piece of information. Then you may need to return to the rules above to finish simplifying your circuit.

MCAT QUESTION

If the problem was a positive charge instead of a mass, and there were a constant E field pointing downward, the voltage would increase as we raised the charge.

Non- Dispersive Medium

If the wave speed depends only on the physical properties of the medium then the wave speed is a constant, independent of frequency. -If the medium were non-dispersive, then the two waves would by definition travel the same speed. The frequency wavelength would necessarily be the same in that case. http://www.acs.psu.edu/drussell/Demos/Dispersion/dispersion.html

Block B weighs 2/5 less than Block A. If Block A is placed a distance x from a fulcrum, where should Block B be placed to balance the fulcrum?

If you go too quickly on this one, you'll probably miss it . . . and hopefully learn a lesson. Block B weighs 2/5 LESS than A, which does not mean it weighs 2/5 as much as Block A; subtract 2/5 from one and you get 3/5. Since B weighs 3/5 as much as A, it will need to be 5/3 as far away from the fulcrum, which is answer A. 1|Page

Which of the above variables must be shared by two waves in order for those waves to have the same phase?

In order to be 100% in phase, two waves would have to have the same frequency, wavelength, and timing of maxima/minima (which could be done if they share the same time/place of origin). -The latter is important because two waves might share the first two variables in common and would therefore be in phase if started from the same point, but would NOT be in phase if started from that same point 2 seconds apart. -If they shared frequency and wavelength they would, by definition, share the same velocity. They do NOT have to share amplitude to be in phase, and therefore intensity can also be different between two waves that are in phase. -Also by definition, if they share the same frequency they must share the same period.

Infrasound

Infrasound is sound of a frequency too low to be perceived by the human ear.

Wave Intensity

Intensity is a measure of power per unit area. Waves have power because they transport energy from one point to another in a given amount of time. -Intensity is proportional to the square of the amplitude and the square of the frequency. The intensity of any sound or mechanical wave is directly proportional to the amplitude squared and the frequency squared: I : A^2f^2. -For light waves, the intensity is also proportional to the amplitude squared, but not to the frequency squared. Units: Watts per square meter I= Power/Area (4πr^2)

A common problem with manipulating equations using Ohm's Law:

It CANNOT be said that if voltage increases, and current remains constant, resistance will increase. -*Resistance is a permanent quality of the resistor its self* -The only way to change the resistance is to either 1) physically remove one or more resistors from the circuit and replace them with other resistors that have different Ohms ratings, or 2) change the temperature of the resistor. If you were very careful, you could say it this way: "If voltage increases, in order for current to remain constant, I would need to increase the resistance in the circuit." Which is something I could do by adding more resistors.

Positive charge in a battery Positively charged ions Positive charge as part of a dipole Moving positive charges

It is labeled positive because it is deficient in electrons relative to the other terminal. -Cations are positively charged because they are deficient in electrons. They have fewer electrons than they do protons. -The positive side of a polar bond is positive because the electrons are being pulled toward the side of the more electronegative atom. The negative side thus has extra electron density and the positive side is slightly deficient in electrons compared to normal. -You have probably seen drawings of positive charges lined up on the surface of an object. This is often seen when discussing induction or static electricity They would have to be some atom or molecule that is deficient in electrons and therefore bears a positive charge.

Without a Machine:

It is often helpful to determine the amount of force necessary to lift or move an object without a machine. You can then compare that to the force necessary with the machine. -These two values will differ by an exact ratio. Notice that each of the formulas below includes this ratio (h/d, L1/L2, etc.). -For example, a ratio of 1/5 gives a 5X machine that reduces the force necessary by a factor of 5 (a.k.a., a "mechanical advantage of 5"). -Or, you could say that it allows a person capable of a maximum force, F, to create a force of 5F when using the machine.

Kinetic Energy Formula

KE = . 1⁄2mv^2

Harmonics (string or pipe with matching ends—both nodes, or both antinodes)

L = nλ/2 Givs all harmonics n= 1,2,3....... Likely need to make a connection with v=fλ Each harmonic has one more node and antinode than the previous http://www.physicsclassroom.com/Class/waves/u10l4d.cfm

Harmonics (one node and one antinode; e.g., pipe open at one end only)

L = nλ/4 *Gives only the odd harmonics* n = 1, 3, 5

Magnification Equation

M = -di/do = hi/ho -If you get a negative number for the magnification, M, that result simply tells you that the image is inverted. hi= image height ho = object height We define the ratio of image height to object height (hi/ho) as the magnification m.

Mechanical Energy (Explanation and Equation)

ME = KE + PE In the absence of non-conservative forces such as friction, drag, air resistance, etc., mechanical energy is always conserved (a.k.a. total energy).

Magnetism

Magnetism = Analogous to electricity, with these changes: 1) Replace positive charges with north poles 2) Replace negative charges with south poles 3) Magnetic field lines proceed from north to south, instead of from positive to negative *Magnetic fields are created by changing electric fields* *Magnetic fields are also created by currents (moving charges)* *Any movement, velocity, rotation, etc., of a charged particle causes a change in the electric field created by that charge, and thus creates a magnetic field.*

Magnification and Power for Two Lens Systems

Magnification: M = m1m2 Power:P=P1+P2

Wave Intensity as Sound Travels

Many waves, such as sound, travel outward from their origin in all directions simultaneously—creating a wave front in the shape of a growing sphere. -Because intensity is measured per square meter, its magnitude decreases according to the area of the growing sphere (i.e., the m2 term increases, decreasing the intensity): A = 4πr^2

Open System

Mass and energy CAN be exchanged with the system

Isolated System

Neither mass nor energy can be exchanged

Will the north pole of a magnet attract or repel positively charged particles?

No force is created between a static electric field and a static magnetic field. -However, if the positively charged particles began to move then they would experience a force vector with a direction that could be determined using right hand rule—assuming that is, that the movement of the charges is NOT parallel to or 180 to the magnetic field vector.

All of the following involve moving charges and thus create a magnetic field

Nuclei with an odd atomic or mass number (because they exhibit nuclear spin) -Electrons (because they orbit and spin) -Current (because it is moving electrons) -Bar Magnets

Static vs. Dynamic Equilibrium

Objects at rest are in static equilibrium; objects moving at a constant velocity are in dynamic equilibrium. -In both cases the net force experienced by the object must be zero.

The Beat Frequency

Occurs when two waves with close to the same frequency interfere (increased amplitude) fbeat =|f1-f2|

Closed System

Only energy can be exchanged with the system

Optical Power Formula

P = 1/f

Electrical Power Equations

P=IV; P=I^2R; P=V^2/R Only memorize one, solve V=IR for missing variable and plug in to get other two variables

Potential Energy Stored by a Capacitor Equation

PE capacitor (U) = 1⁄2QV or *1⁄2CV^2* or 1⁄2Q^2/C Only memorize one of the above equations. Then solve C = Q/V for the missing variable and plug it into the one you've memorized. This will allow you to get both of the other two. We recommend you memorize U = 1⁄2CV2 because it is so similar to the formula for KE.

Elastic Potential Energy Equation Formula

PE elastic = 1⁄2kx^2

Electrical Potential Energy Equation

PE electrical =*Kqq/r* or *qEd* or *qV*

Gravitational Potential Energy Formula

PE gravity = -Gmm/r or mgh

Wave Phase

Phase is a relative measure of how closely two waves (typically with the same frequency) are oriented to one another in space, expressed in radians or degrees. *Two waves that are "in phase" should cross the x-axis at the same point, but may have different amplitudes.*

The 1st Law of Thermodynamics

Put simply, energy change is not always completely due to work; some energy is often lost to heat. Work and heat are the only two ways energy can be transferred into or out of a system. Often, this law is simply stated as the formula below: E=W+Q -Work=energy transfer via a force -Heat=energy transfe rvia energy flow from hot to cold

Visible Light Spectrum

ROY G BIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet) -Red light is the lowest energy, lowest frequency, and longest wavelength; -Violet light is the highest energy, highest frequency, and shortest wavelength.

A hand-held calculator uses two small electrodes separated by a distance of 2 cm, with a potential difference of 10 V. If the current across the electrodes is 1.0 x 10-4 A, how much power is required to run the calculator?

Recall that P = IV; thus P = (1x10-4A)(10V) = 10 x 10-4 or 1 x 10-3, which is equivalent to 1.0 milli-Watt (mW)

Reflection

Reflection is the bouncing of a wave off of an interface between two mediums.

Refraction

Refraction is the bending of light at an interface between two mediums with different indices of refraction

Constructive Interference

Regions where the amplitudes of superimposed waves add to each other, increasing amplitude

Destructive Interference

Regions where the amplitudes of superimposed waves subtract from each other, decreasing amplitude.

Mechanical Waves

Require a medium to propagate; cannot propagate in a vacuum; transfer energy in the direction of propagation, but *do not transfer matter* Transverse Mechanical Waves require a stiff medium to propagate and cannot propagate in air/liquid Longitudinal Mechanical Waves (Ex: sound waves)

Resistance (Equation)

Resistance can be conceptualized as the equivalent of drag in fluids, or friction between solids. The equation below describes resistance in circuits, but the same parameters are roughly applicable to heat flow and fluid flow as well. *R = ρL/A* ρ = resistivity, L = length, A = cross-sectional area shorter wire and larger cross-sectional area are preferred because increased resistance can lead to heating wires (P = I^2R with fixed I in a household)

Resistance on a Molecular Level

Resistance on the molecular level is a function of the ability of the electron to travel in a free path between atoms. -Electrons flow through conductors by striking an atom and thereby ejecting one of the other electrons from that same atom. -This process of absorbing and ejecting electrons is the slowest part of the process (i.e., the rate-limiting step). -Therefore, the more time the electrons spend in free space between atoms the less "impeded" they will be and the faster they will flow through the conduit. -Increased temperature causes increased movement of the atoms in the conduit, increasing the average number of collisions an electron will have with atoms and therefore increasing resistance.

Adding Resistors (Series and Parallel)

Resistors in series: add the resistance of each resistor directly Rtotal =R1+R2+R3... -Resistors in parallel: add the inverses of the resistance for each resistor, then take the inverse of that sum 1/Rtotal = 1/R1 + 1/R2 + 1/R3...

First Step of Solving a Circuit Using Ohm's Law

SIMPLIFY THE CIRCUIT -combine resistors -combine capacitors -combine batteries

Switches

SYMBOL: a diagonal break in the line between circuit components Closed = electrons flow; Open = no electron/current flow

Resistors

SYMBOL: zig-zag line *There is always a voltage drop across any resistor when current flows through it.* -Internal Resistance: Batteries experience internal resistance due to the resistivity of their internal components. This results in a voltage drop per the rule stated above and therefore decreases (slightly) the actual terminal voltage of the battery.

Simple Machines

Simple machines (a.k.a., machines) *reduce the amount of force necessary to perform a given amount of work*. -*Machines never reduce or change the amount of work!* MACHINES REDUCE AMOUNT OF FORCE NEEDED TO PERFORM WORK

Solving Equilibrium Problems

Solve all equilibrium problems by setting the forces or torques equal to each other: -FLeft = FRight ; -Fup = Fdown ; -Tclockwise = Tcounterclockwise. We recommend that you list the opposing forces in two columns on your scratch paper. In the right column, write down all of the forces (or the equations that predict those forces) which push the object to the right. In the left column, write down those forces that push it to the left. One of these forces should be an unknown. Next, add up each column and set the sum of the two columns equal to each other. Finally, solve for the unknown variable. Always draw a free- body diagram and double check your chart for any missing forces.

Sound Production

Sound is always created by a vibrating medium. -These vibrations propagate through liquids or solids, and *generate pressure waves that propagate through gases such as air.* -*As a mechanical wave, sound CANNOT propagate in a vacuum.*

The Particle Model of Light

Supposes that light is a particle -photoelectric effect is the major support for this model

The Wave Model of Light

Supposes that light is a wave -Young's Double Slit Experiment provides support for this model because only waves would show the diffraction and interference patterns necessary to create the characteristic light and dark bands.

Batteries

Symbol: two vertical lines of unequal length. -*The longer line represents the positive terminal and the shorter line represents the negative terminal.* -This convention is very important. Often it will be the only clue as to which direction current/electrons are flowing in a circuit. -THINK OF BATTERIES AS: Electron pumps that push electrons onto the negative terminal of the battery. This creates a separation of charge and therefore a potential difference between terminals that will drive electron flow around the circuit to the positive terminal. -*ANYTHING THAT SEPARATES CHARGE CREATES A VOLTAGE AND CAN BE THOUGHT OF AS A TYPE OF BATTERY*

Torque and Lever Arms Equations

T=Fl (In most cases this equation can be used) T=Frsinθ T=mgl (for gravity) l=lever arm *r=distance between the force and the point of rotation;* rsinθ always = l, but r = l only when θ = 90) *Use rsinθ force applied is not perpendicular to r.*

Wave Amplitude

The "distance" between the equilibrium point and a crest, or between the equilibrium point and a trough. (Distance is in quotes because the units of amplitude are not necessarily meters. -They would be, for a wave on a rope, but not, for example, for a voltage wave or the electric field component of a light wave. Those would have units of volts or volts/m, respectively.) amplitude= loudness

Root Mean Square Calculations

The "root mean square" (RMS) method of calculating both voltage and current are necessary for alternating current applications because the current and voltage over time are sinusoidal. This creates a problem because the average of a sine wave centered at the origin is zero. If you randomly sampled the voltage in your household wiring it could literally have a voltage of 120 V one instant and a voltage of -120 V the next instant. That would average to zero, even though the alternating current does deliver a continuously useful source of power (It can dissipate energy during both cycles). -*Power companies therefore use the RMS method to calculate the average power delivered to your home (otherwise, according to P = V^2/R, V = 0 and you don't owe the power company anything!) -RMS is a mathematical calculation and it can be applied to voltage, current, to sine waves, or even to other waveforms such as square waves. To find RMS, 1) you take readings at various time intervals, square all of those readings, 2) take the average of those squares (i.e., the mean of the squares) and then 3) take the square root of that average. You should understand this mathematical process for the MCAT as well as the general idea behind why it is necessary. *The rms voltage or current is equal to the equivalent DC voltage or current that would deliver the same about of power*

The Decibal System

The decibel system is a rating system for the intensity of sound within the range of human hearing. -10-fold increases in sound intensity are represented by 10.0 unit increases on the decibel scale. For example, a sound 10 times more intense is rated as 10 decibels higher, a sound 100 times more intense is rated as 20 decibels higher, and a sound 1,000 times more intense is rated as 30 decibels higher.

The Dielectric

The dielectric is the substance between the two plates. All capacitors have a dielectric, even if it is just air. -Other dielectrics are often inserted between the plates, such as gels or composites. -Once inserted, some energy stored in the capacitor is used to align the polar molecules in the dielectric (i.e., dipoles) with the field between the plates. -*Increasing the strength of the dielectric increases the capacitance* allowing more charge and energy to be stored. -*The dielectric must be an insulator to minimize the leakage of electrons between plates*

Wavelength

The distance between two adjacent crests (a.k.a., peaks, maxima), or between two adjacent troughs (valleys) - For a more complex wave, the wavelength is the distance between points where the wave begins to repeat itself. For example, the wave used to represent heart rhythm has multiple peaks per cycle, so the distance between peaks would NOT be the wavelength.

Velocity of a wave on a string

The elastic property is its tension -The inertial property is linear mass density (mass per unit length)

Chemical Energy

The energy contained within chemical bonds, or the energy stored/released due to the separation and/or flow of electrons (i.e., in a battery).

Internal Energy

The energy of the internal vibrations and random motions of molecules and/or atoms within a system. Non-conservative forces such as friction or drag acting on a moving object result in the transfer of kinetic energy into internal energy.

Does the power of the human eye increase or decrease when ciliary muscles contract?

The flexing of the ciliary muscles results in an increase in the curvature of the lens. -As the curvature of a lens increases, its focal point decreases. Because power is the inverse of focal length, we know that a more curved lens (i.e., contracted ciliary muscles) produces a shorter focal point and therefore a more powerful lens.

A 120 kg rocket is accelerating toward the ground at 8 m/s2. The engine creates a downward force of 200 N. A small parachute is attached to the rocket and slows its descent. What is the force due to air resistance against the parachute? (Assume all air resistance is due to the parachute.)

The forces acting down on the rocket are: (1200 N) + 200 N = 1400 N. The forces acting up on the rocket are: Fair (only). Adding ma (ma = 120 kg*8 m/s2 = 960 N) to the losing side (upward), the equation is: 1400 N = Fair + 960 N. Therefore Fair = 440 N.

A 15 kg toy rocket is falling toward earth with a constant velocity of 20 m/s. A small amount of fuel still present in the cone creates a downward force of 30 N. What is the force due to air resistance?

The forces pushing the rocket down are: mg (150 N) + 30 N = 180 N. The force due to air resistance is the only upward force, so it must equal 180 N. Air resistance is in equilibrium with the downward force

"fundamental frequency."

The frequency of the first harmonic, each additional harmonic has its own unique frequency and wavelength

What happens to the frequency and wavelength of light when it refracts into a new medium?

The frequency will not change as the wave moves from one medium to another. We like to think of the frequency as the permanent "identifier" of a wave. -For example, you will often hear waves referred to as "a 400 Hz wave, a 200 Hz wave, etc." This makes sense because the frequency stays the same as it passes through different mediums. -The wavelength, however, must change from medium to medium (assuming they have different densities) because we know that the velocity of electromagnetic waves does NOT remain constant from medium to medium—it is generally higher in less dense mediums and lower in more dense mediums. -According to v = fλ if frequency remains constant and velocity changes, wavelength must change. Because velocity increases in low index mediums, wavelength must also increase in low index mediums.

Attenuation

The gradual loss of intensity as a wave passes through a medium. -In non- dispersive mediums this is due to scattering (i.e., reflection) of some waves and absorption of wave energy.

Drawing Harmonics

The harmonics shown below are all for a single vibrating guitar string of the same length. Notice that the 1st harmonic is only one-half of a wavelength, the second harmonic is exactly one wavelength, and the third harmonic is one and one-half wavelengths.

Two Lens Systems (e.g., binoculars, telescopes, etc.)

The image formed by the first lens becomes the object for the second lens. https://www.khanacademy.org/science/physics/geometric-optics/lenses/v/multiple-lens-systems

Values for the Index of Refraction

The index of refraction is a relative comparison of the speed of light in a vacuum (c) to the speed of light in that medium (v): n = c/v. -Therefore, in order to get a value less than one, the speed of light in that medium would have to be greater than the speed of light in a vacuum which is only possible for circumstances beyond what the MCAT would be testing on. -*A value of 1.5 for n simply tells us that the medium has some density, and is more dense than air, which has a value for n that is very close to one.*

What type of lens is found in the human eye?

The lens of the human eye is a converging lens. It creates a real image of the object onto the retina.

Car A is traveling at 20 m/s toward car B, and car B is traveling toward car A at 15m/s. Car B honks its horn, and car A perceives the frequency of that sound as f. After they pass one another, car B slows down to 5m/s and honks its horn again. What must the motion of car A be at that exact moment, in order for the perceived frequency of the second horn to equal f?

The original relative velocity described in the question was a 35 m/s approach between source and observer. -To match the exact frequency shift they must also be approaching one another at the same relative velocity in the second scenario. In the second scenario Car B is traveling 5 m/s away from car A, thus car A must turn around and travel TOWARD car B at a rate of 40 m/s in order to experience the same perceived frequency from car B's horn. (This is the answer using our appropriate formulas; the "correct answer" using the full-fledged formulas will be quite close to that value, but far more difficult to obtain.)

Wave Period

The period is the *amount of time required for one full wavelength* to pass a fixed point (units = seconds) -Amount of time for one full wave cycle T=1/f

The Photoelectric Effect

The photoelectric effect is the observation that electrons are ejected from a material when light of sufficiently high frequency is used—but not until a threshold frequency is reached.

Which of the two scenarios represents the greater voltage (or voltage equivalent, gh)? [Note: Assume gravity near Earth is a constant field] a) A 1 kg rock held 10 m above the Earth's surface vs. the same 1 kg rock held 10 m above the surface of Venus? (g on Venus = 8.8m/s2); b) A 1 kg block held 10 m above Earth's surface vs. A 1 kg block held 20 m above Earth's surface; c) A 1 kg block held 10m above Earth's surface vs. a 20 kg block held 10 m above Earth's surface; d) An electron 2 cm from the positive plate of a parallel plate capacitor vs. an electron 4 cm from the positive plate; e) A charge of -2 C held 2 cm from the positive plate of a parallel plate capacitor vs. a charge of -4 C held 2 cm from the positive plate of the same capacitor.

The similarities between gravitational fields and electric fields are so consistent that some sources refer to mass as "gravitational charge." The primary difference is that gravitational fields are always attractive and electric fields can be attractive or repulsive. We think this is a very serviceable comparison for MCAT students if for no other reason than the fact that you only have to memorize one set of equations. a) Defining gravitational voltage as gh, the rock 10m above Earth has the higher voltage because g is larger; b) The block held 20m high has the greater voltage; c) Both blocks would have the same voltage. ; d) Ignore the fact that there's an electron, since potential is defined relative to positive test charges. A positive charge 2 cm from the positive plate has more potential energy than one 4 cm from it, since if you release the charge at 2 cm it will move away from the positive plate. So the voltage is higher at 2 cm ; e) Both charges would be at the same voltage. Remember that voltage is PE per charge!

Overtone

The terms "1st overtone," "2nd overtone," "3rd overtone," etc., are used occasionally. -The 1st overtone is NOT the same as the 1st harmonic! -The first harmonic is called the fundamental frequency, -The second harmonic is the 1st overtone, the third harmonic is the 2nd overtone, and so forth.

Dual Nature of Light

The two are reconciled by quantum mechanics: photons are described by "wave functions" which sometimes act as macroscopic waves and sometimes as macroscopic particles. -If light were purely a conventional wave, increasing the amplitude sufficiently high would always result in ejection of an electron—which is not seen. -Instead, we observe that the energy of each individual photon (set by its frequency) must itself be high enough for an electron to be ejected. There is a one-to-one correspondence between photons and electrons.

Dispersive Medium

The wave speed depends on the frequency of the wave. . However, now the wave speed depends on frequency, with higher frequencies traveling faster than lower frequencies. As a result, the wave pulse spreads out and changes shape as it travels.

How much work is done when a 1,000kg car traveling at 40 m/s applies its brakes and comes to a complete stop?

The work done is equal to the change in energy from the KE of motion at 40 m/s to zero KE at rest. KE = 1/2mv^2 = (.5)(1,000)(40)2 = 8 x 105J.

What is the work done on a spring compressed by 0.5m?

The work done is equal to the change in potential energy of the spring. PE = 1/2kx2 = (.5)(10)(.5)2 = 1.25 J

Equipotential Lines

These lines are drawn perpendicular to field lines and represent areas of equal voltage (i.e., electrical potential). -Equipotential lines will form concentric circles around a point charge, but not around a dipole, or in a constant electric field such as is found between the plates of a capacitor

Power Equations

Think of power in EXACTLY this way and in this EXACT order: 1) P = ∆E/t 2) P=W/t 3) P = Fdcosθ/t 4) Pi = Fvcosθ CAUTION: Equation (4) gives only "instantaneous power." It should only be used when you are asked to solve for power using force and velocity. UNITS=watts (J/s)

A 10 kg rock is accelerating toward the earth at 8 m/s2. What is the force due to air resistance?

This is a non-equilibrium problem. Set the forces up equal to the forces down and then add ma to the losing side. Alternatively, you can just ask yourself, "What would the acceleration be without air resistance?" It would be 10 m/s2, so we just need to know what force would be necessary to accelerate (or decelerate in this case, but remember according to MCAT they're the same thing) a 10 kg object at 2 m/s2. According to F = ma, that would be 10*2 or 20 N.

Standing Waves

This is a special case of simultaneous constructive and destructive interference between two waves with identical frequencies, moving through the same medium, but in opposite directions. -At points of maximum destructive interference, the waves cancel entirely, forming a node. At points of maximum constructive interference, the waves add completely to form an antinode. -*A standing wave exhibits no net transport of energy and does not itself propagate. In other words, there is no translational movement of nodes or antinodes.* NO TRANSLATIONAL MOVEMENT OR NET ENERGY TRANSPORT

What is the strength of the electric field between the two electrodes described in the previous question?

To answer this question correctly, you must remember that V/m and N/C are equivalent units for electric field strength, E. Simply take the voltage from the problem, divide it by the meters (note you must change cm to meters) and you have the field strength. The correct answer could be given in either N/C or V/m.

An object of mass 500 kg is sliding across a flat surface due to a horizontal rope pulling it with a tension of 1,000 N. If the coefficient of kinetic friction between the block and the surface is 0.05, and the coefficient of static friction is 0.09, what is the acceleration of the object?

To know the acceleration on an object you must know the net force. Here you have the force of 1,000 N being opposed by the force of friction. The force of kinetic friction is given by Fk = ukFnormal. Plug in the coefficient of kinetic friction given and multiply the mass of the vehicle by gravity to get the normal force. You should get a force of 250 N. This means the net force is only 750 N. According to a = F/m, the acceleration is 750/500 or 1.5 m/s2. You can ignore the static friction because the object is sliding. Recall that sliding always indicates kinetic friction and no sliding indicates static friction.

Comparing Electric Field Equations to Gravity:

To learn all of the electric field equations (and there are quite a few), review your gravity equations and only memorize how they relate to each other: -g (strength of gravitational field) = E (strength of electric field) -G (constant) = K (constant) -h (distance) = r or d (both variables are used for distance in electric field equations) -m (mass) = q (charge) -F = F (used straight across) -gh (gravitational potential) = V (voltage, electrical potential)

Fulcrums and Boards on Strings

To solve, set Tclockwise = Tcounterclockwise. -Be sure to include all torques, including the torque created by the mass of the board (Note: some questions define the board as massless, or to be of negligible mass). -For a board with mass, the force due to the mass of the board will act at the center of mass, which will always be at the exact linear center of a uniform board. -*Also, don't forget to set torques equal to each other, NOT forces. Your units should be N*m. * -Finally, forces or tensions located exactly at the center of rotation do not create a torque (since r = 0) and can therefore be ignored. -For example, for a mass centered over the fulcrum, gravity would create no torque.

One tractor engine is found to have two times the power of a second tractor engine. In the same amount of time, compared to the second engine, the first engine can: (Note: assume the mass of the tractor and engine are negligible compared to the mass of the trailer) I. accelerate a trailer with twice the weight from rest to 50 km/h. II. do twice the amount of work. III. accelerate the same trailer from rest to twice the maximum speed.

Twice as much power will mean twice as much work/time. So statement II is true, by definition. In considering statements I and III, you should realize that the work done to accelerate a trailer will be 1⁄2mvfinal2, since the initial kinetic energy is zero (Work = ∆KE). Thus, doubling the mass will double the work, but doubling the final speed will quadruple the work. So statement I is true but statement III is false, leading to choice C as the correct answer. This also demonstrates that a naïve application of P = Fvcos can lead you astray, as this might convince you that doubling the velocity doubles the power. However, this equation cannot easily be used when the velocity is changing. For the MCAT, you should ONLY use this equation for "instantaneous power."

Ultrasound

Ultrasound is sound of a frequency too high to be perceived by the human ear.

Ohm's Law

V=IR

Wave Speed

V=λf 1) Wave speed (velocity) is determined by the medium 2) Frequency *never* changes when a wave moves from medium to medium 3) Wavelength *does* change when a wave moves from medium to medium

Wave Velocity

Velocity is how fast the wave moves in space in m/s. It is given by v = fλ

#2 Way to think of Work

W = Fdcosθ or Favg * d Think of work this way second. Any time a force is applied across a distance, work has been done. Students tend to think of this only as something like pushing a block across a table. However, if a ball falls from a height h, a force (mg) has been applied, across a distance (h). Similarly, if a small asteroid with a velocity v strikes Earth's atmosphere and is gradually slowed down, a force has clearly been exerted on the asteroid by the atmosphere, converting its kinetic energy to heat energy d= displacement UNITS= Joules N*m or kg*m2/s2

#1 Way to Think of Work

W = ∆Energy -*If energy changed, THINK WORK!*

Wave Velocity in Various Mediums

Wave speed equal to square root of an elastic property the medium divided by an inertial property: *v = sqrt(elastic/inertial).* -The elastic property is often called a "modulus". -The inertial property is a type of density.

Draw a charge vs. time graph for the charging and discharging of a capacitor.

When a battery is connected to a series resistor and capacitor, the initial current is high as the battery transports charge from one plate of the capacitor to the other. -The charging current asymptotically approaches zero as the capacitor becomes charged up to the battery voltage. -Charging the capacitor stores energy in the electric field between the capacitor plates.

When a dipole is exposed to an electric field...

When a dipole is exposed to an electric field it will tend to align itself with that field. A dipole that is NOT aligned with the electric field has potential energy because alignment with the field is a lower energy state than alignment against the field.

Perhaps surprisingly, a pattern of fringes can also be produced if the double-slit screen is replaced with a screen having only one slit. Provide possible explanations for this observation.

When only a single slit is used, diffraction can still occur. One way of looking at this is through Huygen's Principle, which states that every point in the slit will act as a source of spherical waves. These waves interfere with each other just like the waves coming through each of the two slits in Young's experiment. However, the interference isn't as drastic as with a double-slit, and what results is a very bright central fringe and much lighter bands on either side.

Fourth Step to Solving An Ohm's Law Problem

When you have a simplified circuit you can use Ohm's Law (V = IR) to solve for any of the three variables.

A 100kg diver jumps directly off a cliff and into the water below. Immediately before hitting the water, his speed is 50 m/s. He continues to a depth of 10 m before being slowed to a stop by the water. Calculate the average force exerted on the diver by the water.

When you see "average force" on the MCAT, it is a dead giveaway that it will be dealing with work (W = Favgdcos0). In this case we can calculate the work done on the diver in slowing him down from 50 m/s to 0 m/s. This will come from the difference in kinetic energy at the two points. Because we were given the distance over which this occurred and F and d are in the same direction, we can just divide work by distance and get the average force (F = W/d). Plug in the numbers and you should get answer D. Alternatively you can find the average acceleration acting as if it were constant from the initial speed and distance traveled (v02 = 2ax), and F follows from F = ma.

White light will shift _________ if the Doppler effect causes a perceived increase in frequency

White light will shift blue if the Doppler effect causes a perceived increase in frequency (perceived decrease in wavelength).

White light will shift ____ if the Doppler effect causes a perceived decrease in frequency

White light will shift red if the Doppler effect causes a perceived decrease in frequency (Perceived increase in wavelength)

Many questions require you to combine the formula for the energy of a photon with the wave speed formula. Can you do this? What does it allow you to do?

You can combine the formula E = hf with the wave speed formula c = fλ (c = the speed of light) to obtain E = hc/λ. -Since h and c are constants, this allows you to calculate the energy of a photon knowing only its wavelength.

Third Step to Solving An Ohm's Law Problem

You can use Ohm's Law across a single resistor. Doing so may be necessary to get a piece of information needed to simplify the circuit. -Be sure you are using only information for that resistor and NOT for the main battery, current through the circuit as a whole, etc. *Ohm's Law across a resistor states that: Voltage drop across that resistor = current through that resistor multiplied by the resistance of that resistor.*

If 20 kg hangs exactly 3.0 meters from the fulcrum, what mass should hang on the other end, 5.0 meters from the fulcrum, to balance the board?

You could solve this problem by setting torques clockwise equal to torques counterclockwise, but it would be better if you could look at this situation conceptually and use your knowledge of manipulating equations. -T = Fl shows us that force and lever arm are inversely related. Therefore, if a mass is a factor of 5/3 farther from the fulcrum than is the first mass, then that mass will need to be 3/5 as large as the first mass. 20 kg*3/5 = 12 kg.

Force Vectors in Two-Dimmensions

You may well have a force that acts in two-dimensions, say at an angle of 30° to the horizontal. -In such a case, simply enter into your table the formula that predicts the component of that force that acts up, down, left or right. -For example, suppose a rope is attached to a box on its right side at an angle of 60° to the horizontal and applies a force of 100N. -On your scratch paper, under the "forces to the right" column, you would input "100cosθ." This is the formula that will give the rightward force (in the x-direction) exerted on the box by the rope.

Young's Double Slit Experiment

Young shone a monochromatic light through a screen with a single slit in it. The purpose of this slit was to create coherent wavefronts (since lasers weren't around in Young's day). -Behind the first screen he placed a second screen with two narrow, parallel slits. These created the diffraction pattern. Finally, behind the second screen he placed a third screen. Light traveled through the first two screens and formed alternating pattern of light and dark bands on the third screen. -For the experiment to work, the light traveling through each of the two slits in the middle screen must be coherent and have the *same frequency* and polarization

What will be the result of adding two otherwise identical waves that are: a) 180 degrees out of phase, b) 360 degrees out of phase, c) 270 degrees out of phase?

a) the waves will exactly cancel, b) 360 out of phase is the same a 0 out of phase, which is the same as being "in phase." Therefore the waves will add to one another to create a wave with an amplitude equal to the sum of the amplitudes of the two previous waves, c) There will be multiple areas of constructive and destructive interference, creating a new waveform with multiple crests and troughs.

Charge is quantized e = _____________

e- = 1.6 x 10^-19 C

Focal Point Equation for *Mirror*

f = 1⁄2r

The frequency of any harmonic is equal to

n*fundamental frequency (e.g., if the first harmonic is exactly 200 Hz, the 2nd is 400 Hz, the 3rd is 600 Hz, etc.)

Index of Refraction:

n=c/v

Examples of Equilibrium

o Terminal velocity o Constant velocity o Objects at rest o Balanced fulcrums or boards hanging from strings o Objects floating in a liquid Watch carefully for clues. -In addition to the clues we've already mentioned, such as "constant speed," "constant velocity," and "terminal velocity" (which all clue you in to the fact that the body is in equilibrium), you now have two new clues you should be familiar with. -If an object with a point of rotation is "stationary," or "exactly balanced," then it must be in equilibrium. If an object is in rotational equilibrium, the net torque on the object must be zero

Young's Double Slit Experiment Equation

x =λL/d x is the distance between fringes, λ is the wavelength of light used, d is the distance between the two slits L is the distance between the "double slit" and the final screen This formula is given solely to help you see relationships and to aid you in answering a specific question type the MCAT tends to ask about Young's experiment—namely, how will changes in wavelength, distance between the slits, etc. alter the pattern of fringes produced.