IN THIS CHAPTER
Summary: To test your readiness for the exam, take these short quizzes on these four fundamental topics of AP Physics.
Key Ideas
Find out what you know—and what you don’t know—about mechanics.
Find out what you know—and what you don’t know—about thermodynamics and fluid mechanics.
Find out what you know—and what you don’t know—about electricity and magnetism.
Find out what you know—and what you don’t know—about waves, optics, atomic and nuclear physics.
Focus your exam preparation time only on the areas you don’t already know well.
These short quizzes may be helpful if you’re looking for some additional review of the most fundamental topics in AP Physics. If you can get all these right, you are READY for the exam!
The answers are printed at the end of this chapter.
1. What is the mass of a block with weight 100 N?
2. Give the equations for two types of potential energy, identifying each.
3. When an object of mass m is on an incline of angle θ, one must break the weight of an object into components parallel to and perpendicular the incline.
i. What is the component of the weight parallel to the incline?________
ii. What is the component of the weight perpendicular to the incline?_________
4. Write two expressions for work, including the definition of work and the work-energy principle.
5. Quickly identify as a vector or a scalar:
_______ acceleration
_______ velocity
_______ work
_______ force
_______ speed
_______ mass
_______ momentum
_______ displacement
_______ kinetic energy
6. Name at least four things that can NEVER go on a free-body diagram.
7. Write two expressions for impulse. What are the units of impulse?
8. In what kind of collision is momentum conserved? In what kind of collision is kinetic energy conserved?
9. What is the mass of a block with weight W?
10. A ball is thrown straight up. At the peak of its flight, what is the ball’s acceleration? Be sure to give both magnitude and direction.
11. A mass experiences a force vector with components 30 N to the right, 40 N down. Explain how to determine the magnitude and direction (angle) of the force vector.
12. Write the definition of the coefficient of friction, μ. What are the units of μ?
13. How do you find acceleration from a velocity-time graph?
14. How do you find displacement from a velocity-time graph?
15. How do you find velocity from a position-time graph?
16. An object has a positive acceleration. Explain briefly how to determine whether the object is speeding up, slowing down, or moving with constant speed.
17. Given the velocity of an object, how do you tell which direction that object is moving?
18. When is the gravitational force on an object mg? When is the gravitational force Gm1m2/r2?
19. What is the direction of the net force on an object that moves in a circle at constant speed?
20. Under what conditions is the equation 
valid? Give a specific situation in which this equation might seem to be valid, but is NOT.
1. What is the equation for linear thermal expansion? What are the units for the coefficient of linear expansion?
2. How do you determine the internal energy of a gas given the temperature of the gas? Define all variables in your equation.
3. How do you determine the rms speed of molecules given the temperature of a gas? Define all variables in your equation.
4. State the equation for the first law of thermodynamics. What does each variable stand for? What are the units of each term?
5. Sketch two isotherms on the PV diagram below. Label which isotherm represents the higher temperature.
6. Describe a situation in which heat is added to a gas, but the temperature of the gas does not increase.
7. Imagine you are given a labeled P-V diagram for one mole of an ideal gas. Note that one of the following is a trick question!
(a) How do you use the graph to determine how much work is done on or by the gas?
(b) How do you use the graph to determine the change in the gas’s internal energy?
(c) How do you use the graph to determine how much heat was added to or removed from the gas?
8. What is the definition of the efficiency of an ideal heat engine? How does the efficiency of a real engine relate to the ideal efficiency?
9. For the equation P = P0 + ρgh,
(a) for what kind of situation is the equation valid?
(b) what does P0 stand for (careful!)
10. Write Bernoulli’s equation.
11. State Archimedes’ principle in words by finishing the following sentence: “The buoyant force on an object in a fluid is equal to …
12. For a flowing fluid, what quantity does Av represent, and why is this quantity the same everywhere in a flowing fluid?
13. Write the alternate expression for mass which is useful when dealing with fluids of known density.
1. Given the charge of a particle and the electric field experienced by that particle, give the equation to determine the electric force acting on the particle.
2. Given the charge of a particle and the magnetic field experienced by that particle, give the equation to determine the magnetic force acting on the particle.
3. What are the units of magnetic flux? What are the units of EMF?
4. A wire carries a current to the left, as shown below. What is the direction and magnitude of the magnetic field produced by the wire at point P?
5. When is the equation kQ/r2 valid? What is this an equation for?
6. The electric field at point P is 100 N/C; the field at point Q, 1 meter away from point P, is 200 N/C. A point charge of + 1 C is placed at point P. What is the magnitude of the electric force experienced by this charge?
7. Can a current be induced in a wire if the flux through the wire is zero? Explain.
8. True or false: In a uniform electric field pointing to the right, a negatively charged particle will move to the left. If true, justify with an equation; if false, explain the flaw in reasoning.
9. Which is a vector and which is a scalar: electric field and electric potential?
10. Fill in the blank with either “parallel” or “series”:
a. Voltage across resistors in ________ must be the same for each.
b. Current through resistors in ________ must be the same for each.
c. Voltage across capacitors in ________ must be the same for each.
d. Charge stored on capacitors in ________ must be the same for each.
11. A uniform electric field acts to the right. In which direction will each of these particles accelerate?
a. proton
b. positron (same mass as electron, but opposite charge)
c. neutron
d. anti-proton (same mass as proton, but opposite charge)
12. A uniform magnetic field acts to the right. In which direction will each of these particles accelerate, assuming they enter the field moving toward the top of the page?
a. proton
b. positron (same mass as electron, but opposite charge)
c. neutron
d. anti-proton (same mass as proton, but opposite charge)
13. How do you find the potential energy of an electric charge?
1. —When light travels from water (n = 1.3) to glass (n = 1.5), which way does it bend?
—When light travels from glass to water, which way does it bend?
—In which of the above cases may total internal reflection occur?
—Write (but don’t solve) an equation for the critical angle for total internal reflection between water and glass.
,
describe in words what each variable means:
x
m
L
d
λ
3. The equation d sin θ = mλ is also used for “light through a slit” types of experiments. When should this equation, rather than the equation in question 2, be used?
4. Describe two principal rays drawn for a convex lens. Be careful to distinguish between the near and far focal points.
1.
2.
5. Describe two principal rays drawn for a concave lens. Be careful to distinguish between the near and far focal points.
1.
2.
6. We often use two different equations for wavelength:
, and 
.
When is each used?
7. Name the only decay process that affects neither the atomic number nor the atomic mass of the nucleus.
1. Weight is mg. So, mass is weight divided by g = 100 N/(10 N/kg) = 10 kg.
2. PE = mgh, gravitational potential energy;
PE = 1/2kx2, potential energy of a spring.
3. i. mg sin θ is parallel to the incline.
ii. mg cos θ is perpendicular to the incline.
4. The definition of work is work = force times parallel displacement The work-energy principle states that net work = change in kinetic energy
5. vectors: acceleration, force, momentum, velocity, displacement
scalars: speed, work, mass, kinetic energy
6. Only forces acting on an object and that have a single, specific source can go on free-body diagrams. Some of the things that cannot go on a free-body diagram but that students often put there by mistake:
motion
centripetal force
mass
velocity
acceleration
inertia
ma
7. Impulse is force times time interval, and also change in momentum. Impulse has units either of newton · seconds or kilogram · meters/second.
8. Momentum is conserved in all collisions. Kinetic energy is conserved only in elastic collisions.
9. Using the reasoning from question #1, if weight is mg, then m = W/g.
10. The acceleration of a projectile is always g; i.e., 10 m/s2, downward. Even though the velocity is instantaneously zero, the velocity is still changing, so the acceleration is not zero. [By the way, the answer “—10 m/s2” is wrong unless you have clearly and specifically defined the down direction as negative for this problem.]
11. The magnitude of the resultant force is found by placing the component vectors tip-to-tail. This gives a right triangle, so the magnitude is given by the Pythagorean theorem, 50 N. The angle of the resultant force is found by taking the inverse tangent of the vertical component over the horizontal component, tan-1 (40/30). This gives the angle measured from the horizontal.
12. 
,
friction force divided by normal force. μ has no units.
13. Acceleration is the slope of a velocity-time graph.
14. Displacement is the area under a velocity-time graph (i.e., the area between the graph and the horizontal axis).
15. Velocity is the slope of a position-time graph. If the position-time graph is curved, then instantaneous velocity is the slope of the tangent line to the graph.
16. Because acceleration is not zero, the object can not be moving with constant speed. If the signs of acceleration and velocity are the same (here, if velocity is positive), the object is speeding up. If the signs of acceleration and velocity are different (here, if velocity is negative), the object is slowing down.
17. An object always moves in the direction indicated by the velocity.
18. Near the surface of a planet, mg gives the gravitational force. Newton’s law of gravitation, Gmm/r2, is valid everywhere in the universe. (It turns out that g can be found by calculating GMplanet/Rplanet2, where Rplanet is the planet’s radius.)
19. An object in uniform circular motion experiences a centripetal, meaning “center seeking,” force. This force must be directed to the center of the circle.
20. This and all three kinematics equations are valid only when acceleration is constant. So, for example, this equation can NOT be used to find the distance travelled by a mass attached to a spring. The spring force changes as the mass moves; thus, the acceleration of the mass is changing, and kinematics equations are not valid. (On a problem where kinematics equations aren’t valid, conservation of energy usually is what you need.)
1. ΔL = αLoΔT. The units of α can be figured out by solving for
The units of length cancel, and we’re left with 1/K or 1/°C. (Either kelvins or degrees Celsius are acceptable here because only a change in temperature appears in the equation, not an absolute temperature.)
2. 
. Internal energy is 3/2 times the number of molecules in the gas times Boltzmann’s constant (which is on the constant sheet) times the absolute temperature, in kelvins. Or, U = 3/2n RT is correct, too, because NkB = nR. (Capital N represents the number of molecules; small n represents the number of moles.)
3. 
kB is Boltzmann’s constant, T is absolute temperature in kelvins, and m is the mass of each molecule in kilograms (NOT in amu!)
4. U = Q + W.
Change in internal energy is equal to (say it in rhythm, now) “heat added to, plus work done on” a gas. Each term is a form of energy, so has units of joules.
5. The isotherm labeled as “2” is at the higher temperature because it’s farther from the origin.
6. Let’s put the initially room-temperature gas into a boiling water bath, adding heat. But let’s also make the piston on the gas cylinder expand, so that the gas does work. By the first law of thermodynamics, if the gas does as much or more work than the heat added to it, then ΔU will be zero or negative, meaning the gas’s temperature stayed the same or went down.
7. (a) Find the area under the graph. (b) Use PV = nRT to find the temperature at each point; then, use 
to find the internal energy at each point; then subtract to find ΔU. (c) You can NOT use the graph to determine heat added or removed. The only way to find Q is to find ΔU and W.
8. For an ideal heat engine.
A real heat engine will have a smaller efficiency than this.
9. (a) This is valid for a static (not moving) column of fluid.
(b) P0 stands for pressure at the top of the fluid; not necessarily, but sometimes, atmospheric pressure.
10. 
11. … the weight of the fluid displaced.
12. Av is the volume flow rate. Fluid can’t be created or destroyed; so, unless there’s a source or a sink of fluid, total volume flowing past one point in a second must push the same amount of total volume past another downstream point in the same time interval.
13. mass = density · volume.
1. F = qE.
2. F = qvB sin θ.
3. Magnetic flux is BA, so the units are tesla·meters2 (or, alternatively, webers). Emf is a voltage, so the units are volts.
4. Point your right thumb in the direction of the current, i.e., to the left. Your fingers point in the direction of the magnetic field. This field wraps around the wire, pointing into the page above the wire and out of the page below the wire. Since point P is below the wire, the field points out of the page.
5. This equation is only valid when a point charge produces an electric field. (Careful—if you just said “point charge,” you’re not entirely correct. If a point charge experiences an electric field produced by something else, this equation is irrelevant.) It is an equation for the electric field produced by the point charge.
6. Do not use E = kQ/r2 here because the electric field is known. So, the source of the electric field is irrelevant—just use F = qE to find that the force on the charge is (1 C)(100 N/C) = 100 N. (The charge is placed at point P, so anything happening at point Q is irrelevant.)
7. Yes! Induced emf depends on the change in flux. So, imagine that the flux is changing rapidly from one direction to the other. For a brief moment, flux will be zero; but flux is still changing at that moment. (And, of course, the induced current will be the emf divided by the resistance of the wire.)
8. False. The negative particle will be forced to the left. But the particle could have entered the field while moving to the right … in that case, the particle would continue moving to the right, but would slow down.
9. Electric field is a vector, so fields produced in different directions can cancel. Electric potential is a scalar, so direction is irrelevant.
10. Voltage across resistors in parallel must be the same for each.
Current through resistors in series must be the same for each.
Voltage across capacitors in parallel must be the same for each.
Charge stored on capacitors in series must be the same for each.
11. The positively charged proton will accelerate with the field, to the right.
The positively charged positron will accelerate with the field, to the right.
The uncharged neutron will not accelerate.
The negatively charged anti-proton will accelerate against the field, to the left.
12. Use the right-hand rule for each:
The positively charged proton will accelerate into the page.
The positively charged positron will accelerate into the page.
The uncharged neutron will not accelerate.
The negatively charged anti-proton will accelerate out of the page.
13. If you know the electric potential experienced by the charge, PE = qV.
1. —Light bends toward the normal when going from low to high index of refraction.
—Light bends away from the normal when going from high to low index of refraction.
—Total internal reflection can only occur when light goes from high to low index of refraction.
—sin θc = 1.3/1.5
2. x is the distance from the central maximum to any other position, measured along the screen.
m is the “order” of the point of constructive or destructive interference; it represents the number of extra wavelengths traveled by one of the interfering waves.
L represents the distance from the double slit to the screen.
d represents the distance between slits.
λ represents the wavelength of the light.
3. 
is used only when distance to the screen, L, is much greater than the distance between bright spots on the screen, x. d sin θ = mλ can always be used for a diffraction grating or double-slit experiment, even if the angle at which you have to look for the bright spot is large.
4. For a convex (converging) lens:
• The incident ray parallel to the principal axis refracts through the far focal point.
• The incident ray through the near focal point refracts parallel to the principal axis.
• The incident ray through the center of the lens is unbent.
[Note that you don’t necessarily need to know this third ray for ray diagrams, but it’s legitimate.]
5. For a concave (diverging) lens:
• The incident ray parallel to the principal axis refracts as if it came from the near focal point.
• The incident ray toward the far focal point refracts parallel to the principal axis.
• The incident ray through the center of the lens is unbent.
[Note that you don’t necessarily need to know this third ray for ray diagrams, but it’s legitimate.]
is used to find the wavelength of a photon only. You can remember this because of the c, meaning the speed of light—only the massless photon can move at the speed of light.
is the de Broglie wavelength of a massive particle. You can remember this because of the m—a photon has no mass, so this equation can never be used for a photon.
7. Gamma decay doesn’t affect the atomic mass or atomic number. In gamma decay, a photon is emitted from the nucleus, but because the photon carries neither charge nor an atomic mass unit, the number of protons and neutrons remains the same.
I’ll bet you didn’t get every question on all of the fundamentals quizzes correct. That’s okay. The whole point of these quizzes is for you to determine where to focus your study.
It’s a common mistake to “study” by doing 20 problems on a topic on which you are already comfortable. But that’s not studying . . . that’s a waste of time. You don’t need to drill yourself on topics you already understand! It’s also probably a mistake to attack what for you is the toughest concept in physics right before the exam. Virtually every student has that one chapter they just don’t get, however hard they try. That’s okay . . . (as long as it’s only one chapter.)
The fundamentals quizzes that you just took can tell you exactly what you should and should not study. Did you give correct answers with full confidence in the correctness of your response? In that case, you’re done with that topic. No more work is necessary. The place to focus your efforts is on the topics where either you gave wrong answers that you thought were right, or right answers that you weren’t really sure about.
Now, take the diagnostic test. Once you’ve used the fundamentals quizzes and diagnostic test to identify the specific content areas you want to work on, proceed to the review in Chapters 9–26. Read a chapter, work through the examples in the chapter, and attempt some of the problems at the end of the chapter. Then come back to these fundamentals quizzes. When you respond to every question confidently, you are ready.