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The AP Physics 2 Practice Exams 2
AP Physics 2: Practice Exam 2
Section 1 (Multiple Choice)
Directions: The multiple-choice section consists of 50 questions to be answered in 90 minutes. You may write scratch work in the test booklet itself, but only the answers on the answer sheet will be scored. You may use a calculator, the equation sheet, and the table of information. These can be found in the appendix or you can download the official ones from the College Board at: https://apstudents.collegeboard.org/courses/ap-physics-2-algebra-based/assessment.
Questions 1—45: Single-Choice Items
Choose the single best answer from the choices provided, and mark the answer with a pencil on the answer sheet.
1. A beam of various particles is launched into the space between two oppositely charged parallel plates as shown in the figure. It is known that the particles are all traveling at the same initial velocity as they enter the region, and that particle P is a proton. What else can be inferred?
(A) Particle A could be a β-particle.
(B) Particle B could be an α-particle.
(C) Particle C must be more massive than a proton.
(D) Particle D could be an electron.
Questions 2 and 3 refer to the following material.
The figure shows an electric potential field created by charges that are not shown.
2. A small negative charge is placed at the location labeled A. Which one of the following vectors most closely depicts the direction of the electric force on the charge?
3. At which location is the electric field strongest, and which direction is the electric field?
4. Two spheres with charges +Q and —Q of equal magnitude are placed a vertical distance d apart on the y-axis as shown in the figure. A third charge +q is brought from a distance x, where x >> d, horizontally toward the midpoint between +Q and —Q. The net force on +q as it is moved to the left along the x-axis:
(A) increases and remains in the same direction
(B) increases and changes direction
(C) remains the same magnitude and in the same direction
(D) remains in the same direction but decreases to zero
5. Two stationary charges are separated by a distance D as shown in the figure. Charge #1, on the left, has a mass of M and a charge of −2Q. Charge #2, on the right, has a mass of 2M and a charge of + Q. The two charges are released. Where will the charges collide and why?
(A) The charges will collide closer to charge #1 because charge #1 has a larger magnitude charge and will exert a larger force on charge #2 giving charge #2 a larger acceleration.
(B) The charges will collide in the middle because the larger charge of #1 cancels the larger mass of #2.
(C) The charges will collide in the middle because the force between the charges will be equal and opposite in direction.
(D) The charges will collide at the center of mass, which is closer to charge #2 because there are no outside forces on the system.
6. The circuit shown has a battery of emf ε; three identical resistors, R; two ammeters, A1 and A2; and a switch that is initially in the open position as shown in the figure. When the switch is closed, what happens to the current reading in the two ammeters?
7. A kitchen toaster is connected to a variable power supply. The voltage difference across and current through the toaster are measured for various settings of the power supply. The figure shows the graph of the data. The resistance of the toaster:
(A) varies up and down with voltage
(B) increases linearly with input voltage
(C) is constant at 0.2 Ω
(D) is constant at 5.0 Ω
Questions 8 and 9 refer to the following material.
The figure shows three resistors, X, Y, and Z, which have different shapes but are made of the same material. Resistors X and Y have a length L. Resistor Z has a length of 3L/2. The resistors as shown are connected to a voltage source.
8. Which of the following correctly ranks the current in the resistors?
(A) IX = IY = IZ
(B) IX > IY > IZ
(C) IY > IX > IZ
(D) IZ > IX > IY
9. Which of the following correctly ranks the potential difference across the resistors?
(A) VX = VY = VZ
(B) VX > VY > VZ
(C) VY > VX > VZ
(D) VZ > VX > VY
10. A capacitor with movable parallel plates is connected to a battery. The plates of the capacitor are originally a distance x apart as shown in the figure. With the battery still connected, what happens to the energy stored in the capacitor and the electric field between the capacitor plates, if the plates are moved to a new distance x/2?
11. A proton with a velocity v is moving directly away from a wire carrying a current I directed to the right in the +x direction as shown in the figure. The proton will experience a force in which direction?
12. A magnetic field directed into the page in the −z direction is placed between the plates of a charged capacitor as shown in the figure. The magnetic and electric fields are adjusted so that a particle of charge +1 e moving at a velocity of v will pass straight through the fields in the +y direction. Which of the following changes will cause the particle to deflect to the left as it passes through the fields?
(A) Increasing the electric field strength
(B) Changing the sign of the charge to −1 e
(C) Increasing the velocity v of the particle
(D) Decreasing the magnetic field strength
13. A stationary charge is placed a small distance from an iron bar magnet as shown in the figure. Which of the following correctly indicates the cause and direction of the force on the charge?
(A) The charge experiences an electric force to the right.
(B) The charge experiences a magnetic force to the right.
(C) The charge experiences a magnetic force to the left.
(D) The charge experiences no force.
14. An electron e is placed in an electric field and a second electron is placed in a magnetic field as shown in the figure. Both are released from rest at the same time. How do the forces on the charges compare?
(A) Both electrons experience a constant force in the same direction.
(B) Both electrons experience a constant force but in different directions.
(C) One electron experiences a constant force in a constant direction, while the other experiences a constant force that changes direction.
(D) One electron experiences a constant force, while the other experiences no force.
15. A technician sets up a red laser pointer and directs light at a strand of hair suspended between two blocks in such a way that the light falls on a screen behind the hair as shown in the figure. This produces a pattern of alternating light and dark fringes on the screen. The technician makes one change to the setup and repeats the procedure. This change produces a similar pattern, but the light and dark fringes are spaced farther apart. Which of the following could account for this different pattern?
(A) The hair was replaced with one of larger diameter.
(B) The screen was moved to the left farther away from the hair.
(C) The red laser was replaced with a blue laser.
(D) The red laser was moved to the right farther away from the hair.
16. Your lab group has been asked to determine the index of refraction of a plastic rectangular prism. Your partner places the prism on a sheet of paper, traces its shape, shines a beam of light through the prism, and traces the incoming ray. The light exits the prism at multiple locations. Your partner marks the exit locations of the three brightest rays on the side of the prism as shown in the figure. Is this enough information to determine the index of refraction of the prism, and why?
(A) Yes, by measuring ray angles with a protractor and using the concepts of refraction
(B) Yes, by measuring the internal reflected angles with a protractor and using the concepts of total internal reflection
(C) No, the exit rays from the prism should have been traced. It is impossible to utilize the concepts of refraction without having the exit ray directions.
(D) No, without knowing the velocity of the beam inside the prism, you cannot use the index of refraction equation.
17. A very slow-moving positron interacts with a stationary electron. Which of the following statements correctly describes a possible outcome of this reaction and why it would occur?
(A) Conservation of mass indicates that if a single new particle were created in the reaction, it must have a total mass equal to the combined masses of the electron and positron.
(B) Conservation of charge indicates that all new particles created in the reaction would have no electric charge.
(C) Conservation of momentum indicates that two identical gamma rays moving off in opposite directions could be created.
(D) Conservation of energy indicates that the antimatter positron could annihilate into energy, leaving the stationary electron behind.
18. Carbon-14 decays into nitrogen-14 and an electron. The half-life of carbon-14 is 5730 years. Carbon-11 decays into boron-11 and a positron. The half-life of carbon-11 is 20 min. Which of the following statements is correct?
(A) Carbon-14 has the same number of protons as carbon-11.
(B) Carbon-14 can be used to determine the age of 120-million-year-old dinosaur bones.
(C) The combined mass of nitrogen-14 and an electron equals the mass of carbon-14.
(D) Carbon-14 and carbon-11 have the same number of neutrons.
19. The figure shows the wave functions Ψ (x) of an unknown particle. Which of the following statements correctly interprets this graph?
(A) The particle is oscillating in charge from positive to negative.
(B) The lowest probability of finding the particle is at 3.0 nm.
(C) There is an equal probability of finding the particle at 1.5 nm as at 4.5 nm.
(D) The length of the particle is 4 nm.
20. A 2-cm diameter hose leads to a lawn sprinkler with ten 2-mm exit holes as shown in the figure. The velocity of the water in the hose is v1. What is the velocity of the water exiting the holes?
(A) 0.1 v1
(C) 2.5 v1
(D) 10 v1
21. Oil is very slowly poured into the container shown in the figure until the fluid has entered all three open tubes X, Y, and Z. The oil does not overflow any of the tubes and comes to rest. Which of the following correctly ranks the height of the oil in each of the three tubes?
(A) Z > Y > X
(B) Z > X > Y
(C) X > Z > Y
(D) X = Y = Z
22. Two identical containers are filled with different amounts of gas. Container 1 is filled with hydrogen and container 2 is filled with nitrogen. Each container is set on a lab table and allowed to come to thermal equilibrium with the room. Which of the following correctly compares the properties of the two gases?
(A) The average kinetic energy of the hydrogen gas is greater than the nitrogen gas.
(B) The average force exerted on the container by the hydrogen gas is greater than the nitrogen gas.
(C) The density of the hydrogen gas is less than the nitrogen gas.
(D) The pressures of the gases cannot be compared without knowing the number of molecules in each container.
23. The graph shows the distribution of speeds for a gas sample at temperature T. The gas is heated to a higher temperature. Which of the following depicts a possible distribution after the gas has been heated? (Horizontal line N and vertical line S are shown for reference.)
24. The graph shows the pressure and volume of a gas being taken from state #1 to state #2, in a very quick process, where there is not enough time for heat to either leave or enter the gas. Which of the following correctly indicates the sign of the work done on the gas, and the change in temperature of the gas?
25. In a region of space, there is an electric potential with isolines as shown in the figure. Which of the following is the most accurate description of the electric field in the region?
(A) An electric field is directed to the left with a uniform strength of 3 V/m.
(B) An electric field is directed to the left with a uniform strength of 75 V/m.
(C) An electric field is directed to the left that increases in strength from left to right with an average magnitude of 75 V/m.
(D) An electric field is directed to the right that increases in strength from right to left with an average magnitude of 75 V/m.
26. Which of the following correctly represents the relationship between the magnitude of the electric field strengths at locations A, B, and C?
(A) EA > EB > EC
(B) EA = EB > EC
(C) EB > EA > EC
(D) EB > EA = EC
27. An electron of charge —e and mass m is launched with a velocity of v0 through a small hole in the right plate of a parallel plate capacitor toward the opposite plate a distance d away. The electric potential of both plates are equal in magnitude, but opposite in sign ±V as shown in the figure. What is the kinetic energy of the electron as it reaches the left plate?
28. The circuit shown in the figure consists of three identical resistors, two ammeters, a battery, a capacitor, and a switch. The capacitor is initially uncharged and the switch is open.
What happens to the readings of the ammeters immediately after the switch is closed?
29. A student connects a single resistor to a 10-V battery and takes measurements to find the power delivered by the battery to the resistor. The student then adds another resistor to the circuit and measures the power delivered to both resistors. This process is repeated, adding one resistor at a time, until the battery is connected to five resistors. The data from the experiment is given. Which of the following can be concluded from the data?
(A) The resistors are all identical and are connected in parallel.
(B) The resistors are all identical and are connected in series.
(C) The resistors are not identical, but they must be connected in series.
(D) The resistors are nonohmic and how they are connected cannot be determined.
30. An electronics manufacturer needs a 1.2-Ω resistor for a phone it is designing. The company has calculated that it is less expensive to build the 1.2-Ω resistor from cheaper 1-Ω and 2-Ω resistors than to purchase the 1.2-Ω resistor from a supplier. Which of the following resistor arrangements is equivalent to 1.2 Ω and is the most effective method to construct the 1.2-Ω resistor?
31. Which of the following shown in the figure will cause current flow in the wire loop?
(A) Rotating a magnet along its vertical axis above a loop of wire as indicated with arrow A
(B) Moving a magnet from above a loop of wire to the right as indicated with arrow B
(C) Moving a loop of wire to the right in a uniform magnetic field as indicated by arrow C
(D) Moving a loop of wire to the right along a long current-carrying wire as indicated by arrow D
32. Under which of the following conditions would it be appropriate to neglect the gravitational force on a charge in a magnetic field?
(A) G << μ0
(B) g << B
(C) mg << qvB
(D) v = 0
33. A child playing with two magnets places them close together and holds them in place to keep them from moving, as shown in the figure. Magnet A has a larger magnetic field and a larger mass than magnet B. What will happen when the magnets are released and free to move?
(A) Magnet A will not move, while magnet B will accelerate away because magnet B is smaller.
(B) Magnet A will accelerate away more slowly than magnet B because magnet B exerts a smaller force on magnet A.
(C) Magnet A will accelerate away more slowly than magnet B because magnet A has a larger mass.
(D) Both magnets will accelerate away at the same rate because the force between them will be the same magnitude.
34. A charge +Q is positioned close to a bar magnet as shown in the figure. If the charge is experiencing a force into the page, which way must the charge be moving?
(A) To the right
(B) To the left
(C) Toward the top of the page
(D) Out of the page
35. You were absent when your AP Physics 2 class performed a lens lab. When you return to school, the teacher says to get the data from a friend and complete the assignment of calculating the focal length of the lens used in the lab. Your friend hands you the graph shown in the figure where do and di are the object and image distances. Which of the following is equal to the focal length of the lens?
(A) The y-intercept of the best-fit line
(B) The inverse of the y-intercept of the best-fit line
(C) The slope of the best-fit line
(D) The inverse of the slope of the best-fit line
36. A scientist is using an electron microscope to study the structure of viruses ranging in size from 20 to 300 nm. The scientist must adjust the accelerating potential of the microscope to create an electron of the proper speed and wavelength to produce a detailed image of the virus. Which of the following graphs best depicts the relationship between accelerating voltage and the wavelength of the electrons?
37. A photon of wavelength λ collides with a stationary electron glancing off at an angle of θ, while the electron moves off with an angle of ϕ measured from the original path of the photon as shown in the figure. Which of the following statements correctly states the effect on the wavelength of the scattered photon and why?
(A) The wavelength of the scattered photon decreases because the photon transfers energy to the electron in the interaction.
(B) The wavelength of the scattered photon decreases because the photon transfers momentum to the electron in the interaction.
(C) The wavelength of the scattered photon remains the same because the photon is acting as a particle during the collision.
(D) The wavelength of the scattered photon increases because the photon transfers energy to the electron in the interaction.
38. A mass is glued to the top of a Styrofoam block that floats in a container of water. The mass is large enough to make the water line flush with the top of the Styrofoam as shown in the figure. What will happen if the Styrofoam is inverted so that the mass is now suspended under the block?
(A) The whole contraption sinks.
(B) The contraption floats with the waterline still flush with the top of the Styrofoam.
(C) The contraption floats with the waterline below the top of the Styrofoam.
(D) It is impossible to determine without knowing the density of the mass and Styrofoam.
39. Three beakers of different sizes are filled with water as shown. Each beaker has a rubber stopper of the identical size and shape fitted to a drain hole in the side. Which correctly ranks the force applied to the stoppers by the water?
(A) X = Y = Z
(B) X > Y = Z
(C) X > Z > Y
(D) Z > Y = X
40. A person can stand outside on a cold day for hours without ill effect, but falling into a cold lake can kill a person in a matter of minutes. Which of the following is the primary reason for this phenomenon?
(A) The molecules of the person are, on average, moving faster than those of the surroundings.
(B) Thermal energy moves from high concentration areas (hot) to low concentration areas (cold).
(C) As heat flows out of the person and warms the fluid surrounding the person, the warmer fluid rises, allowing fresh cool fluid to come in contact with the person and increasing the rate of heat transfer.
(D) Water has more molecules per volume than air, increasing molecular contact with the person.
41. A sample of gas can be taken from an initial pressure P0 and volume V0 to a final pressure and volume along either path 1 or 2 as shown in the figure. Your lab partner states: “Moving along either path won’t make any difference because both paths start and end at the same places. So, everything about the gases during both processes 1 and 2 will be the same.” Which of the following is a proper analysis of your lab partner’s statement?
(A) The change in temperature is the same, but the change in internal energies will be different.
(B) The change in internal energies will be the same, but the thermal energy transferred to the gas will be different.
(C) The thermal energy transferred to the gas will be the same, but the work done by the gas will be different.
(D) The work done by the gas will be the same, but the change in temperature will be different.
42. A glass lens of focal length f = 80 cm in air is submerged in oil. How will submerging the lens in oil affect the focal length of the lens and why?
(A) f > 80 cm because there is now a smaller change in velocity as light passes from oil into the glass.
(B) f = 80 cm because the index of refraction of glass has remained unchanged by placing the lens into the oil.
(C) f = 80 cm because the shape of the lens has remained unchanged by placing the lens into the oil.
(D) f < 80 cm because light travels slower in oil.
43. A lens is placed between a doll and a white sheet of paper in such a way as to produce an image on the paper. On the side of the lens facing the doll, a dark card is slowly lowered to cover the lens as shown in the figure. Which of the following correctly explains what will happen to the image of the doll?
(A) As the descending card blocks more and more of the lens, the focal point of the lens shifts. This causes the image to become increasingly blurry until the image disappears from the screen.
(B) The image remains clear, but the head of the doll in the image disappears first, followed by the feet, as the light from the top of the object is blocked before the light from the feet.
(C) The image remains clear, but since the doll projects an inverted real image on the screen, the doll’s feet will disappear from view first, followed by the head last, as light from the object is blocked.
(D) As the card blocks light from the object, the image remains clear but becomes increasingly dim until the image disappears.
44. Which of the following expressions correctly relates the masses of the constituent particles involved in the nuclear reaction shown?
(A) mC + mH — mN = 0
45. In an experiment, monochromatic violet light shines on a photosensitive metal, which causes electrons to be ejected from the metal. Which of the following graphs best depicts the number of ejected electrons and the maximum energy of the ejected electrons versus the intensity of the violet light shining on the metal?
Questions 46—50: Multiple-Correct Items
Directions: Identify exactly two of the four answer choices as correct, and mark the answers with a pencil on the answer sheet. No partial credit is awarded; both of the correct choices, and none of the incorrect choices, must be marked to receive credit.
46. A technician is experimenting with a sample of gas in a closed container and produces this set of data. What can be concluded from this data? (Select two answers.)
(A) Pressure is inversely proportional to the volume.
(B) Volume is directly proportional to the temperature.
(C) Pressure is linearly related to the temperature.
(D) The number of molecules of gas in the container is 4.4 × 10-4 moles.
47. In which of the following cases would it be appropriate to ignore the gravitational force? (Select two answers.)
(A) A teacher charges a balloon with her hair and demonstrates how the balloon can be stuck to the ceiling by the electrostatic force.
(B) A scientist suspends a charged droplet of oil between two charged horizontal capacitor plates.
(C) Electrons move through a wire in an electrical circuit.
(D) A physics student is asked to calculate the force between the proton and electron in a hydrogen atom.
48. An electroscope is shown with its movable metal leaves in a sequence of events. Originally the electroscope is in a position with the leaves at an outward angle as shown in Figure 1. A negatively charged rod is brought close to the electroscope and the leaves swing downward as shown in Figure 2. Finally, the rod touches the electroscope and the leaves spring outward as shown in Figure 3. Which of the following statements correctly describe this behavior? (Select two answers.)
(A) In Figure 1, the electroscope has a net positive charge.
(B) In Figure 2, the leaves move closer together because the rod discharges the electroscope.
(C) In Figure 2, negative charges are pushed toward the leaves at the bottom of the electroscope.
(D) In Figure 3, positive charges from the electroscope migrate onto the rod, leaving the electroscope negatively charged.
49. The circuit shown has a battery of negligible internal resistance, resistors, and a switch. There are voltmeters, which measure the potential differences V1 and V2, and ammeters A1, A2, A3, which measure the currents I1, I2, and I3. The switch is initially in the closed position. With the switch still closed, which of the following relationships are true? (Select two answers.)
(A) I1 + I2 — I3 = 0
(B) ΔVB — ΔV1 — ΔV2 = 0
(C) ΔV1 > ΔV2
(D) I2 = I3
50. An incandescent bulb is shown in the figure. When connected to the same voltage source, which of the following would make this bulb brighter? (Select two answers.)
(A) Increase the length of the filament
(B) Increase the thickness of the filament
(C) Connect two of the existing filaments in series
(D) Connect two of the existing filaments in parallel
STOP: End of AP Physics 2 Practice Exam, Section 1 (Multiple-Choice)
AP Physics 2: Practice Exam 2
Section 2 (Free Response)
Directions: The free-response section consists of four questions to be answered in 90 minutes. Questions 1 and 3 are longer free-response questions that require about 25 minutes each to answer and are worth 12 points each. Questions 2 and 4 are shorter free-response questions that should take about 20 minutes each to answer and are worth 10 points each. Show all your work to earn partial credit. On an actual exam, you will answer the questions in the space provided. For this practice exam, write your answers on a separate sheet of paper.
1. (12 points—suggested time 25 minutes)
A cylinder, with a sealed movable piston, is filled with a gas and sits on a lab station table in thermal equilibrium with the lab room. The original pressure, volume, and temperature of the gas are P0, V0, and T0, respectively. You have been instructed by the teacher to experimentally determine the work required to compress the gas to half its original volume.
(A) Describe an experimental procedure you could use to determine the work. Include the following:
• all the equipment needed
• a labeled diagram of the setup
• a clear indication of which variables will be manipulated and which will be measured
• a clear explanation of how the work will be calculated from your data
• enough detail so that another student could carry out the procedure
While performing the experiment, your lab partner makes this claim: “If we compress the gas very slowly, the gas will have a lower final temperature than if we compress the gas very quickly. But, the work will be the same in either case, so it doesn’t matter which way we do it.”
(B) Which parts, if any, of your lab partner’s claim are correct? Justify your response.
(C) Which parts, if any, of your lab partner’s claim are incorrect? Justify your response.
(D) On the graph, sketch the pressure as a function of volume as the gas is compressed from its original pressure P0 and volume V0 (shown by a dot on the graph) to half its original volume. Assume that the gas remains in thermal equilibrium with the lab room throughout the compression.
(E) Utilizing your answer from (D), explain how the graph could be utilized to find the work required to compress the gas.
2. (10 points—suggested time 20 minutes)
Two charges (−2q and +q) are situated along the x-axis as shown in the figure.
(A) What is the direction of the electric field at point +2x? Justify your answer.
(B) Write an expression for the electric field at —2x. Show all your work.
(C) On the axis, sketch a graph of the electric field E along the x-axis as a function of position x. Electric fields to the right are defined as positive.
(D) Is there a spot on the x-axis where the electric field will have a magnitude of zero? If so, give the general location of where it will be and explain why it will occur in that location. If not, explain why not.
(E) A charge of −5q is placed at −2x. Calculate the magnitude and direction of the force on 5q.
3. (12 points—suggested time 25 minutes)
A scientist constructs a device shown in the figure. Region I consists of a charged parallel plate capacitor with vertical plates separated by a distance x. The left plate has a small opening that accelerated particles can pass through. Region II has two large horizontal capacitor plates with a separation of y and a magnetic field created by current-carrying solenoid coils, which are not pictured in the figure. The magnetic field is directed upward out of the page.
In an experiment a single proton P is placed at the launch point near the right plate in Region I. The proton accelerates to the left through the hole and continues on a straight path through Region II as seen in the figure.
(A) What is the direction of the electric field in Region I? Justify your answer.
(B) Which capacitor plate has the higher potential in Region II? Justify your answer.
(C) The experiment is repeated, replacing the proton with an alpha particle that has a mass approximately four times larger than the proton and a charge two times larger than the proton. The alpha particle is released from the launch point and passes through the hole in the left plate. Compare the motion of the alpha particle to the motion of the proton through Regions I and II. Justify your reasoning.
The Region I capacitor plates have a potential difference of 5400 V and a plate separation x of 0.14 m. The Region II capacitor plates have a separation y of 0.060 m and a magnetic field of 0.50 T.
(D) A proton is again placed at the launch point near the right plate in Region I. Derive an algebraic expression for the velocity of the proton as it passes through the hole in the left plate. Use your expression to calculate the numerical value of the velocity.
(E) Using your work from (D), derive an algebraic expression for the potential difference that must be applied to the capacitor in Region II so that the proton moves in a straight line through the region. Use your expression to calculate the numerical value of the potential difference.
(F) Keeping the potential difference the same as the calculated value from (E), the scientist places an unknown particle at the launch point and observes that it travels straight through both Regions I and II just as the proton did. Discuss what the scientist can deduce about the unknown particle. Justify your answer, making appropriate reference to the algebraic expressions derived in (D) and (E).
4. (10 points—suggested time 20 minutes)
The figures show two different representations of the same plane wave traveling through medium #1 and approaching a boundary between two transparent media. The left figure shows a light ray representation. The right figure shows a wave front representation. The index of refraction of medium #1 is greater than that of medium #2.
(A) i. On the left figure, complete the diagram by sketching the path of all four rays in medium #2.
ii. On the right figure, complete the diagram by sketching all four wave fronts in medium #2.
(B) The figure represents another series of plane waves traveling toward and incident on a barrier in its path. One wave model treats every point on a wave front as a point source.
i. Use the point source model to help you sketch the wave as it passes the barrier.
ii. In a clear, coherent paragraph-length response, describe how this point source model explains the shape of the wave as it passes the barrier and why an interference pattern is produced beyond the barrier on the right.
(C) The figure represents another series of plane waves traveling toward and incident on a barrier with two identical openings.
i. Sketch a representation of the interference pattern produced on the wall beyond the barrier. The wall is marked with centimeters for your reference. The 80-cm mark is aligned with the center of the barrier. Indicate locations of constructive interference with the letter C and locations of destructive interference with the letter D.
ii. The distance between the wave fronts is increased. How does this affect the interference pattern? Explain your answer.
STOP: End of AP Physics 2 Practice Exam, Section 2 (Free Response)
Solutions: Section 1 (Multiple Choice)
Questions 1—45: Single-Choice Items
1. A—Particle A bends in the opposite direction with a tighter radius, indicating that it is negative with a smaller mass. A β-particle would satisfy these requirements. Particle B must be negative and have a larger mass. All charged particles would be affected in some way by the electric field; thus particle C must have no charge. Particle D must be positive and have a smaller mass than a proton. Perhaps it is a positron?
2. C—The electric field is always perpendicular to the potential isolines, pointing away from higher potential and toward lower potential, which would be downward and to the left. However, an electron would receive a force in the opposite direction to the field.
3. C—Electric fields always point toward decreasing electric potential, are perpendicular to the potential isolines, and are strongest where the change in potential is greatest: (i.e., isolines of potential are closer together).
4. A—In its original location x, the two electrostatic forces on +q add as shown in the figure.
As the charge +q is moved toward +Q and —Q, the electrostatic forces increase in strength, and their direction also shifts as shown in the figure. Thus, the net force increases in strength, but continues to point directly downward due to the symmetry of the charge arrangement.
5. D—The force between the charges is identical but in opposite directions (Newton’s third law). The more massive object will have a smaller acceleration, so they collide closer to it. Or, using the ideas of conservation of momentum, the center of mass of the system is closer to the right mass, and the original velocity of the center of mass is zero. Since there are no external forces on the system, the two charges will collide at the center of mass.
6. C—With the switch open, the circuit is a simple series circuit with an equivalent resistance of 2R. Both ammeters will receive the same current:
When the switch is closed, the two resistors in parallel on the right add to give , which, when added in series to the resistor in the main line, gives a new equivalent resistance for the circuit of . This will give a new, larger total current passing through the battery and ammeter A1:
Ammeter A2, however, receives only half of this total current as the total current splits evenly to pass through each of the parallel section on the right of the circuit:
Thus, the current in A2 decreases when the switch is closed.
7. D—There is some data scatter, but the data appears to be linear with a slope of about 1/5. Current, as a function of voltage, is given by: . Thus, the slope of the line should equal 1/R. Therefore, the resistance is approximately 5 Ω.
8. A—The currents must be the same because there are no branching paths for the current to take.
9. D—ΔV = IR. The currents are all the same. Thus, the potential difference depends on the resistance of the three shapes. Higher resistance = Higher potential difference .
Therefore, the longest/skinniest shape has the largest potential difference, and the shortest/fattest shape has the smallest potential difference.
10. A—Capacitance for a parallel plate capacitor is: . Since distance decreases, capacitance must have gone up. Energy stored in a capacitor is . Capacitance has increased while the voltage has stayed the same, because the capacitor is still connected to the battery. Therefore, the energy has increased. The electric field of a capacitor is and the charge on a capacitor can be found from . We already know that capacitance has increased but the voltage has stayed the same. This means that the charge on the plates Q has increased. Therefore, the electric field must have also increased.
11. C—Using the right-hand rule (RHR) for a current-carrying wire, we can determine that the magnetic field around the wire points in the −z direction in the vicinity of the proton. Using the RHR for forces on moving charges, we can determine that the proton will experience a magnetic force in the +x direction.
12. C—For a charged particle to cross undeflected straight through crossed, perpendicular, magnetic, and electric fields, the electric and magnetic forces on the charge must cancel:
Note that since the velocity is perpendicular to the magnetic field: sin θ = sin (90°) = 1. Therefore, E = vB when the charge travels in a straight line through the fields, the electric force on the proton is directed to the right, while the magnetic force is directed to the left. Therefore, to make the charge deflect to the left, one of the following must happen: the electric field must decrease, the magnetic field must increase, or the velocity of the charge must increase. Note that changing the charge will have no effect as the charge q cancels out of the equation above.
13. A—Nonmoving charges do not experience a magnetic force. However, the charge will polarize the magnet. This charge separation will cause an electric attraction force between the two.
14. D—Stationary charges do not experience a magnetic force. Electric fields always exert a force on charges.
15. B—From the equation that models this interference pattern (d sin θ = mλ), we see that in order to make the fringe spacing farther apart, we need the angle θ to get larger. This could be accomplished by decreasing d (the width of the hair) or increasing λ (the wavelength of the laser). Neither of these is listed. The spacing could also be spread farther apart by simply moving the screen farther away from the hair.
16. A—This is plenty of information! Just trace a line from the entrance location of the light beam to the exit location of the brightest ray. Measure the angles of incidence and refraction and use Snell’s law to calculate the index of refraction of the plastic rectangle.
17. C—A and D are not correct. The matter and antimatter particles would annihilate into energy (EM waves). In addition, neither conservation of mass nor conservation of energy properly model the interactions of the nano-world. We must use the new physics model of conservation of mass/energy. Conservation of charge dictates only that the final products must add to the same net charge as the original products. The initial momentum of the particles is approximately zero. Two identical gamma rays traveling off in opposite directions would satisfy both conservation of momentum and conservation of charge.
18. A—Different isotopes of atoms have the same number of protons but different numbers of neutrons. The half-life of carbon-14 is too short to date the age of dinosaur bones. There is little to no measurable carbon-14 left in bones that are millions of years old. During a spontaneous decay of a nucleus, energy is released and the mass of the daughter nuclei is less than the original nucleus.
19. C—The amplitude of the wave function (positive or negative) indicates the probability of finding the particle at that location. The probability of finding the particle is the same at locations 1.5 nm and 4.5 nm.
20. D—Using the conservation of mass/continuity equation: A1v1 = A2v2.
The area is proportional to the diameter squared , there are 10 openings on the sprinkler, and d1 = 10d2. This gives us the equation: . Canceling terms and solving for v2, the velocity of the water exiting the sprinkler holes is 10 v1.
21. D—In a static fluid, the pressure must be the same along any horizontal line. If this were not true, the differential pressure would cause the fluid to move. Since all the tubes are open to the same atmosphere at the top, and the pressure at the bottom of each tube must be the same, each tube must have the same height of fluid: p = p0 + ρgh.
22. D—At the same temperature, the average kinetic energies are the same for each gas even though the hydrogen will have a higher average velocity due to its lighter mass . Without knowing the amount of gas in each container, we cannot determine the pressure (PV = nRT ) or the density of the gases . Just because the containers are the same size does not mean they contain the same number of molecules!
23. D—The average speed of the molecules will increase with temperature, with some still moving slow but others moving faster. This moves the peak of the graph to the right and spreads the graph out more than before. Since the number of molecules has not changed, the peak of the graph is lower than before but the total area under the graph should be the same.
24. D—The gas is expanding indicating that it is doing work on the environment, thus losing energy to the environment (−W ). Heat transfer is zero. Therefore, by the first law of thermodynamics (ΔU = Q + W ), ΔU is also negative. This indicates that the gas has lost energy and has decreased in temperature.
25. B—Electric fields are always perpendicular to the electric potential isolines and directed from more positive potentials toward more negative potentials. The electric field strength is calculated with the equation .
26.C—The electric fields from the two charges add up at location B, making it the strongest. The electric field from the two charges are in opposite directions at A and C. However, at location A, the electric field must be larger than that at location C, due to its proximity to the largest charge.
27. D—Using conservation of energy:
28. C—The capacitor is originally uncharged. When the switch is closed, the capacitor acts as a short circuit wire and effectively takes the middle resistor out of the circuit. All current through A1 will stop. The total resistance of the circuit temporarily decreases and the current through A2 increases.
29. B—. Since voltage is being held constant and resistance is being varied, it seems most beneficial to consider the equation: . Each time a resistor is added, the power decreases. Therefore, the resistance must be increasing, which implies that resistors are being added in series. To confirm this suspicion, use the power equation and the voltage of the battery to calculate that one resistor is 20 Ω, Two resistors is 40 Ω, three resistors is 60 Ω, and so on.
30. D—Adding the 1-Ω and 2-Ω resistors in series produces an equivalent resistance of 3 Ω. Next, add the resulting 3-Ω resistor to the 2-Ω resistor in parallel to produce the required 1.2-Ω resistor:
Note that both answer choices A and D produce an equivalent resistance of 1.2 Ω! However, answer choice D only needs two 2-Ω resistors while answer choice A needs five 2-Ω resistors, making answer D a more effective and cheaper solution.
31. B—To produce current in the wire, we need to create a change in magnetic flux through the wire loop. This is accomplished by changing one of the following: magnetic field strength, orientation of the magnetic field through the loop, or the magnetic flux area. By moving the magnet to the right, away from the loop, we change the flux by changing the magnetic field strength through the wire loop.
32. C—The gravitational force can only be neglected when it is very small in comparison to the magnetic force.
33. C—The force between the magnets is equal in size and opposite in direction, but magnet A is more massive and will, therefore, have a smaller acceleration.
34. B—According to the right-hand rule for magnetic forces on moving charges and because the magnetic field is upward at the location of the charge, the charge must be moving to the left.
35. B—First off, choosing a point on the graph and plugging it into the lens equation will get you a number, but you will be wasting all the other data from the lab. This is not the best use of the data. This line was obtained by rearranging the lens equation to produce a straight line (linearization). This is a great way to eliminate error and get a more accurate answer. Rearrange the lens equation to linearize the data: . From this we can see that, if we plot 1/d0 on the y-axis and 1/di on the x-axis, we should get a graph with a −1 slope and a y-intercept of 1/f. So, draw a best-fit line, find the y-intercept, and take the reciprocal, and you will have the focal length of the lens.
36. A—The wavelength of a proton is given by: . Thus, the faster the electron is moving, the smaller its wavelength; the greater the accelerating potential, the higher the velocity will be. Therefore, as the accelerating potential increases, the wavelength decreases (an inverse relationship).
37. D—During the collision, the photon transferred energy and momentum to the electron. This means the wavelength must have increased: .
38. C—The mass and Styrofoam block are originally floating as a unit, and must be displacing enough volume of water to produce a buoyancy force equal to their combined weight. Because both shapes are solid and cannot be filled with water, turning the contraption over will not change the fact that they can still displace enough water to float. However, the submerged mass displaces water, requiring less water displacement by the Styrofoam to produce the same required buoyancy force. Thus, the contraption floats with some of the Styrofoam sticking out of the water.
39. A—All stoppers have the same height of fluid above them and thus all have the same static fluid pressure.
40. D—All the answer choices are true, but the primary reason cold water can kill a person so quickly is that water is denser than air. Water has more molecules per unit volume, facilitating more collisions between slower-moving molecules of water and faster-moving molecules in the person. This conducts heat away faster.
41. B—The beginning and ending points are the same. Therefore, change in temperature and change in internal energies will be the same. The areas under the graphs are different. Therefore, the work will not be the same for the two paths. Since the ΔU are the same but the W is not the same for the two paths, the heat Q must also be different for the two paths (ΔU = Q + W).
42. A—When submerged in water, the light will not refract as much passing through the lens, because the speed of the light will not change as much traveling from oil to glass as it did traveling from air to glass. This will move the focal point farther from the lens. In fact, if the oil has the same index of refraction as the glass, light will not change direction as it passed through the lens, because it did not change speed passing through the lens.
43. D—Blocking part of the lens does not keep other parts of the lens from producing an image. It just makes the image dimmer because less of the lens is being used to produce the image. This is what happens when you squint to block a bright light. You can still see everything clearly. You just make the image dimmer.
44. C—Mass/energy is conserved in nuclear reactions. The mass of the carbon + mass of the hydrogen = mass of the nitrogen + the mass equivalent of the gamma ray .
45. C—Higher intensity (brighter light) simply means more photons. Therefore, higher-intensity light will eject more electrons. Lower-intensity light ejects fewer electrons. When the intensity is zero, no electrons will be emitted. So we have answer choices B and C to choose from. The light is monochromatic (same wavelength and frequency); therefore, the maximum energy of each ejected photon is the same no matter how bright the light intensity is. Kmax = hf — ϕ.
Questions 46—50: Multiple-Correct Items
(You must indicate both correct answers; no partial credit is awarded.)
46. C and D—The volume is being held constant. Therefore, no relationships can be found from this set of data concerning the volume. From the data, we can see that each time pressure increases 10 kPa the temperature increases 20°C. This indicates a linear relationship. The number of moles can be calculated using the ideal gas law. Just remember to convert the units of volume to m3 and temperature to K.
47. C and D—The gravitational force can only be neglected when it has little influence on the behavior of the object, or when it is very small in comparison to other forces. Even though the electric force is larger than the gravitational force acting on the balloon, gravity is still a sizable component of the overall forces on the balloon. The gravity force and electric force must be equal for the droplet of oil to levitate. However, the gravitational force on subatomic particles is negligible compared to the electric force experienced in electrical circuits and between charged particles in an atom.
48. A and C—The electroscope is initially charged in Figure 1 because the leaves repel each other. When the negatively charged rod is brought close, but not in contact with the electroscope, it repels electrons toward the bottom of the electroscope. Since this brings the leaves closer together, the original charge must have been positive. Note that the rod cannot “discharge” the electroscope without touching it. Positive charge carriers do not move through solid objects, because they are buried in the nucleus.
49. A and B—Applying Kirchhoff’s junction rule to the node above the A2 ammeter we get:
Applying Kirchhoff’s current rule to the loop on the right of the circuit containing the battery we get:
I2 < I3: Ammeter 3 is in the main circuit line and carries the total current. This current splits with half going through ammeter 1 and 2.
ΔV1 = ΔV2: If you work out the math you will see that these voltages are the same.
50. B and D—P = IV to increase power, the current must increase and/or the voltage must increase. Increasing the current can be accomplished by decreasing the resistance of the bulb’s filament by making it thicker: . Another method to decrease the resistance would be to connect two filaments in parallel. Remember that the net resistance decreases in parallel.
Solutions: Section 2 (Free Response)
Your answers will not be word-for-word identical to what is written in this key. Award points for your answer as long as it contains the correct physics explanation and as long as it does not contain incorrect physics or contradict the correct answer.
5 points total. There is more than one way to accomplish this lab. Here are two possibilities:
1 point—Choose a force sensor and a ruler.
1 point—Force will be manipulated by pushing down on the piston with the force sensor, and the distance the gas in the cylinder is compressed will be measured.
1 point—Labeled diagram that shows the piston, how the force will be measured, and how the distance the gas is compressed will be measured.
1 point—Work will be calculated by using W = FΔx = area under the graph of force versus distance the gas is compressed.
1 point—Procedure: Cylinder is placed vertically on the lab table. Force sensor is used to push the piston down in 0.01-m increments until we have reached half the original volume. Force and distance compressed are recorded for each. Plot force as a function of distance compressed on a graph. The work will equal the area under the graph.
1 point—Choose a pressure sensor and a ruler.
1 point—The pressure is manipulated and the distance the gas in the cylinder is compressed will be measured.
1 point—Labeled diagram that shows the piston, how the force will be applied and the pressure is measured, how compression distance will be measured.
1 point—Work is calculated using: W = PΔV = area under the graph of pressure versus volume of gas inside the cylinder.
1 point—Procedure: Cylinder is placed vertically on the lab table. Push the piston down in 0.01-m increments until we have reached half the original volume. Pressure and height of the cylinder are recorded for each increment. Calculate volume using V = (area of piston) (height of gas). Plot pressure as a function of volume on a graph. The work will equal the area under the graph.
Note: As the gas is compressed, the pressure inside the gas does not remain constant. The third and fourth points are not awarded unless the student demonstrates an acceptable method for taking this into account while calculating the work. Here are two possible methods a student could use:
• Calculating work by using the area under the F versus x graph or P versus V graph
• A student could state that the force/pressure is not constant and that they will estimate an average force/pressure.
1 point—Correct statement: The temperatures will be different depending on the speed of compression.
1 point—Justification: When compressing the gas very slowly, heat has time to escape, lowering the final temperature. If the compression is done quickly, there is no time for heat to escape and the final temperature will be higher.
1 point—Incorrect statement: The work will be the same in either case.
1 point—Justification: Compressing the gas quickly will not allow time for heat to escape to the environment. This will give the gas a higher final temperature and thus a higher final pressure for the same final volume. This means more force is required to compress the gas quickly and thus more work is required as well.
1 point—Sketching a path that starts at P0, V0, ends at 2 P0, V0/2.
1 point—The sketch is concave upward: an isothermal line.
1 point—The work would be calculated by finding the area under the sketched line.
1 point—For stating that the net electric field will be to the right.
1 point—For a correct explanation. For example: The electric field is directly proportional to the size of the charge and inversely proportional to the radius squared . Since the −2q is twice the charge and three times the distance of the +q charge, the electric field will be dominated by the +q charge.
1 point—For any statement that shows that the net electric field is the vector addition of the two separate electric fields created by −2q and +q. AND that the two fields are in the opposite direction.
1 point—For a correct expression for the magnitudes of the electric fields from both charges: (Note that the correct directions are not needed to earn this point.)
1 point—For the correct expression and direction of the net electric field from both charges:
1 point—For a sketch that shows asymptotic behavior near —x and +x. See figure.
1 point—For positive concave upward lines to the left of —x and to the right of +x. AND a negative concave downward line between —x and +x. See figure.
1 point—For indicating that there will be a zero electric field somewhere to the right of the +q charge.
1 point—For a complete explanation of why there will be a zero electric field somewhere to the right of the +q charge. For example: The electric fields from the two charges are in the opposite directions beyond +x and −x. Since the left charge is larger than the right charge, there can only be a zero electric field location to the right of the +q charge. This means that our graph in part (d) will eventually cross the horizontal axis and become negative somewhere to the right of point +q.
1 point—For using the equation FE = Eq, substituting the answer form part (B) for the electric field, and indicating that the direction will be to the left. Work must be shown to receive this point.
Electric field is to the left.
1 point—For correct justification: The electric field points in the direction of force on a positive charge. The proton accelerates to the left; therefore, the force is to the left and the electric field is also to the left. No credit is awarded without justification.
The upper plate must have a higher potential.
1 point—For utilizing the right-hand rule for forces on moving positive charges, and showing that the proton receives a magnetic force upward from the magnetic field.
1 point—For indicating that the electric force is equal and opposite in direction to the magnetic force so that the proton will travel in a straight line.
1 point—For indicating that electric fields point from higher potential to lower potential. Thus, the upper plate is a higher potential.
The alpha particle will curve downward in Region II.
1 point—For explaining that the alpha particle will exit Region I with a slower velocity. The electric potential energy has doubled, but the mass has quadrupled leading to a smaller exit velocity. (Or, for explaining that in Region I the electric force on the charge has doubled, but the mass has quadrupled, leading to a smaller acceleration and exit velocity.)
1 point—For explaining that the electric force will now be larger than the magnetic force causing the alpha particle to arc downward.
The electric force will double as the change doubles: FE = Eq
The magnetic force will not increase as much as the electric force. Even though the charge doubles, the velocity is now slower: FM = qvB.
Conservation of energy: ΔUE = K
1 point—For the correct expression of conservation of energy:
1 point—For the correct numerical answer:
To move in a straight line: FE = FM
1 point—For the correct expression of magnetic force equal to electric force: Eq = qvB
1 point—For the correct equations with substitutions:
1 point—From the equation derived in (E) ΔV = yvB, we know that the velocity of the particle is the same because ΔV, y, and B are all the same.
1 point—From the equation in (D) , we know that both v and ΔV are the same. Thus, we can deduce the charge to mass ratio q/m of the unknown particle.
1 point—The left figure rays should all be parallel and pointing downward, with the angle of refraction larger than angle of incidence.
1 point—The right figure should also show the waves traveling in a more downward direction. All wave fronts should be parallel, and the wavelength between the wave fronts should be larger in medium #2.
1 point—The sketched waves should bend around the boundary and overlap in circular paths that maintain the same wavelength.
1 point—The point source model says that every point on the wave is the source of a new wavelet that propagates outward.
1 point—For the plane waves approaching the barrier, the sum of all the wavelets produces another plane wave in front of the last one.
1 point—The barrier blocks the center wavelets. The plane waves on either side of the boundary continue forward, but the wavelets on the end of the blocked wave produce curved waves that propagate inward to fill the central area beyond the boundary.
1 point—These curved waves will overlap and form constructive interference, where crests meet crests and troughs meet troughs. They will create destructive interference where crests meet troughs.
There are several ways to draw this. The interference pattern could be drawn as alternating dark and light patches to show the constructive interference points as shown in this sample diagram. An amplitude function could also be used to represent the interference pattern. We do not have enough information to calculate the exact locations of the constructive and destructive interference. However, the patterns should be symmetrical about the center line (the 80-cm mark).
1 point—For a drawing that is symmetrical along central axis and showing a central maximum at 80 cm marked with a C.
1 point—For drawing an alternating pattern of evenly spaced maxima’s and minima’s. The maxima’s and minima’s must be marked with C and D as seen in the figure.
1 point—For indicating that the pattern will get wider and spread out from the central maximum with a coherent explanation. For example: As the distance between the wave fronts is increased, the wavelength gets larger. This means the pattern will spread out as the angle θ gets larger: dsin θ = mλ.
How to Score Practice Exam 2
The practice exam cut points are based on historical exam data and will give you a ballpark idea of where you stand. The bottom line is this: If you can achieve a 3, 4, or 5 on the practice exam, you are doing great and will be well prepared for the real exam in May. This is the curve I use with my own students, and it is has been a good predictor of their actual exam scores.
Calculating Your Final Score
Final Score = (1.136 × Free-Response Total) + (Multiple-Choice Score)
Final Score: _____________ (100 points maximum)
Round your final score to the nearest point.
Raw Score to AP Grade Conversion Chart
AP Physics 2: Practice Exam 3