STEP 5 Build Your Test-Taking Confidence
The AP Physics 2 Practice Exams 3
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 your answer with a pencil on the answer sheet.
1. Two identical insulating spheres of mass m are separated by a distance d as shown in the scale drawing. Both spheres carry a uniform charge distribution of Q. The magnitude of Q is much larger than the magnitude of m. What additional information is needed to write an algebraic expression for the net force on the spheres?
(A) No other information is needed.
(B) The sign of the charge on the spheres
(C) The mass of the spheres
(D) The radius of the spheres
2. The figure shows the electric field in a region surrounding two charges. The vectors in the diagram are not scaled to represent the strength of the electric field but show only the direction for the field at that point. Which two points have electric fields of the same magnitude?
(A) A and B
(B) B and C
(C) C and D
(D) D and A
3. A grounded metal tank containing water has a spout at the bottom through which water flows out in a steady stream. A negatively charged ring is placed near the bottom of the tank such that the water flowing out of the tank passes through without touching the ring. See figure above. Which of the following statements about the charge of the water flowing out of the tank is correct?
(A) Water exiting the tank is neutral because the tank is grounded.
(B) Water exiting the tank is negative because charges jump from the ring to the water.
(C) Water exiting the tank will be positive because the ring repels negative charges in the water and tank toward the top of the tank and ground.
(D) Water exiting the tank will be positive at first but negative as the water level in the tank goes down. The ring attracts positive charges to the bottom of the tank and pushes negative charges to the top of the tank. The positive water flows out first and negative water flows out last.
4. Two parallel metal plates are connected to a battery as shown in the figure. A small negative charge is placed at location O and the force on the charge is measured. Compared to location O, how does the force on the charge change as it is moved to locations A, B, C, and D?
(A) The force at location A is the same magnitude as at location O but in the opposite direction.
(B) The force at location B is smaller than at location O but in the same direction.
(C) The force at location C is smaller than at location O but in the same direction.
(D) The force at location D is the same magnitude as at location O but in the opposite direction.
5. 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. Which of the following correctly compares the original open switch readings of the ammeters to their readings after the switch has been closed for a very long time?
6. A battery is connected to a section of wire bent into the shape of a square. The lower end of the loop is lowered over a magnet. Which of the following orientations of the wire loop and magnet will produce a force on the wire in the positive x direction?
7. A charge +Q is positioned close to a bar magnet as shown in the figure. Which way should the charge be moved to produce a magnetic force into the page on the bar magnet?
(A) To the right
(B) Toward the top of the page
(C) Out of the page
(D) Moving the charge will not produce a force on the magnet.
8. In an experiment, a scientist sends an electron beam through a cloud chamber and observes that the electron accelerates in a downward direction at a constant rate as shown in the figure. Which of the following could the scientist conclude?
(A) Earth’s gravitational field is causing the beam to change direction.
(B) A uniform electric field is causing the beam to change direction.
(C) A uniform magnetic field is causing the beam to change direction.
(D) The electron beam collided with another particle.
9. A sphere, cube, and cone are each suspended stationary from strings in a large container of water as shown in the figure. Each has a width and height of x. Which of the following properly ranks the buoyancy force on the objects? (Assume the vertical distance between points A and B is small.)
(A) A > B > C
(B) B > A > C
(C) C > B > A
(D) It is impossible to determine the ranking without knowing the tension in the strings.
10. Bubbles in a carbonated liquid drink dispenser flow through a tube as shown in the figure. Which of the following correctly describes the behavior of the bubbles as they move from point A to point B? The vertical distance between points A and B is small.
(A) The bubbles increase in speed and expand in size.
(B) The bubbles increase in speed and decrease in size.
(C) The bubbles decrease in speed and expand in size.
(D) The bubbles decrease in speed and decrease in size.
11. The circumference of a helium-filled balloon is measured for three different conditions: at room temperature, after being in a warm oven for 30 minutes, and after being in a freezer for 30 minutes. A student plotting the circumference cubed C3 as a function of temperature T, should expect to find which of the following?
(A) A cubic relationship between C3 and T
(B) An indirect relationship between C3 and T
(C) A linear relationship between C3 and T that passes through T = 0 when C3 = 0.
(D) A maximum C3 as the temperature T increases
12. A group of physics students has been asked to confirm that air exhibits properties of an ideal gas. Using a sealed cylindrical container with a movable piston, baths of cool and warm water, a thermometer, a pressure gauge, and a ruler, the students are able to produce this table of data.
Which of the following data analysis techniques, when employed by the students, could be used to verify ideal gas behavior of air?
(A) Using trials 1, 2, 3, and 4, plot pressure as a function of volume and check for linearity.
(B) Using trials 1, 5, and 9, plot pressure as a function of temperature and check for linearity.
(C) Using trials 5, 6, 7, and 8, plot volume as a function of temperature and check for linearity.
(D) Using trials 4, 8, and 12, plot the reciprocal of volume (1/V) as a function of temperature and check for linearity.
13. A gas is initially at pressure P and volume V as shown in the graph. Along which of the labeled paths could the gas be taken to achieve the greatest increase in temperature?
(A) Path A
(B) Path B
(C) Path C
(D) Path D
14. It is observed that sounds can be heard around a corner but that light cannot be seen around a corner. What is a reasonable explanation for this observation?
(A) Light travels at 3 × 108 m/s, which is too fast to change direction around a corner.
(B) Sound has a longer wavelength, which increases its diffraction around corners.
(C) Light is an electromagnetic wave that is behaving as a particle.
(D) Sound is a mechanical wave that can change direction in its propagation media.
15. A bug crawls directly away from a mirror of focal length 10 cm as shown in the figure. The bug begins at 13 cm from the mirror and ends at 20 cm. What is happening to the image of the bug?
(A) The image inverts.
(B) The image gets larger in size.
(C) The image is becoming the same size as the bug.
(D) The image is moving away from the lens to the right.
16. A student looks at a key through a lens. When the lens is 10 cm from the key, what the student sees through the lens is shown in the figure. The student estimates that the image is about half the size of the actual key. What is the approximate focal length of the lens being used by the student?
(A) —10 cm
(B) —0.1 cm
(C) 0.3 cm
(D) 3.0 cm
17. A neutron is shot into a uranium atom, producing a nuclear reaction:
Which of the following best describes this reaction?
(A) The reaction products include two neutrons.
(B) Combining uranium with a neutron is characteristic of nuclear fusion.
(C) The released energy in the reaction is equal to the kinetic energy of the neutron shot into the uranium.
(D) The combined mass of uranium-235 and a neutron will be greater than the sum of the mass of the reaction products.
18. Two opposite charges of equal magnitude are connected to each other by an insulated bar and placed in a uniform electric field as shown in the figure. Assuming the object is free to move, how will the object move and why?
(A) It will remain stationary because the object has a net charge of zero.
(B) It will rotate clockwise at a constant rate because both charges and the electric field are constant.
(C) It will rotate at a constant rate until aligned with the electric field and then stop rotating because the net force will equal zero when aligned with the field.
(D) It will rotate back and forth clockwise and counterclockwise because the torque changes as the object rotates.
19. Which of the following best represents the isolines of electric potential surrounding two identical positively charged spheres?
Questions 20 and 21 refer to the following material.
The diagram shows a circuit that contains a battery with a potential difference of VB and negligible internal resistance; five resistors of identical resistance; three ammeters A1, A2, A3; and a voltmeter.
20. Which of the following correctly ranks the readings of the ammeters?
(A) A1 = A2 = A3
(B) A1 = A2 > A3
(C) A1 > A2 > A3
(D) A2 > A1 > A3
21. What will be the reading of the voltmeter?
22. A battery of unknown potential difference is connected to a single resistor. The power dissipated in the resistor is calculated and recorded. The process is repeated for eight resistors. A plot of the data with a best-fit line was made and is displayed in the figure. The potential difference provided by the battery is most nearly:
(A) 3 V
(B) 6 V
(C) 18 V
(D) 36 V
23. A high-energy proton beam is used in hospitals to treat cancer patients. The beam is shot through a small aperture surrounded by four solenoids with iron cores that are used to direct the beam at cancer cells to kill them. (The direction of the current around the solenoids is indicated by the arrows.) During routine maintenance, technicians calibrate the machine by pointing the beam at the center of a screen and then directing it toward designated target points. Which of the four solenoids will the technician use to direct the beam toward the target “X” on the right side of the screen?
(A) The top solenoid
(B) The right solenoid
(C) The bottom solenoid
(D) The left solenoid
24. A lab cart with a rectangular loop of metal wire fixed to its top travels along a frictionless horizontal track as shown. While traveling to the right, the cart encounters a region of space with a strong magnetic field directed into the page. The cart travels through locations A, B, and C on its way to the right as shown in the figure. Which of the following best describes any current that is induced in the loop or wire?
(A) Current is induced in the loop at all three locations A, B, and C.
(B) Current is induced in the loop only at locations A and C.
(C) Current is induced in the loop only at location B.
(D) No current is induced in the loop, because the area of the loop, the magnetic field strength, and the orientation of the loop with respect to the magnetic field all remain constant while the cart moves to the right.
25. Two blocks of the same size are floating in a container of water as shown in the figure. Which of the following is a correct statement about the two blocks?
(A) The buoyancy force exerted on both blocks is the same.
(B) The density of both blocks is the same.
(C) The pressure exerted on the bottom of each block is the same.
(D) Only the volume of the blocks is the same.
26. A large container of water sits on the floor. A hole in the side a distance y up from the floor and 2y below the surface of the water allows water to exit and land on the floor a distance x away as shown in the figure. If the hole in the side was moved upward to a distance 2y from the floor and y below the surface of the water, where would the water land?
27. A cylinder with a movable piston contains a gas at pressure P = 1 × 105 Pa, volume V = 20 cm3, and temperature T = 273 K. The piston is moved downward in a slow steady fashion allowing heat to escape the gas and the temperature to remain constant. If the final volume of the gas is 5 cm3, what will be the resulting pressure?
(A) 0.25 × 105 Pa
(B) 2 × 105 Pa
(C) 4 × 105 Pa
(D) 8 × 105 Pa
28. An equal number of hydrogen and carbon dioxide molecules are placed in a sealed container. The gases are initially at a temperature of 300 K when the container is placed in an oven and brought to a new equilibrium temperature of 600 K. Which of the following best describes what is happening to the molecular speeds and kinetic energies of the gases’ molecules as they move from 300 K to 600 K?
(A) The molecules of both gases, on average, end with the same speed and the same average kinetic energy.
(B) The molecules of hydrogen, on average, end with a higher speed, but the molecules of both gases end with the same average kinetic energy.
(C) The molecules of hydrogen, on average, end with a higher speed and higher average kinetic energy.
(D) The molecules of carbon dioxide, on average, end with a slower speed but a higher average kinetic energy.
29. A convex lens of focal length f = 0.2 m is used to examine a small coin lying on a table. During the examination, the lens is held a distance 0.3 m above the coin and is moved slowly to a distance of 0.1 m above the coin. During this process, what happens to the image of the coin?
(A) The image continually increases in size.
(B) The image continually decreases in size.
(C) The image gets smaller at first and then bigger in size.
(D) The image flips over.
30. Light from inside an aquarium filled with water strikes the glass wall as shown in the figure. Knowing that nwater = 1.33 and nglass = 1.62, which of the following represents a possible path that the light could take?
31. A beam of ultraviolet light shines on a metal plate, causing electrons to be ejected from the plate as shown in the figure. The velocity of the ejected electrons varies from nearly zero to a maximum of 1.6 × 106 m/s. If the brightness of the beam is increased to twice the original amount, what will be the effect on the number of electrons leaving the metal plate and the maximum velocity of the electrons?
32. Scientists shine a broad spectrum of electromagnetic radiation through a container filled with gas toward a detector. The detector indicates that three specific wavelengths of the radiation were absorbed by the gas. The figure shows the energy level diagram of the electrons that absorbed the radiation. Which of the following correctly ranks the wavelengths of the absorbed electromagnetic radiation?
(A) A = B > C
(B) A > B = C
(C) A > C > B
(D) B > C > A
33. Three identical uncharged metal spheres are supported by insulating stands. They are placed as shown in the left figure with S1 and S2 touching. A sequence of events is then performed.
• S3 is given a negative charge.
• S1 is moved to the left away from S2.
• S3 is brought into contact with S2 and then placed back in its original position.
This leaves the spheres in the positions shown in the right figure. Which of the following most closely shows the signs of the final net charge on the spheres?
34. Three identical objects with an equal magnitude of charge are placed on the corners of a square with sides of length x as shown in the figure. Which of the following correctly expresses the magnitude of the net force F acting on each charge due to the other two charges?
(A) FA = FC
(B) FA > FC
(C) FB = FC
(D) FB < FC
35. In an experiment, a long wire is connected to a battery and the current passing through the wire is measured. The wire is then removed and replaced with new wire of the same length and material, but having a different diameter. The figure shows the experimental data graphed with the current as a function of the wire diameter. Which of the following statements does the data support?
(A) The resistance of the wire is directly proportional to the diameter of the wire.
(B) The resistance of the wire is directly proportional to the diameter of the wire squared.
(C) The resistance of the wire is inversely proportional to the diameter of the wire.
(D) The resistance of the wire is inversely proportional to the diameter of the wire squared.
36. Four identical batteries of negligible resistance are connected to resistors as shown. A voltmeter is connected to the points indicated by the dots in each circuit. Which of the following correctly ranks the potential difference measured by the voltmeter?
(A) ΔVA = ΔVB > ΔVC
(B) ΔVA > ΔVB > ΔVC
(C) ΔVB > ΔVA > ΔVC
(D) ΔVC > ΔVA = ΔVB
37. A capacitor, with parallel plates a distance d apart, is connected to a battery of potential difference ΔV as shown in the figure. The plates of the capacitor can be moved inward or outward to change the distance d. To increase both the charge stored on the plates and the energy stored in the capacitor, which of the following should be done?
(A) Keep the capacitor connected to the battery, and move the plates closer together.
(B) Keep the capacitor connected to the battery, and move the plates farther apart.
(C) Disconnect the battery from the capacitor first, and then move the plates closer together.
(D) Disconnect the battery from the capacitor first, and then move the plates farther apart.
38. A loop of wire with a counterclockwise current is immersed in a uniform magnetic field that is pointing up out of the paper in the +z direction, as seen in the figure. The loop is free to move in the field. Which of the following is a correct statement?
(A) There is a torque that rotates the loop about the x-axis.
(B) There is a torque that rotates the loop about the z-axis.
(C) There is a force that moves the loop along the z-axis.
(D) There is a net force of zero and the loop does not move.
39. Two long wires pass vertically through a horizontal board that is covered with an array of small compasses placed in a rectangular grid pattern as seen in the figure. The wire on the left has a current passing upward through the board, while the right wire has a current passing downward through the board. Both currents are identical in magnitude. Each compass has an arrow that points in the direction of north. Looking at the board from above, which of the following diagrams best depicts the directions that the array of compasses are pointing?
40. A long wire carries a current as shown in the figure. Three protons are moving in the vicinity of the wire as shown. All three protons are in the plane of the page. Proton 1 in moving downward at a velocity of v. Proton 2 is moving out of the page at a velocity of v. Proton 3 is moving to the right at a velocity of 2v. Which of the following correctly ranks the magnetic force on the protons?
(A) 1 = 2 = 3
(B) 1 = 2 > 3
(C) 1 = 3 > 2
(D) 3 > 1 > 2
41. A gas is confined in a sealed cylinder with a movable piston that is held in place as shown in the figure. The gas begins at an original volume V and pressure 2 P, which is greater than atmospheric pressure. The piston is released and the gas expands to a final volume of 2 V. This expansion occurs very quickly such that there is very little heat transfer between the gas and the environment. Which of the following paths on the PV diagram best depicts this process?
42. An ideal gas is sealed in a fixed container. The container is placed in an oven, and the temperature of the gas is doubled. Which of the following correctly compares the final force the gas exerts on the container and the average speed of the molecules of the gas compared to the initial values?
43. When hot water is poured into a beaker containing cold alcohol, the temperature of the mixture will eventually reach a uniform temperature. Which of the following is the primary reason for this phenomenon?
(A) The high temperature water will rise to the top of the container until it has cooled and then mixes with the alcohol.
(B) The molecules of the water continue to have a higher kinetic energy than the molecules of the alcohol, but the two liquids mix until the energy is spread evenly throughout the container.
(C) The hot water produces thermal radiation that is absorbed by the cold alcohol until the kinetic energy of all the molecules is the same.
(D) The water molecules collide with the alcohol molecules, transferring energy until the average kinetic energy of both the water and alcohol molecules are the same.
44. In an experiment, monochromatic light of frequency f1 and wavelength λ1 passes through a single slit of width d1 to produce light and dark bands on a screen as seen in pattern 1. The screen is a distance L1 from the slit. A single change to the experimental setup is made and pattern 2 is created on the screen. Which of the following would account for the differences seen in the patterns?
(A) f1 < f2
(B) λ1 < λ2
(C) L1 < L2
(D) d1 > d2
45. A bird is flying over the ocean and sees a fish under the water. The actual positions of the bird and fish are shown in the figure. Assuming that the water is flat and calm, at which location does the bird perceive the fish to be?
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. 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. The switch is now opened. Which of the following values increases? (Select two answers.)
47. Particle 1, with a net charge of 3.2 × 10—19 C, is injected into a magnetic field directed upward out of the page and follows the path shown in the figure. Particle 2 is then injected into the magnetic field and follows the path shown. Which of the following claims about the particles would be a plausible explanation for the differences in their behavior? (Select two answers.)
(A) Particle 2 could have twice the energy of particle 1.
(B) Particle 2 could have twice the momentum of particle 1.
(C) Particle 2 could have half the charge of particle 1.
(D) Particle 2 could have half mass than particle 1.
48. Three samples of gas in different containers are put into thermal contact and insulated from the environment as shown in the figure. The three gases, initially at different temperatures, reach a final uniform temperature of 310 K. Which of the following correctly describes the flow of thermal energy from the initial condition until thermal equilibrium? (Select two answers.)
(A) Heat flows from sample 1 to sample 2 during the entire time until thermal equilibrium of the system is reached.
(B) Heat flows into sample 2 only from sample 1 until both reach the equilibrium temperature of 310 K.
(C) Heat flows into sample 2 from both samples 1 and 3 until thermal equilibrium of the system is reached.
(D) Heat initially flows from sample 3 into sample 2 and then back from sample 2 into sample 3.
49. In an experiment, students collect data for light traveling from medium 1 into medium 2. The angles of incidence θ1 and refraction θ2 as measured from the perpendicular to the surface are given in the table. The data in the table supports which of the following statements? (Select two answers.)
(A) The index of refraction of medium 1 is approximately 1.2.
(B) Light travels slowest in medium 2.
(C) There are some angles at which the light will not be able to enter medium 2.
(D) Medium 1 and medium 2 are not the same material.
50. Which of the following phenomena can be better understood by considering the wave properties of electrons? (Select two answers.)
(A) There are discrete electron energy levels in a hydrogen atom.
(B) Monochromatic light of various intensities eject electrons of the same maximum energy from a metal surface.
(C) A beam of electrons reflected off the surface of a crystal creates a pattern of alternating intensities.
(D) An X-ray colliding with a stationary electron causes it to move off with a velocity.
STOP: End of AP Physics 2 Practice Exam, Section 1 (Multiple-Choice)
AP Physics 2: Practice Exam 3
Section 2 (Free Response)
Directions: The free-response section consists of four questions to be answered in 90 minutes. Questions 2 and 4 are longer free-response questions that require about 25 minutes each to answer and are worth 12 points each. Questions 1 and 3 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. (10 points—suggested time 20 minutes)
In a classroom demonstration, a small conducting ball is suspended vertically from a light thread near a neutral Van de Graaff generator as shown on the left of the figure. A grounding wire is attached to the ball and removed. Then the Van de Graaff generator is turned on, giving it a positive charge. After the Van de Graaff is turned on, the ball swings over toward, and touches, the Van de Graaff as shown in the middle diagram of the figure. After touching the Van de Graaff, the small ball swings away from the Van de Graaff toward the right and past the vertical position as shown in the figure at the right. The ball remains to the right of the vertical position.
(A) In a clear, coherent paragraph-length response, completely explain the entire sequence of events that cause the ball to behave as it does. Clearly indicate the behavior of subatomic particles and how any forces are generated.
(B) The dot represents the small ball after it has swung away from the Van de Graaff when it is in its final position with an angle to the right of vertical. Draw a free-body diagram showing and labeling the forces (not components) exerted on the ball. Draw the relative lengths of all vectors to reflect the relative magnitudes of all the forces. (A grid is provided to assist you.)
(C) In its final position the ball, mass m, is a distance d from the surface of the Van de Graaff generator and an angle θ from the vertical as shown in the figure. The Van de Graaff has a net charge of Q. Derive an expression for the magnitude of the net charge q of the small ball in its final position. Express your answer in terms of m, d, R, Q, θ, and any necessary constants.
2. (12 points—suggested time 25 minutes)
The figure shows a circuit with a battery of emf ε and negligible internal resistance, and four identical resistors of resistance R numbered 1, 2, 3, and 4. There are three ammeters (A1, A2, and A3) that measure the currents I1, I2, and I3, respectively. The circuit also has a switch that begins in the closed position.
(A) A student makes this claim: “The current I3 is twice as large as I2.” Do you agree or disagree with the student’s statement? Support your answer by applying Kirchhoff’s loop rule and writing one or more algebraic expressions to support your argument.
(B) Rank the power dissipated into heat by the resistors from highest to lowest, being sure to indicate any that are the same. Justify your ranking.
The switch is opened. A student makes this statement: “The power dissipation of resistors 2 and 3 remains the same because they are in parallel with the switch. The power dissipation of resistor 1 decreases because opening the switch cuts off some of the current going through resistor 1.”
(C) i. Which parts of the student’s statement do you agree? Justify your answer with appropriate physics principles.
ii. Which parts of the student’s statement do you disagree with? Justify your answer utilizing an algebraic argument.
The switch remains open. Resistor 4 is replaced with an uncharged capacitor of capacitance C. The switch is now closed.
(D) i. Determine the current in resistor 1 and the potential difference across the capacitor immediately after the switch is closed.
ii. Determine the current in resistor 1 and the potential difference across the capacitor a long time after the switch is closed.
iii. Calculate the energy (U) stored on the capacitor a long time after the switch is closed.
3. (10 points—suggested time 20 minutes)
In a laboratory experiment, an optics bench consisting of a meter stick, a candle, a lens, and a screen is used, as shown in the figure. A converging lens is placed at the 50-cm mark of the meter stick. The candle is placed at various locations to the left of the lens. The screen is adjusted on the right side of the lens to produce a crisp image. The candle and screen locations on the meter stick produced in this lab are given in the table. Extra columns are provided for calculations if needed.
(A) Calculate the focal length of the lens. Show your work.
(B) Use the data to produce a straight line graph that can be used to determine the focal length of the lens. Calculate the focal length of the lens using this graph and explain how you found the focal length from the graph.
(C) Sketch a ray diagram to show how the candle would produce an upright image with a magnification larger than 1.0. Draw the object, at least two light rays, and the image. Indicate the locations of the focus on both sides of the lens.
(D) A student says that virtual images can be projected on a screen. Do you agree with this claim? How could you perform a demonstration to support your stance with evidence?
4. (12 points—suggested time 25 minutes)
A mole of ideal gas is enclosed in a cylinder with a movable piston having a cross-sectional area of 1 × 10—2 m2. The gas is taken through a thermodynamic process, as shown in the figure.
(A) Calculate the temperature of the gas at state A, and describe the microscopic property of the gas that is related to the temperature.
(B) Calculate the force of the gas on the piston at state A, and explain how the atoms of the gas exert this force on the piston.
(C) Predict qualitatively the change in the internal energy of the gas as it is taken from state B to state C. Justify your prediction.
(D) Is heat transferred to or from the gas as it is taken from state B to state C? Justify your answer.
(E) Discuss any entropy changes in the gas as it is taken from state B to state C. Justify your answer.
(F) Calculate the change in the total kinetic energy of the gas atoms as the gas is taken from state C to state A.
(G) On the axis provided, sketch and label the distribution of the speeds of the atoms in the gas for states A and B. Make sure that the two sketches are proportionally accurate.
STOP: End of AP Physics 2 Practice Exam, Section 2 (Free Response)
Solutions: Section 1 (Multiple Choice)
Questions 1—45: Single—Correct Items
1. D—Since the magnitude of Q is much greater than (>>) the magnitude of m, the electric force will be many orders of magnitude larger than the force of gravity and we can neglect gravity. where r is the distance between the two centers of charge. The radius of both spheres must be added to d.
2. D—The electric field is symmetrical along a horizontal axis through the two charges. Points A and D are the same distance away from both charges where the electric fields will have the same strength.
3. C—The negative ring polarizes the tank and drives negative charges toward the ground, creating a tank of positively charged water.
4. B—The electric field produced by a charged parallel plate capacitor is uniform in strength and direction everywhere between the plates away from the edges of the capacitor. Therefore, the electric force on the charges must be identical for locations A, C, and O. Near the edges of the capacitor, the field bows out a bit and is not quite as strong. This is consistent with answer choice B. Outside the capacitor the electric field is much weaker.
5. D—After the switch is closed and the capacitor has been connected to the circuit for a very long time, it has had time to fully charge and it will behave like an open circuit line. No current will bypass the middle resistor and, for all intents and purposes, the circuit looks just like it did before the switch was ever closed, with the exception that the capacitor now stores both charge and energy.
6. C—Conventional current will be moving around the wire in a counterclockwise direction, meaning that the current is traveling in the +x direction for answer choices A and B and in the −y direction for answer choices C and D. The magnetic field exits out of the north and into the south end of the magnet. This gives a magnetic field in the +z direction for answer choices A and C and in the −z direction for answer choices B and D. Using the right-hand rule for forces on a current-carrying wire gives us a magnetic force in the +y direction for A, −y direction for B, +x direction for C, and —x direction for D.
7. A—Think Newton’s third law here! If we can get a magnetic force on the charge out of the page, that means we will have an equal but opposite force on the magnet into the page. Moving the charge to the right produces a force on the charge out of the page and thus an opposite-direction force on the magnet into the page.
8. B—Since the acceleration is constant in direction, this cannot be a collision or a force from a magnetic field. The electron mass is very small, so any gravitational acceleration on the election will be too small to see in a cloud chamber. However, a uniform electric field could easily produce this parabolic trajectory effect.
9. B—Buoyancy force is proportional to the displaced volume and the density of the fluid displaced. The density of the fluid is the same for each. The volume of the cube > volume of the sphere > volume of the cone.
10. A—Due to conservation of mass (continuity), the fluid must increase in velocity when the cross-sectional area decreases. Due to conservation of energy (Bernoulli), as the velocity of the fluid increases, the static pressure in the fluid decreases. This means the pressure on the bubbles will decrease, allowing them to expand in size.
11. C—The circumference of the balloon is related to the radius, and thus C3 is proportional to the volume of the balloon. Temperature and volume of a gas are directly related. Therefore, as the temperature decreases, the circumference also decreases. Extrapolating the three data points will lead to a point on the graph where the circumference and thus the volume of the gas is zero. This temperature will be an experimental estimate for absolute zero.
12. B—To show ideal gas behavior, air must follow the relationships in the ideal gas law: PV = nRT. One variable should be plotted as a function of another, while the rest of the variables are held constant. With T held constant, P . With P held constant, V ∝ T. With V held constant, P ∝ T. Answer choice C is looking for the correct relationship but is using the wrong data set. Only answer choice B is looking for the correct relationship while holding the proper variable constant.
13. C—The largest final temperature will be at the location of the highest pressure times volume, PV location. The highest final of 6PV is along path C.
14. B—The point source model of waves tells us that waves display diffraction more prominently when the wavelength is about the same size or larger than the obstructions they are passing around. Sound can have a large wavelength similar in size to the corner it is bending around, while light has a wavelength that is much smaller. Thus light does not diffract very much going around corners.
15. C—The bug is walking from a position where the image is real, larger, and inverted toward 2f, where the image will be real, inverted, and the same size as the bug.
16. A—First off, the student is seeing a smaller, upright, virtual image. This means this has to be a diverging lens with a negative focal length and a negative image distance.
Using the magnification equation:
gives an image distance of −5 cm.
Using the lens equation:
, the focal length equals −10 cm.
17. D—This is a fission reaction where a large nucleus splits into two major chunks and released energy. Since energy is released in the reaction, conservation of mass/energy indicates that the final mass must be less than the initial mass. Answer choice A is a good distractor! Don’t forget that the left side of the nuclear equation has a uranium nucleus and one neutron.
18. D—The positive and negative charges will receive forces in the opposite direction, creating a torque and causing it to rotate about its center of mass. When the bar is aligned with the electric field, it will already have an angular velocity and will overshoot the vertical alignment position. The process will repeat in the opposite angular direction, creating an oscillating motion that rotates the bar back and forth.
19. A—Answer choices B and D depict electric field diagram lines that begin on positive charges and end on negative charges. Electric field vectors are always perpendicular to the potential isolines. Answer choice C implies that there would be an electric field directed to the right or to the left between the two charges. This could be true only if the two charges have opposite signs. Two identical positive charges would produce a location of zero electric field directly between the two charges. This is implied by there not being any isolines in the middle of diagram A.
20. D—The resistance of the parallel set of three resistors on the far right is . Thus the total resistance of the circuit to the right of the battery is . The loop on the left has a resistance of 2R. This means that the reading of A2 > A1. The current that goes through A3 must be less than A2 because it is in a branching pathway. Answer choice D is the only option that meets these requirements.
21. C— Ammeter A2 is in the main line supplying the current to the right-hand side of the circuit. The total resistance of the circuit to the right of the battery is (as described in the answer to question 20). This gives a total current passing through ammeter A2 of:
Using this current we can calculate the voltage drop through the resistor in the wire passing through ammeter A2:
This leaves the remaining voltage drop of that will be read by the voltmeter.
22. A—, which means that the slope of the graph equals ΔV2. The slope of the graph is approximately 9, which gives: ΔV ≈ 3 V.
23. A—We need a force on the proton beam pointed to the right. The velocity of the proton is forward or into the page. The top solenoid will produce a magnetic field pointing upward at the aperture. Using the right-hand rule for magnetic forces on moving charges, we can see that the proton will experience a force to the right in the upward magnetic field.
24. B—An induced current occurs when there is a change in magnetic flux through the loop:
This occurs only when the cart is entering the front edge and leaving the back edge of the field, because the flux area is changing. No current is induced while the cart is fully immersed in the magnetic field, because the magnetic field is completely covering the loop area; thus, the flux area is not changing.
25. D—The blocks are the same size yet sink to different depths, implying they have different masses and densities. The buoyancy force equals the weight of floating objects and thus cannot be the same. The boxes sink to different depths and static fluid pressure depends on the depth of the fluid.
26. C—x = (velocity)(time). From Bernoulli’s equation we can derive that: where h is the height above the hole to the top of the water. Time can be derived from kinematics: where h is the height below the hole to the ground. Multiplying these together gives the horizontal distance: .
When the hole is moved to the new location, the height above is cut in half while the height below is doubled. Thus x remains the same.
27. C—nRT are all remaining constant. This means that PV = constant. Since the volume is decreased to ¼ of its original value, the pressure must have gone up by a factor of 4.
28. B—Both gases end with the same temperature and consequently end with the same average molecular kinetic energy. To have the same average molecular kinetic energy as carbon dioxide, hydrogen, with its smaller mass, must have a higher average molecular velocity.
29. D—The object begins at a distance beyond the focal length. This will produce an image that is inverted and real. As the lens is moved closer to the object, the image gets bigger and bigger. When the object is one focal length from the lens, no image will form. As the lens is moved even closer, the object is now inside the focal length where the image will be virtual and upright. This virtual image begins very large and decreases in size as we move the lens from 0.2 m to its final location of 0.1 m.
30. C—Light traveling from the water to the glass should bend toward the normal as it slows down in the glass. This eliminates answer choices B and D. The light will then travel from the glass to the air on the left where it will bend away from the normal because it is traveling fastest in the air. Answer choice A seems to show the angle in the air being the same as it was in the water, which cannot be true. The light travels faster in air than in water, which means the angle to the normal must be bigger than inside the aquarium. What about answer choice C? Since the light bends away from the normal entering air, it is possible that the angle of incidence between the glass and the air is beyond the critical angle, thus causing total internal reflection at the glass/air boundary; C is the best answer.
31. B—Increasing the brightness of the light increases only the number of photons not the energy of the individual photons. Thus, the number of ejected electrons goes up but their maximum energy and velocity will still be the same.
32. D—, therefore, wavelength is inversely proportional to the energy of the absorbed photon. The energy of the absorbed photon is equal to the jump in energy of the electron: Efinal — Einitial. Electron B has the smallest energy jump, and electron A has the largest energy jump.
33. C—When S3 is charged negative, it will polarize the left two spheres. Since S1 and S2 are touching, S1 becomes negative and S2 positive during this polarization. When S1 and S2 are separated, they take their net charges with them. When the negative S3 touches the positive S2, their charges cancel each other out by conduction.
34. B—Note two things: (1) the force between pairs of charges must be equal and opposite and (2) due to a longer distance between them, the force between A and C is smaller than the forces between A and B or B and C. The forces are shown in the diagram. FA must be larger than FC. FB must be larger than FC.
35. D—When the diameter of the wire is 1 mm the current is 0.1 A. When the diameter of the wire is doubled to 2 mm the current quadruples to 0.4 A. This means that when the diameter doubles, the resistance must be cut to one-fourth of its original value. Now let’s look at what happens with the diameter triples to 3 mm. The current goes up nine times to 0.9 A. This means the resistance must have decreased to one-ninth of its original value when the wire had a diameter of 1 mm. Therefore, the resistance of the wire is inversely proportional to the diameter of the wire squared.
36. A—Using Kirchhoff’s loop rule it is easy to see that the voltages of A and B must be the same because both resistors are directly connected to the battery in a single loop. The voltages across A and B must equal the potential of the battery. The loop rule also shows us that in case C, there will be two resistors in any loop drawn between the plus and minus side of the battery. Therefore, the potential difference measured in case C must be less that of cases A and B.
37. A—Disconnecting the battery will ensure that the original charge Q on the capacitor cannot change, because there is nowhere for the charge to go and no way to add any new charge to the capacitor. Thus disconnecting the battery cannot be one of our choices. Decreasing the distance d between the plates will increase the capacitance C of the capacitor:
Keeping the capacitor connected to the battery ensures that the voltage ΔV of the capacitor stays the same. This means that the change Q on the capacitor must increase as the capacitance C increases because the plates have been moved closer together:
Since both capacitance C and charge Q are increasing, the energy stored in the capacitor must also increase:
38. D—Using the right-hand rule for magnetic force on a current-carrying wire, we can see there is a magnetic force directed radially outward on the wire loop that will try to expand the loop but will not move the loop.
39. A—Two background concepts: First, the magnetic field around current-carrying wire can be visualized using the right-hand rule by grasping the wire with your right hand with your thumb in the direction of the current. Your fingers will curl around the wire in the direction that the magnetic field rotates around the wire. Second, a magnetic dipole will rotate to align with the north end pointing in the direction of the magnetic field. With this in mind, looking at the board from the top, the magnetic field around the right wire will circulate clockwise and counterclockwise around the wire on the left. This is best depicted by answer choice A. Answer choice B shows clockwise circulation around both wires. Answer choices C and D depict fields pointing either away or toward the wires.
40. C—Using the right-hand rule for finding the magnetic field around current-carrying wires, we can see that the magnetic field points into the page on the right of the wire and out of the page on the left of the wire. Notice that proton 2 is moving parallel to the magnetic field from the wire. This means there will be no magnetic force on proton 2:
Protons 1 and 3 are moving perpendicular to the field. Thus the sin θ equals 1.
We know that the magnetic field around a wire is:
Substituting this into the magnetic force on moving charges equation we get:
Since both the velocity and the radius from the wire are doubled for proton 3 compared to proton 1, the magnetic forces are the same on both protons.
41. D—There is no heat transfer to, or from, the environment. Therefore, this must be an adiabatic process: Q = 0. The gas is expanding (+ΔV), which means that the work will be negative: W = —PΔV. From the first law of thermodynamics, we see that the change in internal energy of the gas must be negative: ΔU = Q + W. Since the internal energy of the gas is directly related to the temperature of the gas , the temperature of the gas must be decreasing. Finally, using the ideal gas law (PV = nRT), we can see that if the temperature is decreasing, the value of PV must also be decreasing. Only path D has a final PV value less than the initial value.
42. B—Doubling the temperature of a gas in a sealed container will double the pressure of the gas: PV = nRT. Doubling the pressure will also double the force, since the size of the container will stay the same: F = PA. Doubling the temperature of the gas will double the average kinetic energy of the gas molecules: . But, kinetic energy is proportional to v2. Therefore, the average speed of the molecules will only increase only by a factor of .
43. D—While there will be convection and radiation, the collisions between faster- and slower-moving molecules are the primary energy-transferring mechanism. The molecules literally collide themselves into transferring energy/momentum until the system is in thermal equilibrium and the average kinetic energy of the molecules is the same.
44. A—Pattern 2 has a closer fringe spacing than pattern 1. We could decrease the pattern spacing by simply moving the screen closer to the slit. Since that is not an option, answer choice C can be eliminated. Let’s take a look at the interference pattern equation that models this 'margin-top:12.0pt;margin-right:0cm; margin-bottom:12.0pt;margin-left:0cm;text-align:center;line-height:normal; text-autospace:none'>
To get a pattern with a tighter spacing, we need to have a smaller angle θ. Rearranging the equation:
The variable m is just the counter to find the angle for different order maxima and minima so we can neglect it. To get a smaller angle θ, we need to have a decreased λ or increased d. Neither of those is an option, so we can eliminate answer choices B and D. This leaves choice A as the correct answer. This makes sense because if we increase the frequency f of the light, the wavelength λ will decrease, making the pattern tighter, which is what we wanted!
45. A—Light traveling from water to air speeds up and will refract away from the normal. Draw several rays coming from the fish in the direction of the bird and backtrack the refracted rays to locate the image location.
Questions 46—50: Multiple-Correct Items
(You must indicate both correct answers; no partial credit is awarded.)
46. B and C—With the switch closed, the equivalent resistance of the circuit is 4 Ω. When the switch is opened, the equivalent resistance of the circuit goes up to 6 Ω. This means that the current passing through A3 decreases when the switch is opened, and that the voltage difference measured by V1 must also decrease due to less current passing through the resistor. By process of elimination, the other two answer choices are correct. Note: This is not the only way to solve this problem, but seemed the fastest.
47. B and C—3.2 × 10—19 C is the charge of two electrons/protons. It is physically possible to have a charge exactly half this size as this would be the the net charge of a single electron/proton. Knowing that the magnetic force on the charge causes the particle to arc into a circular path, we can derive: , which gives us . If the particle has twice the momentum or half the charge, it would turn in a circular arc with twice the radius.
48. A and D—Thermal energy always flows from high temperature to low temperature. Initially heat must flow into sample 2 from both samples 1 and 3. This will lower the temperature of sample 3 below the final equilibrium temperature of 310 K. Thus, as the temperature of sample 2 rises, heat will eventually have to flow back into sample 3 to bring its temperature back up to the equilibrium temperature of 310 K.
49. C and D—Since the angles in the two media are different, the speed of light must be different in the materials and the two media cannot be the same. The angle of refraction in media 2 is larger than the incidence angle, meaning that there will be a critical angle beyond which there will be total internal reflection. Note: We cannot assume that either of these two mediums is air (n = 1).
50. A and C—The discrete electron energy levels in hydrogen can be understood as being orbits of constructive wave interference locations for the electron. The alternating intensities seen in diffraction patterns are evidence of the wave nature of electrons reflecting off the atoms in the crystal. Both of the other choices are examples of the particle nature of electromagnetic waves.
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.
1 point—For indicating that the ball is originally neutral.
1 point—For explaining that the ball becomes polarized when the Van de Graaff becomes positively charged. During polarization some electrons in the ball are attracted to the left of the ball. This causes a charge separation with the left side of the ball more negatively charged and the right side of the ball more positively charged.
1 point—For indicating that due to charge polarization the ball is attracted to the Van de Graaff. The negative side of the ball is attracted to the Van de Graaff with a greater electrostatic force than the electrostatic repulsion of the positive Van de Graaff and the positive side of the ball because of the difference in distances between the two sides of the ball and the charged Van de Graaff.
1 point—For explaining that when the ball contacts the sphere, the ball and the Van de Graaff become the same charge. Electrons move from the ball to the Van de Graaff leaving the ball with a net positive charge.
1 point—For indicating that the positive ball will now be repelled by an electrostatic force to the right and will no longer hang vertically.
1 point—For drawing the electric force the same number of squares on the grid to the right of the ball as the tension force is drawn to the left of the ball.
1 point—For drawing the gravity force the same number of squares downward from the ball as the tension force is drawn upward from the ball.
Note: No points are awarded for incorrectly labeled forces. Deduct a point for each incorrect additional force vector drawn. The minimum score is zero.
1 point—For the correct expression of the electric force:
1 point—For equating the horizontal component of the tension to the electric force and for equating the vertical component of the tension to the gravitational force.
There are two methods to do this:
1 point—For the correct formula for the charge on the ball:
1 point—For correctly applying Kirchhoff’s loop rule for the upper loop:
1 point—For correctly applying Kirchhoff’s loop rule to the outer loop:
1 point—For correctly using the two equations to show that I3 is twice as large as I2:
No points are awarded for the correct ranking of: P1 > P4 > P2 = P3.
1 point—For indicating that Power = I 2R and that all the resistors are the same. Therefore, the ranking is based on the current passing through the resistors.
1 point—For indicating that resistor 1 receives the most current as all the current must pass through it AND that resistor 4 receives more current than resistors 2 and 3 AND that resistors 2 and 3 receive the same current because they are in the same conductive pathway.
(i.) Agree that the power will go down for resistor 1.
1 point—For indicating that when the switch is opened, there is only one path left for the current to pass through. This means the total resistance of the circuit increases. The potential difference across resistor 1 will decrease, which will bring its power dissipation down as well.
(ii.) Disagree that resistors 2 and 3 are unaffected.
1 point—For deriving a correct expression for the original current passing through resistors 2 and 3:
1 point—For deriving a correct expression for the new current passing through resistors 2 and 3:
The new current is larger than the old; therefore, the power dissipation goes up. (Note that this argument can be also be made using potential difference and would also receive credit.)
(i.) Immediately after the switch is closed, the capacitor acts like a short-circuit wire that allows the current to bypass resistors 2 and 3.
1 point—For indicating that the current through resistor 1 will be , and that the potential difference across the capacitor is zero (ΔVC = 0).
(ii.) After a long period of time, the capacitor becomes fully charged and acts like an open switch in the circuit.
1 point—For indicating the current through resistor 1 will be: .
1 point—For indicating that the potential difference across the capacitor will be equal to that of resistors 2 and 3 combined, because the capacitor is in parallel with them: . Note this can be stated in words or symbolically to receive credit.
1 point—For calculating the potential energy stored by the capacitor:
1 point—For correctly calculating an appropriate set of image and object distances.
For example: Knowing that the lens is located at 50 cm and using the first set of data, we get the following:
1 point—For correctly calculating the focal length of the lens:
1 point—For explaining how to produce a straight line from the data and why the y-intercept equals 1/f.
1 point—For plotting 1/so on the x-axis and 1/si on the y-axis and drawing a best fit line through the data.
1 point—For calculating the correct focal length using the y-intercept.
Example: The lens equation can be rearranged to produce a straight line:
Thus, if we plot 1/so on the x-axis and 1/si on the y-axis, we should get a graph with a slope of —1 and an intercept of 1/f .
From our graph, the intercept is 0.067 1/cm, which gives us a focal length of 15 cm (the same as part A).
1 point—For drawing the candle or other object between the focus and the lens. This point cannot be awarded if the focal points are not designated on the drawing.
1 point—For drawing two correct rays from the object and passing through the lens. This point cannot be awarded if the focal points are not designated on the drawing. However, the point can be earned even if the object is not correctly located between the focus and the lens as long as the rays are correct for the object and lens placement.
1 point—For drawing a correct virtual image. The image should be upright, located at the intersection of the two outgoing rays, and be larger than the object.
Here is an example drawing:
(An upright image will be virtual. The object will need to be between the lens and the focal point. Sketches will differ, and image locations will vary a bit depending on where the object is placed between the focal point and the lens.)
1 point—For disagreeing and stating that virtual images can be seen but cannot be projected on a screen.
1 point—For describing an appropriate demonstration to prove that virtual images cannot be projected on a screen.
For example: Produce a real image and show that it can be projected on a screen. Then create a virtual image and show that the image cannot be made to show up on the screen.
Note that all the numbers in this problem are rounded to two significant digits because that is the accuracy of the data from the graph.
1 point—For the correct value of temperature with supporting equation and work: PV = nRT, T = 480 K.
1 point—For an explanation that the temperature of the gas is directly related to the average kinetic energy of the gas molecules.
1 point—For the correct force with supporting equation and work: F = PA = 2,000 N.
1 point—For an explanation of the mechanism that produces gas force on the piston.
For example: The gas molecules collide with the piston in a momentum collision that imparts a tiny force on the piston. The sum of all the individual molecular collision forces is the net force on the piston.
1 point—For indicating that the temperature of the gas is decreasing and explaining why this occurs.
For example: Since the PV value of the gas decreases, the temperature of the gas decreases in this process as indicated by the ideal gas law.
1 point—For indicating that the internal energy of the gas will decrease and explaining why this occurs.
For example: ΔU = nRΔT and the temperature is decreasing. Therefore, the internal energy of the gas also must decrease.
1 point—For indicating that the work in this process is positive because the process is moving to the left on the graph and that the thermal energy of the gas is decreasing because the temperature is decreasing.
1 point—For using the first law of thermodynamics to determine that heat is being removed from the gas.
For example: work is positive and the gas internal energy is decreasing. Therefore, using the first law of thermodynamics, ΔU = Q + W, we can see that heat must be leaving the gas during this process.
1 point—For indicating that the entropy of the gas is decreasing because thermal energy is being removed in this process. This reduces the spread of the speed distribution of the gas, thus reducing disorder.
1 point—For the correct answer with supporting work:
Based on the PV values, the temperature at point A is higher than that at point B. Thus, the peak for A must be at a higher speed than for B.
1 point—For both curves showing a roughly bell shape, and curve A having a higher average speed than curve B.
The area under the graphs must be equal because the number of molecules remains the same. This means the peak for A must be lower than that for B.
1 point—For curve A having a lower maximum than curve B, and both curves having roughly the same area beneath them.
How to Score Practice Exam 3
The practice exam cut points are based on historical 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