We’ve compiled a sortable list of all AP Physics 1 past prompts! The AP Physics 1 FRQs are 50% of the exam including short-answer questions, experimental design questions, qualitative/quantitative translation questions, and a paragraph-length response.

Short-answer questions (SAQs) are your standard multi-part free-response questions asking to solve for a given variable or quantity or to label a diagram or graph. Experimental design questions will ask you to design an experiment given a certain scenario. Qualitative/quantitative translation questions will challenge you to explore the relationship between the conceptual understanding of a model and the mathematical representations of that model. Finally, the paragraph-length response will be where you’ll write a paragraph showing your conceptional knowledge of why a system behaves the way it does.

It’s important that you understand the question styles going into the exam. Use this list to practice!

Since the Physics 1 exam was first released in 2015, there are only five years of released exams with questions using this format.

AP 1 Past Prompts Table

Year	Type	Unit (Topic)	Prompt	Mean Score
2019	SAQ	multiple units (Velocity, Angular Momentum)	Identical blocks 1 and 2 are placed on a horizontal surface at points A and E, respectively, as shown. The surface is frictionless except for the region between points C and D, where the surface is rough. Beginning at time At , block 1 is pushed with a constant horizontal force from point A to point B by a mechanical plunger. Upon reaching point B, block 1 loses contact with the plunger and continues moving to the right along the horizontal surface toward block 2. Block 1 collides with and sticks to block 2 at point E, after which the two-block system continues moving across the surface, eventually passing point F. (a) On the axes below, sketch the speed of the center of mass of the two-block system as a function of time, from time At until the blocks pass point F at time Ft . The times at which block 1 reaches points A through F are indicated on the time axis. (b) The plunger is returned to its original position, and both blocks are removed. A uniform solid sphere is placed at point A, as shown. The sphere is pushed by the plunger from point A to point B with a constanthorizontal force that is directed toward the sphere’s center of mass. The sphere loses contact with the plunger at point B and continues moving across the horizontal surface toward point E. In which interval(s), if any, does the sphere’s angular momentum about its center of mass change? Briefly explain your reasoning.	3.49/7
2019	Q/QT	Dynamics (Newton's Second Law)	This problem explores how the relative masses of two blocks affect the acceleration of the blocks. Block A, of mass m A, rests on a horizontal tabletop. There is negligible friction between block A and the tabletop. Block B, of mass mB , hangs from a light string that runs over a pulley and attaches to block A, as shown above. The pulley has negligible mass and spins with negligible friction about its axle. The blocks are released from rest. (a)(i)Suppose the mass of block A is much greater than the mass of block B. Estimate the magnitude of the acceleration of the blocks after release. Briefly explain your reasoning without deriving or using equations. (ii)Now suppose the mass of block A is much less than the mass of block B. Estimate the magnitude of the acceleration of the blocks after release. Briefly explain your reasoning without deriving or using equations. (b)Now suppose neither block’s mass is much greater than the other, but that they are not necessarily equal. The dots below represent block A and block B, as indicated by the labels. On each dot, draw and label the forces (not components) exerted on that block after release. Represent each force by a distinct arrow starting on, and pointing away from, the dot. (c)Derive an equation for the acceleration of the blocks after release in terms of mA , mB , and physical constants, as appropriate. If you need to draw anything other than what you have shown in part (b) to assist in your solution, use the space below. Do NOT add anything to the figure in part (b). (d)Consider the scenario from part (a)(ii), where the mass of block A is much less than the mass of block B. Does your equation for the acceleration of the blocks from part (c) agree with your reasoning in part (a)(ii) ? Briefly explain your reasoning by addressing why, according to your equation, the acceleration becomes (or approaches) a certain value when m A is much less than mB . (e)While the blocks are accelerating, the tension in the vertical portion of the string is T1. Next, the pulley of negligible mass is replaced with a second pulley whose mass is not negligible. When the blocks are accelerating in this scenario, the tension in the vertical portion of the string is T2. How do the two tensions compare to each other? Briefly explain your reasoning.	4.65/12
2019	EDQ	Dynamics (Hooke's Law, Projectile Motion)	A projectile launcher consists of a spring with an attached plate, as shown in Figure 1. When the spring is compressed, the plate can be held in place by a pin at any of three positions A, B, or C. For example, Figure 2 shows a steel sphere placed against the plate, which is held in place by a pin at position C. The sphere is launched upon release of the pin. A student hypothesizes that the spring constant of the spring inside the launcher has the same value for different compression distances. (a)The student plans to test the hypothesis by launching the sphere using the launcher. (i)State a basic physics principle or law the student could use in designing an experiment to test the hypothesis. (ii)Using the principle or law stated in part (a)(i), determine an expression for the spring constant in terms of quantities that can be obtained from measurements made with equipment usually found in a school physics laboratory. (b)Design an experimental procedure to test the hypothesis in which the student uses the launcher to launch the sphere. Assume equipment usually found in a school physics laboratory is available. In the table below, list the quantities and associated symbols that would be measured in your experiment. Also list the equipment that would be used to measure each quantity. You do not need to fill in every row. If you need additional rows, you may add them to the space just below the table. Describe the overall procedure to be used to test the hypothesis that the spring constant of the spring inside the launcher has the same value for different compression distances, referring to the table. Provide enough detail so that another student could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use the symbols defined in the table and/or include a simple diagram of the setup. (c)Describe how the experimental data could be analyzed to confirm or disconfirm the hypothesis that the spring constant of the spring inside the launcher has the same value for different compression distances. (d) Another student uses the launcher to consecutively launch several spheres that have the same diameter but different masses, one after another. Each sphere is launched from position A. Consider each sphere’s launch speed, which is the speed of the sphere at the instant it loses contact with the plate. On the axes below, sketch a graph of launch speed as a function of sphere mass.	5.38/12
2019	Paragraph Length Response	multiple units (Series & Parallel Circuits, Work, Power)	A motor is a device that when connected to a battery converts electrical energy into mechanical energy. The motor shown above is used to lift a block of mass M at constant speed from the ground to a height H above the ground in a time interval Dt. The motor has constant resistance and is connected in series with a resistor of resistance R1 and a battery. Mechanical power, the rate at which mechanical work is done on the block, increases if the potential difference (voltage drop) between the two terminals of the motor increases. (a) Determine an expression for the mechanical power in terms of M, H, Dt, and physical constants, as appropriate. (b) Without M or H being changed, the time interval Dt can be decreased by adding one resistor of resistance R 2 , where R R 2 > 1, to the circuit shown above. How should the resistor of resistance R 2 be added to the circuit to decrease Dt ? In a clear, coherent, paragraph-length response that may also contain figures and/or equations, justify why your selection would decrease Dt.	2.08/7
2019	SAQ	Mechanical Waves and Sound (Resonance)	A tuning fork vibrating at 512 Hz is held near one end of a tube of length L that is open at both ends, as shown above. The column of air in the tube resonates at its fundamental frequency. The speed of sound in air is 340 m s. (a) Calculate the length L of the tube. (b) The column of air in the tube is still resonating at its fundamental frequency. On the axes below, sketch a graph of the maximum speed of air molecules as they oscillate in the tube, as a function of position x, from x = 0 (left end of tube) to x = L (right end of tube). (Ignore random thermal motion of the air molecules.) (c) The right end of the tube is now capped shut, and the tube is placed in a chamber that is filled with another gas in which the speed of sound is 1005 m s. Calculate the new fundamental frequency of the tube.	2.62/7
2018	SAQ	Dynamics (Gravitation and Forces)	A spacecraft of mass m is in a clockwise circular orbit of radius R around Earth. The mass of Earth is ME. (a)In the figure below, draw and label the force (not components) that act on the spacecraft. Each force must be represented by a distinct arrow starting on, and pointing away from, the spacecraft. (b)(i)Derive an equation for the orbital period T of the spacecraft in terms of m, ME, R, and physical constants as appropriate. If you need to draw anything other than what you have drawn in part (a) to assist in your solution, use the space below. (ii)A second spacecraft of mass 2m is placed in a circular orbit with the same radius R. Is the orbital period of the second spacecraft greater than, less than, or equal to the orbital period of the first spacecraft? Briefly explain your reasoning. (c)The first spacecraft moved into a new circular orbit that has a radius greater than R. Is the speed of the spacecraft in the new orbit greater than, less than, or equal to the original speed? Briefly explain your reasoning.	2.17/7
2018	EDQ	DC (Circuits Resistivity)	A group of students prepare a large batch of conductive dough (a soft substance that can conduct electricity) and the mold the dough into several cylinders with various cross-sectional areas A and lengths l. Each student applies a potential difference ∆V across the ends of a dough cylinder and determines the resistance R of the cylinder. The results of their experiments are shown in the table below. (a)The students want to determine the resistivity of the dough cylinders. (i)Indicate below which quantities could be graphed to determine a value for the resistivity of the dough cylinders. (ii)On the grid below, plot the appropriate to determine the resistivity of the dough cylinders. Clearly scale and label all axes, including units as appropriate. (iii)Use the above graph to estimate a value for the resistivity of the dough cylinders. (b)Another group of students perform the experiment described in part (a) but shape the dough into long rectangular shapes instead of cylinders. Will this change affect the value of the resistivity determined by the second group of students? (c)Describe an experimental procedure to determine whether or not the resistivity of the dough cylinders depends on the temperature of the dough. Give enough detail so that another student could replicate the experiment. As needed, include a diagram of the experimental setup. Assume equipment usually found in a school physics laboratory is available.	4.57/12
2018	Q/QT	Torque and Rotational Motion (Torque and Rotation)	The disk shown above spins about the axle at its center. A students' experiments reveal that, while the disk is spinning, friction between the axle and the disk exerts a constant torque on the disk. (a)At time t = 0 the disk has an initial counterclockwise (positive) angular velocity omega0. The disk later comes to rest at time t = t1. (i)On the grid at left below, sketch a graph that could represent the disk's angular velocity as function of time t from t = 0 until the disk comes to rest at t = t1. (ii)On the grid at right below, sketch the disk's angular acceleration as a function of time from t = 0 until the disk comes to rest at t = t1. (b)The magnitude of the frictional torque exerted on the disk is tau0. Derive an equation for the rotational inertia I of the disk in terms of tau0, omega0, t1, and physical constants, as apporopriate. (c)In another experiment, the disk again has an initial positive angular velocity omega0 at time t = 0. At time t = 1/2t1, the student starts dripping oil on the contact surface between the axle and the disk to reduce the friction. As time passes, more and more oil reaches the contact surface, reducing the friction even further. (i)On the grid at left below, sketch a graph that could represent the disk's angular velocity as a function of time from t = 0 to t = t1, which is the time at which the disk came to rest in part (a). (ii)On the grid at right below, sketch the disk's angular acceleration as function of time from t = 0 to t = t1. (c)The student is trying to mathematically model the magnitude tau of the torque exerted by the axle on the disk when the oil is present at time > t = 1/2t1. The student writes down the following two equations, each of which includes a positive constant (C1 or C2) with appropriate units. Which equation better mathematically models this experiment? Briefly explain why the equation you selected is plausible and why the other equation is not plausible.	6.06/12
2018	SAQ	Mechanical Waves and Sound (Waves)	A transverse wave travels to the right along a string. (a)Two dots have been painted on the string. In the diagrams below, those dots are labeled P and Q. (i)The figure below shows the string at an instant in time. At the instant shown, dot P has maximum displacement and dot Q has zero displacement from equilibrium. At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous velocity of that dot. If either dot has zero velocity, write "v = 0" next to that dot. (ii)The figure below shows the string at the same instant shown in part (a)(i). At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous acceleration of that dot. If either dot has zero acceleration, write "a = 0" next to that dot. The figure below represents the string at t = 0, the same instant shown in part (a) when dot P is at its maximum displacement from equilibrium. For simplicity, dot Q is not shown. (b)(i)On the grid below, draw the string at a later time t = T/4, where T is the period of the wave. (ii)On your drawing above, draw a dot to indicate the position of dot P on the string at time t = T/4 and clearly label the dot with the letter P. (c)Now consider the wave at time t = T. Determine the distance traveled (not the displacement) by dot P between times t = 0 and t = T.	2.48/7
2018	Paragraph Length Response	multiple units (Simple Harmonic Motion, Conservation of Momentum, and Conservation of Energy)	Block P of mass m is on a horizontal, frictionless surface and is attached to a spring with a spring constant k. The block is oscillating with period TP and amplitude AP about the spring's equilibrium position x0. A second block Q of mass 2m is then dropped from rest and lands on block P at the instant it passes through the equilibrium position, as shown above. Block Q immediately sticks to the top of Block P, and the two-block system oscillates with period TPQ and amplitude APQ. (a)Determine the numerical value of the ration TPQ/TP. (b)How does the amplitude of oscillation APQ of the two-block system compare with the original amplitude AP of block P alone? In a clear, coherent paragraph-length response that may also contain diagrams and/or equations, explain your reasoning.	0.94/7
2017		DC Circuits (Series & Parallel Circuits & Ohm's Law)	In the three circuits shown above, the batteries are all identical, and the lightbulbs are all identical. In circuit 1 a dingle lightbulb is connected to the battery. In circuits 2 and 3, two lightbulbs are connected to the battery in different ways, as shown. The lightbulbs are labeled A-E. (a)Rank the magnitudes of the potential difference across lightbulbs A, B, C, D, and E from largest to smallest. If any of the lightbulbs have the same potential difference across them, state that explicitly. Briefly explain how you determined your ranking. (b)The batteries all start with an identical amount of usable energy and are all connected to the lightbulbs in the circuits at the same time. In which circuit will the battery run out of usable energy first? In which circuit will the battery run out of usable energy last? In a clear, coherent, paragraph-length response that may also contain equations and drawings, explain your reasoning.	2.38/7
2017	EDQ	Dynamics (Friction)	A student wants to determine the coefficient of static friction between a long, flat wood board and a small wood block. (a)Describe an experiment for determining the coefficient of friction between the wood board and the wood block. Assume equipment usually found in a school physics laboratory is available. (i)Draw a diagram of the experimental setup of the board and the block. In your diagram, indicate each quantity that would be measured and draw or state what equipment would be used to measure each quantity. (ii)Describe the overall procedure to be used, including any steps necessary to reduce experimental uncertainty. Give enough detail so that another student could replicate the experiment. (b)Derive an equation for the coefficient of static friction in terms of quantities measured in part (a). A physics class consisting of six lab groups wants to test the hypothesis that the coefficient of static friction between the board and the block equals the coefficient of kinetic friction between the board and the block. Each group determines the coefficients of static and kientic friction between the board and the block. The groups' results are shown below, with class averages indicated in the bottom row. (c)Based on these data, what conclusion should the students make about the hypothesis that static and kinetic friction are equal? Briefly justify your reasoning. (d)A metal disk is glued to the top of the wood block. The mass of the block-disk system is twice the mass of the original block. Does the coefficient of static friction between the bottom of the block and the board increase, decrease, or remain the same when the disk is added to the block? Briefly state your reasoning.	5.47/12
2017	Q/QT	Torque and Rotational Motion (Conservation of Angular Momentum)	The left end of a rod of length d and rotational inertia I is attached to a frictionless horizontal surface by a frictionless pivot, as shown above. Point C markes the center (midpoint) of the rod. The rod is initially motionless but is free to rotate around the pivot. A student will slide a disk of mass mdisk toward the rod with velocity v0 perpendicular to the rod, and the disk will stick to the rod a distance x from the pivot. The student wants the rod-disk system to end up with as much angular speed as possible. (a)Suppose the rod is much more massive than the disk. To give the rod as much angular speed as possible, should the student make the disk hit the rod to the left of Point C, and Point C, or to the right of Point C? Briefly explain your reasoning without manipulating equations. (b)On the Internet, a student finds the following equation for the postcollision angular speed omega of the rod in this situation: omega. Regardless of whether this equation for angular speed is correct, does it agree with your qualitative reasoning in part (a)? In other words, does this equation for omega have the expected dependence as predicted in part (a)? Another student deriving an equation for the postcollision angular speed omega makes a mistake and comes up with (equation). Without deriving the correct equation, how can you tell that this equation is not plausible—in other words, that it does not make physical sense? Briefly explain your reasoning. For parts (d) and (e), do not assume that the rod is much more massive than the disk. (d)Immediately before colliding with the rod, the disk's rotational inertia about the pivot is mdiskx^2 and its angular momentum with respect to the pivot is mdiskv0x. Derive an equation for the postcollision angualr speed omega of the rod. Express your answer in terms of d, mdisk, I, x, v0, and physical constants as appropriate. (e)Consider the collision for which your equation in part (d) was derived, except now suppose the disk bounces backward off the rod instead of sticking to the rod. Is the postcollision angular speed when the disk bounces off it greater than, less than, or equal to the postcollision angular speed when disk sticks to it? Briefly explain your reasoning.	3.48/12
2017	SAQ	Energy (Conservation of Energy)	A physics class is asked to design a low-friction slide that will launch a block horizontally from the end of a lab table. Teams 1 and 2 assemble the slides shown above and use identical blocks 1 and 2, respectively. Both slides start at the same height d above the tabletop. However, team 2's table is lower than team 1's table. To compensate for the lower table, team 2 constructs the right end of the slide to rise above the tabletop so that the block leaves the slide horizontally at the same height h above the floor as does team 1's block. (a)Both blocks are released from rest at the top of their respective slides. Do block 1 and block 2 land at the same distance from their respective tables? Justify your answer. In another experiment, team 1 and 2 use tables and low-friction slides with the same height. However, the slides have different shapes, as shown below. (b)Both blocks are released from rest at the top of their respective slides at the same time. (i)Which block, if either, lands farther from its respective table? Briefly explain your answer without manipulating equations. (ii)Which block, if either, hits the floor first? Briefly explain your answer without manipulating equations.	2.01/7
2017	SAQ	Mechanical Waves and Sound (Waves)	Two wave pulses are traveling in opposite directions on a string. The shape of the string at t = 0 is shown above. Each pulse is moving at a speed of one unit per second in the direction indicated. (a) Between time t = 0 and t = 5 seconds, the entire left-hand pulse approaches and moves beyond point P on the string. On the coordinate axes below, plot the velocity of the piece of string located at point P as a function of time between t = 0 and t = 5 seconds. (b)At t = 5 seconds, the pulses completely overlap. On the grid provided below, sketch the shape of the entire graph at t = 5 seconds.	2.63/7

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AP Physics 1 Free-Response Questions (FRQ) – Past Prompts

17 min read•july 11, 2024

Avanish Gupta

It’s important that you understand the question styles going into the exam. Use this list to practice!

Since the Physics 1 exam was first released in 2015, there are only five years of released exams with questions using this format.

AP 1 Past Prompts Table

Year	Type	Unit (Topic)	Prompt	Mean Score
2019	SAQ	multiple units (Velocity, Angular Momentum)	Identical blocks 1 and 2 are placed on a horizontal surface at points A and E, respectively, as shown. The surface is frictionless except for the region between points C and D, where the surface is rough. Beginning at time At , block 1 is pushed with a constant horizontal force from point A to point B by a mechanical plunger. Upon reaching point B, block 1 loses contact with the plunger and continues moving to the right along the horizontal surface toward block 2. Block 1 collides with and sticks to block 2 at point E, after which the two-block system continues moving across the surface, eventually passing point F. (a) On the axes below, sketch the speed of the center of mass of the two-block system as a function of time, from time At until the blocks pass point F at time Ft . The times at which block 1 reaches points A through F are indicated on the time axis. (b) The plunger is returned to its original position, and both blocks are removed. A uniform solid sphere is placed at point A, as shown. The sphere is pushed by the plunger from point A to point B with a constanthorizontal force that is directed toward the sphere’s center of mass. The sphere loses contact with the plunger at point B and continues moving across the horizontal surface toward point E. In which interval(s), if any, does the sphere’s angular momentum about its center of mass change? Briefly explain your reasoning.	3.49/7
2019	Q/QT	Dynamics (Newton's Second Law)	This problem explores how the relative masses of two blocks affect the acceleration of the blocks. Block A, of mass m A, rests on a horizontal tabletop. There is negligible friction between block A and the tabletop. Block B, of mass mB , hangs from a light string that runs over a pulley and attaches to block A, as shown above. The pulley has negligible mass and spins with negligible friction about its axle. The blocks are released from rest. (a)(i)Suppose the mass of block A is much greater than the mass of block B. Estimate the magnitude of the acceleration of the blocks after release. Briefly explain your reasoning without deriving or using equations. (ii)Now suppose the mass of block A is much less than the mass of block B. Estimate the magnitude of the acceleration of the blocks after release. Briefly explain your reasoning without deriving or using equations. (b)Now suppose neither block’s mass is much greater than the other, but that they are not necessarily equal. The dots below represent block A and block B, as indicated by the labels. On each dot, draw and label the forces (not components) exerted on that block after release. Represent each force by a distinct arrow starting on, and pointing away from, the dot. (c)Derive an equation for the acceleration of the blocks after release in terms of mA , mB , and physical constants, as appropriate. If you need to draw anything other than what you have shown in part (b) to assist in your solution, use the space below. Do NOT add anything to the figure in part (b). (d)Consider the scenario from part (a)(ii), where the mass of block A is much less than the mass of block B. Does your equation for the acceleration of the blocks from part (c) agree with your reasoning in part (a)(ii) ? Briefly explain your reasoning by addressing why, according to your equation, the acceleration becomes (or approaches) a certain value when m A is much less than mB . (e)While the blocks are accelerating, the tension in the vertical portion of the string is T1. Next, the pulley of negligible mass is replaced with a second pulley whose mass is not negligible. When the blocks are accelerating in this scenario, the tension in the vertical portion of the string is T2. How do the two tensions compare to each other? Briefly explain your reasoning.	4.65/12
2019	EDQ	Dynamics (Hooke's Law, Projectile Motion)	A projectile launcher consists of a spring with an attached plate, as shown in Figure 1. When the spring is compressed, the plate can be held in place by a pin at any of three positions A, B, or C. For example, Figure 2 shows a steel sphere placed against the plate, which is held in place by a pin at position C. The sphere is launched upon release of the pin. A student hypothesizes that the spring constant of the spring inside the launcher has the same value for different compression distances. (a)The student plans to test the hypothesis by launching the sphere using the launcher. (i)State a basic physics principle or law the student could use in designing an experiment to test the hypothesis. (ii)Using the principle or law stated in part (a)(i), determine an expression for the spring constant in terms of quantities that can be obtained from measurements made with equipment usually found in a school physics laboratory. (b)Design an experimental procedure to test the hypothesis in which the student uses the launcher to launch the sphere. Assume equipment usually found in a school physics laboratory is available. In the table below, list the quantities and associated symbols that would be measured in your experiment. Also list the equipment that would be used to measure each quantity. You do not need to fill in every row. If you need additional rows, you may add them to the space just below the table. Describe the overall procedure to be used to test the hypothesis that the spring constant of the spring inside the launcher has the same value for different compression distances, referring to the table. Provide enough detail so that another student could replicate the experiment, including any steps necessary to reduce experimental uncertainty. As needed, use the symbols defined in the table and/or include a simple diagram of the setup. (c)Describe how the experimental data could be analyzed to confirm or disconfirm the hypothesis that the spring constant of the spring inside the launcher has the same value for different compression distances. (d) Another student uses the launcher to consecutively launch several spheres that have the same diameter but different masses, one after another. Each sphere is launched from position A. Consider each sphere’s launch speed, which is the speed of the sphere at the instant it loses contact with the plate. On the axes below, sketch a graph of launch speed as a function of sphere mass.	5.38/12
2019	Paragraph Length Response	multiple units (Series & Parallel Circuits, Work, Power)	A motor is a device that when connected to a battery converts electrical energy into mechanical energy. The motor shown above is used to lift a block of mass M at constant speed from the ground to a height H above the ground in a time interval Dt. The motor has constant resistance and is connected in series with a resistor of resistance R1 and a battery. Mechanical power, the rate at which mechanical work is done on the block, increases if the potential difference (voltage drop) between the two terminals of the motor increases. (a) Determine an expression for the mechanical power in terms of M, H, Dt, and physical constants, as appropriate. (b) Without M or H being changed, the time interval Dt can be decreased by adding one resistor of resistance R 2 , where R R 2 > 1, to the circuit shown above. How should the resistor of resistance R 2 be added to the circuit to decrease Dt ? In a clear, coherent, paragraph-length response that may also contain figures and/or equations, justify why your selection would decrease Dt.	2.08/7
2019	SAQ	Mechanical Waves and Sound (Resonance)	A tuning fork vibrating at 512 Hz is held near one end of a tube of length L that is open at both ends, as shown above. The column of air in the tube resonates at its fundamental frequency. The speed of sound in air is 340 m s. (a) Calculate the length L of the tube. (b) The column of air in the tube is still resonating at its fundamental frequency. On the axes below, sketch a graph of the maximum speed of air molecules as they oscillate in the tube, as a function of position x, from x = 0 (left end of tube) to x = L (right end of tube). (Ignore random thermal motion of the air molecules.) (c) The right end of the tube is now capped shut, and the tube is placed in a chamber that is filled with another gas in which the speed of sound is 1005 m s. Calculate the new fundamental frequency of the tube.	2.62/7
2018	SAQ	Dynamics (Gravitation and Forces)	A spacecraft of mass m is in a clockwise circular orbit of radius R around Earth. The mass of Earth is ME. (a)In the figure below, draw and label the force (not components) that act on the spacecraft. Each force must be represented by a distinct arrow starting on, and pointing away from, the spacecraft. (b)(i)Derive an equation for the orbital period T of the spacecraft in terms of m, ME, R, and physical constants as appropriate. If you need to draw anything other than what you have drawn in part (a) to assist in your solution, use the space below. (ii)A second spacecraft of mass 2m is placed in a circular orbit with the same radius R. Is the orbital period of the second spacecraft greater than, less than, or equal to the orbital period of the first spacecraft? Briefly explain your reasoning. (c)The first spacecraft moved into a new circular orbit that has a radius greater than R. Is the speed of the spacecraft in the new orbit greater than, less than, or equal to the original speed? Briefly explain your reasoning.	2.17/7
2018	EDQ	DC (Circuits Resistivity)	A group of students prepare a large batch of conductive dough (a soft substance that can conduct electricity) and the mold the dough into several cylinders with various cross-sectional areas A and lengths l. Each student applies a potential difference ∆V across the ends of a dough cylinder and determines the resistance R of the cylinder. The results of their experiments are shown in the table below. (a)The students want to determine the resistivity of the dough cylinders. (i)Indicate below which quantities could be graphed to determine a value for the resistivity of the dough cylinders. (ii)On the grid below, plot the appropriate to determine the resistivity of the dough cylinders. Clearly scale and label all axes, including units as appropriate. (iii)Use the above graph to estimate a value for the resistivity of the dough cylinders. (b)Another group of students perform the experiment described in part (a) but shape the dough into long rectangular shapes instead of cylinders. Will this change affect the value of the resistivity determined by the second group of students? (c)Describe an experimental procedure to determine whether or not the resistivity of the dough cylinders depends on the temperature of the dough. Give enough detail so that another student could replicate the experiment. As needed, include a diagram of the experimental setup. Assume equipment usually found in a school physics laboratory is available.	4.57/12
2018	Q/QT	Torque and Rotational Motion (Torque and Rotation)	The disk shown above spins about the axle at its center. A students' experiments reveal that, while the disk is spinning, friction between the axle and the disk exerts a constant torque on the disk. (a)At time t = 0 the disk has an initial counterclockwise (positive) angular velocity omega0. The disk later comes to rest at time t = t1. (i)On the grid at left below, sketch a graph that could represent the disk's angular velocity as function of time t from t = 0 until the disk comes to rest at t = t1. (ii)On the grid at right below, sketch the disk's angular acceleration as a function of time from t = 0 until the disk comes to rest at t = t1. (b)The magnitude of the frictional torque exerted on the disk is tau0. Derive an equation for the rotational inertia I of the disk in terms of tau0, omega0, t1, and physical constants, as apporopriate. (c)In another experiment, the disk again has an initial positive angular velocity omega0 at time t = 0. At time t = 1/2t1, the student starts dripping oil on the contact surface between the axle and the disk to reduce the friction. As time passes, more and more oil reaches the contact surface, reducing the friction even further. (i)On the grid at left below, sketch a graph that could represent the disk's angular velocity as a function of time from t = 0 to t = t1, which is the time at which the disk came to rest in part (a). (ii)On the grid at right below, sketch the disk's angular acceleration as function of time from t = 0 to t = t1. (c)The student is trying to mathematically model the magnitude tau of the torque exerted by the axle on the disk when the oil is present at time > t = 1/2t1. The student writes down the following two equations, each of which includes a positive constant (C1 or C2) with appropriate units. Which equation better mathematically models this experiment? Briefly explain why the equation you selected is plausible and why the other equation is not plausible.	6.06/12
2018	SAQ	Mechanical Waves and Sound (Waves)	A transverse wave travels to the right along a string. (a)Two dots have been painted on the string. In the diagrams below, those dots are labeled P and Q. (i)The figure below shows the string at an instant in time. At the instant shown, dot P has maximum displacement and dot Q has zero displacement from equilibrium. At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous velocity of that dot. If either dot has zero velocity, write "v = 0" next to that dot. (ii)The figure below shows the string at the same instant shown in part (a)(i). At each of the dots P and Q, draw an arrow indicating the direction of the instantaneous acceleration of that dot. If either dot has zero acceleration, write "a = 0" next to that dot. The figure below represents the string at t = 0, the same instant shown in part (a) when dot P is at its maximum displacement from equilibrium. For simplicity, dot Q is not shown. (b)(i)On the grid below, draw the string at a later time t = T/4, where T is the period of the wave. (ii)On your drawing above, draw a dot to indicate the position of dot P on the string at time t = T/4 and clearly label the dot with the letter P. (c)Now consider the wave at time t = T. Determine the distance traveled (not the displacement) by dot P between times t = 0 and t = T.	2.48/7
2018	Paragraph Length Response	multiple units (Simple Harmonic Motion, Conservation of Momentum, and Conservation of Energy)	Block P of mass m is on a horizontal, frictionless surface and is attached to a spring with a spring constant k. The block is oscillating with period TP and amplitude AP about the spring's equilibrium position x0. A second block Q of mass 2m is then dropped from rest and lands on block P at the instant it passes through the equilibrium position, as shown above. Block Q immediately sticks to the top of Block P, and the two-block system oscillates with period TPQ and amplitude APQ. (a)Determine the numerical value of the ration TPQ/TP. (b)How does the amplitude of oscillation APQ of the two-block system compare with the original amplitude AP of block P alone? In a clear, coherent paragraph-length response that may also contain diagrams and/or equations, explain your reasoning.	0.94/7
2017		DC Circuits (Series & Parallel Circuits & Ohm's Law)	In the three circuits shown above, the batteries are all identical, and the lightbulbs are all identical. In circuit 1 a dingle lightbulb is connected to the battery. In circuits 2 and 3, two lightbulbs are connected to the battery in different ways, as shown. The lightbulbs are labeled A-E. (a)Rank the magnitudes of the potential difference across lightbulbs A, B, C, D, and E from largest to smallest. If any of the lightbulbs have the same potential difference across them, state that explicitly. Briefly explain how you determined your ranking. (b)The batteries all start with an identical amount of usable energy and are all connected to the lightbulbs in the circuits at the same time. In which circuit will the battery run out of usable energy first? In which circuit will the battery run out of usable energy last? In a clear, coherent, paragraph-length response that may also contain equations and drawings, explain your reasoning.	2.38/7
2017	EDQ	Dynamics (Friction)	A student wants to determine the coefficient of static friction between a long, flat wood board and a small wood block. (a)Describe an experiment for determining the coefficient of friction between the wood board and the wood block. Assume equipment usually found in a school physics laboratory is available. (i)Draw a diagram of the experimental setup of the board and the block. In your diagram, indicate each quantity that would be measured and draw or state what equipment would be used to measure each quantity. (ii)Describe the overall procedure to be used, including any steps necessary to reduce experimental uncertainty. Give enough detail so that another student could replicate the experiment. (b)Derive an equation for the coefficient of static friction in terms of quantities measured in part (a). A physics class consisting of six lab groups wants to test the hypothesis that the coefficient of static friction between the board and the block equals the coefficient of kinetic friction between the board and the block. Each group determines the coefficients of static and kientic friction between the board and the block. The groups' results are shown below, with class averages indicated in the bottom row. (c)Based on these data, what conclusion should the students make about the hypothesis that static and kinetic friction are equal? Briefly justify your reasoning. (d)A metal disk is glued to the top of the wood block. The mass of the block-disk system is twice the mass of the original block. Does the coefficient of static friction between the bottom of the block and the board increase, decrease, or remain the same when the disk is added to the block? Briefly state your reasoning.	5.47/12
2017	Q/QT	Torque and Rotational Motion (Conservation of Angular Momentum)	The left end of a rod of length d and rotational inertia I is attached to a frictionless horizontal surface by a frictionless pivot, as shown above. Point C markes the center (midpoint) of the rod. The rod is initially motionless but is free to rotate around the pivot. A student will slide a disk of mass mdisk toward the rod with velocity v0 perpendicular to the rod, and the disk will stick to the rod a distance x from the pivot. The student wants the rod-disk system to end up with as much angular speed as possible. (a)Suppose the rod is much more massive than the disk. To give the rod as much angular speed as possible, should the student make the disk hit the rod to the left of Point C, and Point C, or to the right of Point C? Briefly explain your reasoning without manipulating equations. (b)On the Internet, a student finds the following equation for the postcollision angular speed omega of the rod in this situation: omega. Regardless of whether this equation for angular speed is correct, does it agree with your qualitative reasoning in part (a)? In other words, does this equation for omega have the expected dependence as predicted in part (a)? Another student deriving an equation for the postcollision angular speed omega makes a mistake and comes up with (equation). Without deriving the correct equation, how can you tell that this equation is not plausible—in other words, that it does not make physical sense? Briefly explain your reasoning. For parts (d) and (e), do not assume that the rod is much more massive than the disk. (d)Immediately before colliding with the rod, the disk's rotational inertia about the pivot is mdiskx^2 and its angular momentum with respect to the pivot is mdiskv0x. Derive an equation for the postcollision angualr speed omega of the rod. Express your answer in terms of d, mdisk, I, x, v0, and physical constants as appropriate. (e)Consider the collision for which your equation in part (d) was derived, except now suppose the disk bounces backward off the rod instead of sticking to the rod. Is the postcollision angular speed when the disk bounces off it greater than, less than, or equal to the postcollision angular speed when disk sticks to it? Briefly explain your reasoning.	3.48/12
2017	SAQ	Energy (Conservation of Energy)	A physics class is asked to design a low-friction slide that will launch a block horizontally from the end of a lab table. Teams 1 and 2 assemble the slides shown above and use identical blocks 1 and 2, respectively. Both slides start at the same height d above the tabletop. However, team 2's table is lower than team 1's table. To compensate for the lower table, team 2 constructs the right end of the slide to rise above the tabletop so that the block leaves the slide horizontally at the same height h above the floor as does team 1's block. (a)Both blocks are released from rest at the top of their respective slides. Do block 1 and block 2 land at the same distance from their respective tables? Justify your answer. In another experiment, team 1 and 2 use tables and low-friction slides with the same height. However, the slides have different shapes, as shown below. (b)Both blocks are released from rest at the top of their respective slides at the same time. (i)Which block, if either, lands farther from its respective table? Briefly explain your answer without manipulating equations. (ii)Which block, if either, hits the floor first? Briefly explain your answer without manipulating equations.	2.01/7
2017	SAQ	Mechanical Waves and Sound (Waves)	Two wave pulses are traveling in opposite directions on a string. The shape of the string at t = 0 is shown above. Each pulse is moving at a speed of one unit per second in the direction indicated. (a) Between time t = 0 and t = 5 seconds, the entire left-hand pulse approaches and moves beyond point P on the string. On the coordinate axes below, plot the velocity of the piece of string located at point P as a function of time between t = 0 and t = 5 seconds. (b)At t = 5 seconds, the pulses completely overlap. On the grid provided below, sketch the shape of the entire graph at t = 5 seconds.	2.63/7

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