Learn Extracted exam questions AP Physics 1 2022 Free Response
2022 Free Response
Source PDF on the left, extracted YAML on the right. Compare numbering, marks, options and text.
Two blocks are connected by a string that passes over a pulley, as shown above. Block 1 is on a horizontal surface and is attached to a spring that is at its unstretched length. Frictional forces are negligible in the pulley's axle and between the block and the surface. Block 2 is released from rest and moves downward before momentarily coming to rest.
$k_0$ is the spring constant of the spring.
$M_1$ is the mass of block 1.
$M_2$ is the mass of block 2.
$\Delta y$ is the distance block 2 moves before momentarily coming to rest.
[Figure: A horizontal tabletop with a spring of constant $k_0$ attached to a wall on the left, connected to Block 1 ($M_1$) resting on the table. A string runs from Block 1 horizontally to a pulley at the right edge of the table, then down to a hanging Block 2 ($M_2$), which is shown displaced a distance $\Delta y$ downward from its initial position.]
Block 2 starts from rest and speeds up, then it slows down and momentarily comes to rest at a position below its initial position. In terms of only the forces directly exerted on block 2, explain why block 2 initially speeds up and explain why it slows down to a momentary stop.
Derive an expression for the distance $\Delta y$ that block 2 travels before momentarily coming to rest. Express your answer in terms of $k_0$, $M_1$, $M_2$, and physical constants, as appropriate.
Indicate whether the total mechanical energy of the blocks-spring-Earth system changes as block 2 moves downward.
___ Changes ___ Does not change
Briefly explain your reasoning.
Consider the system that includes the spring, Earth, both blocks, and the string, but not the surface. Let the initial state be when the blocks are at rest just before they start moving, and let the final state be when the blocks first come momentarily to rest. Diagram A below is a bar chart that represents the energies in the scenario where there is negligible friction between block 1 and the surface.
The shaded-in bars in the energy bar charts represent the potential energy of the spring and the gravitational potential energy of the blocks-Earth system, $U_s$ and $U_g$, respectively, in the initial and final states. Positive energy values are above the zero-point line ("0") and negative energy values are below the zero-point line.
[Diagram A: Negligible Friction — two bar charts labeled "Initial" and "Final", each with two bars $U_s$ and $U_g$, on a vertical axis with a zero-point line "0". Initial: $U_s$ bar is a thin sliver just above 0 (near zero), $U_g$ bar is tall, extending well above 0. Final: $U_s$ bar extends above 0 to a moderate height, $U_g$ bar is a thin sliver just below 0 (near zero, slightly negative).]
[Diagram B: Nonnegligible Friction — two bar charts labeled "Initial" and "Final", each with two bars $U_s$ and $U_g$. Initial state already provided: $U_s$ bar is a thin sliver just above 0, $U_g$ bar is tall extending well above 0 (same as Diagram A's initial state). Final state is blank/empty, to be completed by the student.]
Complete diagram B (at right above) for the scenario in which friction is nonnegligible. The energies for the initial state are already provided. Shade in the energies in the final state using the same scale as in diagram A.
- Shaded regions should start at the solid line representing the zero-point line.
- Represent any energy that is equal to zero with a distinct line on the zero-point line.
[Figure: Two moons (Moon A and Moon B) orbit a Planet, aligned in a row with the Planet. Moon A is farthest from the Planet, Moon B is between Moon A and the Planet. Dashed circles indicate their orbits around the Planet. $R_A$ is the distance from the Planet's center to Moon A; $R_B$ is the distance from the Planet's center to Moon B, with $R_B < R_A$. Note: Figure not drawn to scale.]
Two identical moons, Moon A and Moon B, orbit a planet. The mass $m_0$ of each moon is significant, but less than the mass $m_p$ of the planet. At some point in their orbits, the planet and the two moons are aligned as shown in the figure.
The following dots represent the two moons when they are at the locations shown in the previous figure. On each dot, draw and label the forces (not components) exerted on Moon A and on Moon B. Each force must be represented by a distinct arrow starting on, and pointing away from, the appropriate dot.
[Two labeled dots side by side: "Moon A" on the left, separated by a vertical divider line, "Moon B" on the right. Students draw force vectors originating from each dot.]
Consider the net gravitational force exerted on each moon due to the planet and the other moon.
Justify why the magnitude of the net force exerted on Moon A could be larger than the magnitude of the net force exerted on Moon B.
Justify why the magnitude of the net force exerted on Moon B could be larger than the magnitude of the net force exerted on Moon A.
Derive expressions for both of the following quantities. Express your answers in terms of $m_0$, $m_p$, $R_A$, $R_B$, and physical constants, as appropriate.
- The net force $F_A$ exerted on Moon A
- The net force $F_B$ exerted on Moon B
Could the expressions in part (c) support your reasoning in part (b)(i)?
___ Yes ___ No
Explain your reasoning.
Could the expressions in part (c) support your reasoning in part (b)(ii)?
___ Yes ___ No
Explain your reasoning.
[Figure: A wheel mounted on a horizontal axle, standing on a support post above a floor. A string is wrapped around the wheel's rim and hangs down to a small hanging block. Labels: "Wheel" (top, pointing to the wheel), "Axle" (pointing to the horizontal axle at the wheel's center), "Hanging Block" (pointing to the small block hanging from the string), "Floor" (the ground below).]
A wheel is mounted on a horizontal axle. A light string is attached to the wheel's rim and wrapped around it several times, and a small block is attached to the free end of the string, as shown in the figure. When the block is released from rest and begins to fall, the wheel begins to rotate with negligible friction.
Two students are discussing how different forms of energy change as the block falls. One student says that the kinetic energy of the block increases as it falls. The second student says that this is because gravitational potential energy is converted to kinetic energy. The students decide to test whether the decrease in gravitational potential energy is equal to the increase in the block's kinetic energy from when the block starts moving to immediately before it reaches the floor.
Design an experimental procedure that the students could use to compare the increase in the block's translational kinetic energy with the decrease in the gravitational potential energy of the block-Earth system as the block falls.
In the table, list the quantities that would be measured in your experiment. Define a symbol to represent each quantity and 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 in the space just below the table.
In the space to the right of the table, describe the overall procedure. 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.
If needed, you may include a simple diagram of the setup with your procedure.
| Quantity to Be Measured | Symbol for Quantity | Equipment for Measurement | Procedure (and diagram, if needed) |
|---|---|---|---|
Explain how the students could determine the kinetic energy of the block immediately before it reaches the floor using the quantities you indicated in the table in part (a).
[Graph: "Energy (J)" on the y-axis from $-0.4$ to $0.4$ J (gridlines at $-0.4, -0.2, 0, 0.2, 0.4$), "$d$ (cm)" on the x-axis from 0 to 20 cm (gridlines at 5, 10, 15, 20). A solid line labeled "Kinetic energy gained by the falling block" starts near $(0,0)$ and rises gently to about $(20, 0.15)$. A dashed line labeled "Change in gravitational potential energy of the block-wheel-Earth system" starts near $(0,0)$ and falls to about $(20, -0.35)$.]
The graph above represents both the change in the gravitational potential energy of the block-wheel-Earth system and the translational kinetic energy gained by the block as functions of the block's falling distance $d$. On the graph, draw a line or curve to represent the rotational kinetic energy of the wheel as a function of the block's falling distance $d$.
The students also measure the angular velocity $\omega$ of the wheel as the block falls and determine the rotational kinetic energy $K_R$ of the wheel. The students then make a graph of $K_R$ as a function of $\omega^2$, as shown.
[Graph: "$K_R$ (J)" on the y-axis from 0.0 to 1.2 J (gridlines at 0.0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2), "$\omega^2$ (rad/s)$^2$" on the x-axis from 0 to 40 (gridlines at 0, 10, 20, 30, 40). Data points (approximate): $(5, 0.15)$, $(8, 0.28)$, $(10, 0.35)$, $(17, 0.5)$, $(24, 0.65)$, $(32, 0.95)$, $(35, 1.15)$.]
On the above graph, draw a straight line that best represents the data.
Using the line you drew for part (d)(i), calculate an experimental value for the rotational inertia of the wheel.
A student has a piece of clay and a rubber sphere, both of the same mass. Both objects are thrown horizontally at the same speed at identical blocks that are at rest at the edge of identical tables, as shown, where friction between the blocks and the table is negligible. After the collisions, both blocks fall to the floor.
In Case A, the clay sticks to Block A after the collision. In Case B, the rubber sphere bounces off of Block B after the collision.
[Figure: Two setups side by side. Left: "Case A: Clay and Block A Before Collision" — a piece of Clay is shown moving horizontally (arrow) toward Block A resting at the edge of a table. Right: "Case B: Rubber Sphere and Block B Before Collision" — a Rubber Sphere is shown moving horizontally (arrow) toward Block B resting at the edge of an identical table.]
[Figure: Two grid diagrams below, each with a dot at center. Left: "Case A: Momentum of Clay-Block System Immediately After Collision" — the dot has a solid arrow pointing to the right, representing nonzero momentum. Right: "Case B: Momentum of Sphere-Block System Immediately After Collision" — just a dot shown, no arrow (to be completed by the student).]
In the figure at left above, the arrow represents the momentum immediately after the collision for the clay-block system in Case A. In the figure at right above, draw an arrow starting on the dot to represent the momentum of the sphere-block system immediately after the collision in Case B. If the momentum is zero, write "zero" next to the dot. The momentum, if it is not zero, must be represented by an arrow starting on, and pointing away from, the dot. The length of the vector, if not zero, should reflect the magnitude of the momentum relative to Case A.
After the clay and Block A collide, Block A lands a horizontal distance $d_A$ from the edge of the table. Does Block B land on the floor at a horizontal distance from the edge of the table that is greater than, less than, or equal to $d_A$? In a clear, coherent, paragraph-length response that may also contain equations and/or drawings, explain your reasoning. Neglect any frictional effects due to the table or air resistance.
[Figure: A spring hangs vertically from a ceiling (shown as a hatched surface at top). A lightweight hanger is attached to the lower end of the spring. Below the hanger, a vertical distance of "1.00 m" is marked down to a "Motion Detector" resting on the floor, facing upward directly under the hanger.]
A spring of unknown spring constant $k_0$ is attached to a ceiling. A lightweight hanger is attached to the lower end of the spring, and a motion detector is placed on the floor facing upward directly under the hanger, as shown in the figure above. The bottom of the hanger is 1.00 m above the motion detector.
A 0.50 kg object is placed on the hanger and allowed to come to rest at the equilibrium position. The spring is then stretched downward a distance $d_0$ from equilibrium and released at time $t=0$. The motion detector records the height of the bottom of the hanger as a function of time. The output from the motion detector is shown in the graph on the following page.
[Graph: "Height (cm)" on the y-axis from 50 to 70 cm (gridlines at 50, 55, 60, 65, 70), "Time (s)" on the x-axis from 0.00 to 2.00 s (gridlines at 0.00, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00). A smooth sinusoidal curve oscillates between about 55 cm and 65 cm, starting near a minimum around $t=0$, with "Equilibrium Position" labeled at the horizontal midline around 60 cm. The curve appears to have a period of about 1.00 s.]
Using the information given and information taken from the graph, calculate the spring constant.
At time 0.75 s, the object-spring-Earth system has a total kinetic energy $K_0$ and a total potential energy $U_0$. At 1.13 s, the object-spring-Earth system again has a total kinetic energy $K_0$ and a total potential energy $U_0$.
Explain how a feature of the graph indicates that the total kinetic energy of the system is the same at these two times.
Briefly explain why the total potential energy of the system is the same at these two times.
The experiment is repeated with a spring of spring constant $4k_0$ and that has the same length as the original spring. The 0.50 kg object is hung from the new spring and allowed to come to rest at a new equilibrium position.
Determine the new equilibrium position above the motion detector.
The object is again pulled down the same distance $d_0$ from the equilibrium position and released. On the following graph, draw a curve representing the motion of the object after it is released. Label the vertical axis with an appropriate numerical scale. A grid for scratch (practice) work is also provided.
[Graph: "Height (cm)" on the y-axis (unlabeled scale, to be filled in by student), "Time (s)" on the x-axis from 0.00 to 2.00 s (gridlines at 0.00, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00). "Equilibrium Position" labeled at the horizontal midline. Blank grid for the student to draw the curve.]
The following graph is provided for scratch work only and will not be graded.
[Two "Not Graded / Scratch Work" grids follow, each labeled "Height (cm)" vs. "Time (s)" from 0.00 to 2.00 s, with "Equilibrium Position" marked at the midline — for student scratch work, not graded.]