Learn Extracted exam questions AP Physics C: Mechanics 2016 Free Response
2016 Free Response
Source PDF on the left, extracted YAML on the right. Compare numbering, marks, options and text.
[Figure: A dynamics-track setup. On the left, a "Motion Sensor" (a tall rectangular box) sits at the left end of a level track. To its right on the track sits a "Cart" of mass $m$ on wheels. A "String" connects the cart to a "Force Sensor" (a small box) on the right, which is held by a hand pulling to the right.]
A cart of mass $m$ is pulled along a level dynamics track as shown above. A force sensor is attached to the cart with a string and used to measure the horizontal force exerted on the cart to the right. A motion sensor is used to measure the acceleration of the cart with the positive direction toward the right. Friction is not negligible.
On the dot below, which represents the cart, draw and label the forces (not components) that act on the cart. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.
[A single large dot is shown, representing the cart, for the student to draw force vectors on.]
A student pulls the force sensor with a constant force, and the cart accelerates. This is repeated for several trials, with a different constant force used for each trial. The data are recorded in the table below.
| Trial | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Force sensor reading (N) | 0.32 | 0.38 | 0.44 | 0.50 | 0.60 |
| Acceleration $(\text{m/s}^2)$ | 0.12 | 0.22 | 0.33 | 0.50 | 0.70 |
On the grid below, plot data points for the acceleration of the cart as a function of the force sensor reading. Clearly scale all axes. Draw a straight line that best represents the data.
[A blank grid is provided for plotting, labeled with y-axis "Acceleration $(\text{m/s}^2)$" and x-axis "Force Sensor Reading (N)". No data is pre-plotted; axes are unscaled gridlines only.]
Using the straight line from the graph, calculate the mass of the cart.
Using the straight line from the graph, determine the magnitude of the force of friction.
The above experiment is repeated by using a constant force sensor reading of 0.45 N. The cart starts from rest at time $t = 0$ s and is pulled for a time of 2.0 s along the dynamics track.
Determine the acceleration of the cart.
The string breaks at time $t = 2.0$ s. Calculate the time it takes for the cart to stop after the string breaks.
The experiment and analysis in parts (a) and (b) are repeated with a cart that has the same mass but a greater force of friction.
Will the slope of your new line be greater than, less than, or equal to the slope of your line in part (b)i?
____ Greater than ____ Less than ____ Equal to
Will the horizontal intercept of your new line be greater than, less than, or equal to the horizontal intercept of your line in part (b)i?
____ Greater than ____ Less than ____ Equal to
[Figure: A horizontal table. On the left, a spring (drawn as a coil) is anchored to a wall and attached to a block labeled "2M" at position marked "0". On the right, separated by open space, a block labeled "3M" moves to the left with initial velocity $v_0$ (arrow pointing left labeled $v_0$).]
A block of mass $2M$ rests on a horizontal, frictionless table and is attached to a relaxed spring, as shown in the figure above. The spring is nonlinear and exerts a force $F(x) = -Bx^3$, where $B$ is a positive constant and $x$ is the displacement from equilibrium for the spring. A block of mass $3M$ and initial speed $v_0$ is moving to the left as shown.
On the dots below, which represent the blocks of mass $2M$ and $3M$, draw and label the forces (not components) that act on each block before they collide. Each force must be represented by a distinct arrow starting on, and pointing away from, the appropriate dot.
[Two dots are shown side by side, labeled "Block of Mass $2M$" (left dot) and "Block of Mass $3M$" (right dot), for the student to draw force vectors on.]
[Figure: The spring (coil) anchored at the wall on the left is now attached to a combined block labeled "2M" next to "3M" (the two blocks shown adjacent, having moved together). A distance $D$ is marked from the wall/spring's compressed end to a reference position "0".]
The two blocks collide and stick to each other. The two-block system then compresses the spring a maximum distance $D$, as shown above. Express your answers to parts (b), (c), and (d) in terms of $M$, $B$, $v_0$, and physical constants, as appropriate.
Derive an expression for the speed of the blocks immediately after the collision.
Determine an expression for the kinetic energy of the two-block system immediately after the collision.
Derive an expression for the maximum distance $D$ that the spring is compressed.
In which direction is the net force, if any, on the block of mass $2M$ when the spring is at maximum compression?
____ Left ____ Right ____ The net force on the block of mass $2M$ is zero.
Justify your answer.
Which of the following correctly describes the magnitude of the net force on each of the two blocks when the spring is at maximum compression?
____ The magnitude of the net force is greater on the block of mass $2M$. ____ The magnitude of the net force is greater on the block of mass $3M$. ____ The magnitude of the net force on each block has the same nonzero value. ____ The magnitude of the net force on each block is zero.
Justify your answer.
Do the two blocks, which remain stuck together and attached to the spring, exhibit simple harmonic motion after the collision?
____ Yes ____ No
Justify your answer.
[Figure 1: A circular platform of radius $R = 2d$ viewed from above, with a vertical rod of length $d$ fixed at the central axis (a small circle marking the pivot at the center). A spring of natural (unstretched) length $d/2$ sits along the rod, connected to a block (shown as a small dark rectangle) at distance $d/2$ from the outer end of the rod.] [Figure 2: The same circular platform now rotating counterclockwise (as viewed from above) at angular speed $\omega$ (curved arrow at top indicating rotation direction). The block has moved outward; the spring is now stretched, shown with two segments each labeled $d/2$ (i.e., the spring plus the gap between block and rod end each measure $d/2$).]
A uniform rod of length $d$ has one end fixed to the central axis of a horizontal, frictionless circular platform of radius $R = 2d$. Fixed at the other end of the rod is an ideal spring of negligible mass to which a block is attached. The block is set in frictionless grooves so that it can only move along a radius of the platform, as shown in Figure 1 above. The equilibrium length of the spring is $d/2$. Below is a table showing the mass of the block and the masses and rotational inertias of the rod and platform.
| Mass | Rotational Inertia | |
|---|---|---|
| Block | $m$ | |
| Rod | $m_R = 3m$ | $\dfrac{m_R d^2}{3}$ (about the end of the rod) |
| Platform | $m_P = 5m$ | $\dfrac{m_P R^2}{2}$ (about the central axis) |
A motor begins to slowly rotate the platform counterclockwise as viewed from above until the platform reaches a constant angular speed $\omega$. Under these conditions, the spring has stretched by an additional length $d/2$, as shown in Figure 2.
Answer the following questions for the platform rotating at constant angular speed $\omega$. Express all algebraic answers in terms of $m$, $d$, $\omega$, and physical constants, as appropriate.
Derive an expression for the spring constant of the spring.
Determine an expression for the rotational inertia of the block around the axis of the platform.
Derive an expression for the rotational inertia of the entire system about the axis of the platform.
Determine an expression for the angular momentum of the entire system about the axis of the platform.
[Figure 3: The same circular platform, rotating counterclockwise at $\omega$. The rod's block position is shown partway along the rod, with the spring stretched by amount $x$ and a remaining segment labeled $d/2$ below it.]
While the system continues to rotate, a small mechanism in the pivot moves the rod slowly until the center of the rod is positioned on the axis, as shown in Figure 3 above. The same constant angular speed $\omega$ is maintained by the motor driving the platform.
Derive an expression for the distance $x$ that the spring is stretched when the rod reaches the position shown in Figure 3 above.
For parts (e), (f), and (g), assume the center of the rod is still moving toward the axis of the platform.
Is the angular momentum of the entire system increasing, decreasing, or staying the same?
____ Increasing ____ Decreasing ____ Staying the same
Justify your answer.
In order to keep the system rotating with constant angular speed $\omega$, is the motor doing positive work, negative work, or no work on the rotating system?
____ Positive ____ Negative ____ No work
Justify your answer.
On the block in Figure 4 below, draw a single vector representing the direction of the acceleration of the block. Draw the vector so that it is starting on, and pointing away from, the block.
[Figure 4: The circular platform rotating counterclockwise at $\omega$, with the block shown at the center on the axis (a small dark square marker), a dashed horizontal line through it, and a dot below the platform on the vertical rod line, for the student to draw an acceleration vector on the block.]