Learn Extracted exam questions AP Physics 1 2017 Free Response
2017 Free Response
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[Figure: Three circuit diagrams side by side, each showing a battery with a "+" terminal on the left post and a "−" terminal on the right post. Circuit 1: the battery is connected to a single lightbulb, labeled $A$. Circuit 2: the battery is connected to two lightbulbs, labeled $B$ and $C$, wired in parallel (both bulbs connected across the battery terminals via separate branches). Circuit 3: the battery is connected to two lightbulbs, labeled $D$ and $E$, wired in series (one loop through both bulbs in sequence).]
In the three circuits shown above, the batteries are all identical, and the lightbulbs are all identical. In circuit 1 a single 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 $A$–$E$.
Rank the magnitudes of the potential differences across lightbulbs $A$, $B$, $C$, $D$, and $E$ from largest to smallest. If any lightbulbs have the same potential difference across them, state that explicitly.
Ranking:
Briefly explain how you determined your ranking.
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?
____ Circuit 1 ____ Circuit 2 ____ Circuit 3
In which circuit will the battery run out of usable energy last?
____ Circuit 1 ____ Circuit 2 ____ Circuit 3
In a clear, coherent paragraph-length response that may also contain equations and drawings, explain your reasoning.
A student wants to determine the coefficient of static friction between a long, flat wood board and a small wood block.
Describe an experiment for determining the coefficient of static friction between the wood board and the wood block. Assume equipment usually found in a school physics laboratory is available.
Draw a diagram of the experimental setup of the board and block. In your diagram, indicate each quantity that would be measured and draw or state what equipment would be used to measure each quantity.
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.
Derive an equation for the coefficient of static friction in terms of quantities measured in the procedure from 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 kinetic and static friction between the board and the block. The groups' results are shown below, with the class averages indicated in the bottom row.
| Lab Group Number | Coefficient of Kinetic Friction | Coefficient of Static Friction |
|---|---|---|
| 1 | 0.45 | 0.54 |
| 2 | 0.46 | 0.52 |
| 3 | 0.42 | 0.56 |
| 4 | 0.43 | 0.55 |
| 5 | 0.74 | 0.23 |
| 6 | 0.44 | 0.54 |
| Average | 0.49 | 0.49 |
Based on these data, what conclusion should the students make about the hypothesis that the coefficients of static and kinetic friction are equal?
____ The static and kinetic coefficients are equal.
____ The static and kinetic coefficients are not equal.
Briefly justify your reasoning.
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?
____ Increase ____ Decrease ____ Remain the same
Briefly state your reasoning.
[Figure, "Top View": a horizontal rod of length $d$ lies along a line, with its left end marked "Pivot" (shown as a circled X, indicating an axis perpendicular to the page) and its right end free. Point $C$ is marked at the center (midpoint) of the rod, at distance $d$ from the pivot (the full length $d$ is indicated by a double-headed arrow spanning from the pivot to the rod's right end). Below the rod, a disk is shown approaching with velocity $v_0$ directed upward (perpendicular to the rod), at a horizontal distance $x$ from the pivot (indicated by a double-headed arrow from the pivot to the point below the disk).]
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 $C$ marks 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 $m_{\text{disk}}$ toward the rod with velocity $v_0$ 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.
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 $C$, at point $C$, or to the right of point $C$?
____ To the left of $C$ ____ At $C$ ____ To the right of $C$
Briefly explain your reasoning without manipulating equations.
On the Internet, a student finds the following equation for the postcollision angular speed $\omega$ of the rod in this situation: $\omega = \dfrac{m_{\text{disk}}\, x v_0}{I}$. 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 reasoned in part (a)?
____ Yes ____ No
Briefly explain your reasoning without deriving an equation for $\omega$.
Another student deriving an equation for the postcollision angular speed $\omega$ of the rod makes a mistake and comes up with $\omega = \dfrac{I x v_0}{m_{\text{disk}}\, d^4}$. 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.
Immediately before colliding with the rod, the disk's rotational inertia about the pivot is $m_{\text{disk}} x^2$ and its angular momentum with respect to the pivot is $m_{\text{disk}} v_0 x$. Derive an equation for the postcollision angular speed $\omega$ of the rod. Express your answer in terms of $d$, $m_{\text{disk}}$, $I$, $x$, $v_0$, and physical constants, as appropriate.
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 of the rod when the disk bounces off it greater than, less than, or equal to the postcollision angular speed of the rod when the disk sticks to it?
____ Greater than ____ Less than ____ Equal to
Briefly explain your reasoning.
[Figure, top pair of diagrams: "Team 1" shows a curved low-friction slide starting at height $d$ above "Table 1", with Block 1 released from rest at the top of the slide (shown as a small square at the top, at the height-$d$ level, connected by a dashed horizontal line to the top of the slide). The slide curves down and flattens out level with the tabletop, launching the block horizontally off the right edge of Table 1, which sits at height $h$ above the floor. "Team 2" shows a similar slide starting at height $d$ above "Table 2" (Table 2's tabletop is lower than Table 1's), with Block 2 released from rest at the top. Because Table 2 is lower, the right end of team 2's slide rises above the tabletop before leveling off, so Block 2 leaves the slide horizontally at the same height $h$ above the floor as Block 1 does. Both $d$ and $h$ are marked with double-headed vertical arrows; the floor is a common horizontal line beneath both tables.]
A physics class is asked to design a low-friction slide that will launch a block horizontally from the top 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 (see figure above).
Both blocks are released from rest at the top of their respective slides. Do block 1 and block 2 land the same distance from their respective tables?
____ Yes ____ No
Justify your answer.
[Figure, bottom pair of diagrams: In another experiment, "Team 1" and "Team 2" use tables and low-friction slides of the same height (tabletops at the same level, table height $h$ equal for both). The two slides have different shapes, as shown: Team 1's slide (Block 1 released from rest at the top, height $d$ above Table 1) curves steeply downward near the top and flattens out quickly, remaining close to tabletop height over most of its horizontal run before leveling off at the tabletop edge. Team 2's slide (Block 2 released from rest at the top, height $d$ above Table 2) stays higher for longer, curving downward more gradually and flattening out only near the tabletop edge. Both blocks leave their slides horizontally at the tabletop, height $h$ above the floor.]
In another experiment, teams 1 and 2 use tables and low-friction slides with the same height. However, the two slides have different shapes, as shown below.
Both blocks are released from rest at the top of their respective slides at the same time.
Which block, if either, lands farther from its respective table?
____ Block 1 ____ Block 2 ____ The two blocks land the same distance from their respective tables.
Briefly explain your reasoning without manipulating equations.
Which block, if either, hits the floor first?
____ Block 1 ____ Block 2 ____ The two blocks hit the floor at the same time.
Briefly explain your reasoning without manipulating equations.
[Graph, "shape of the string at $t=0$": x-axis is horizontal position (unlabeled numeric scale, gridlines spaced in units of "1 unit" as marked), y-axis is vertical displacement of the string in cm, gridlines at $-4$ cm, $-2$ cm, $0$ cm, $2$ cm, $4$ cm. The string is flat at 0 cm on the far left, rises in a narrow triangular pulse peaking at $2$ cm (labeled "Speed = 1 unit/second" with an arrow pointing right, indicating this pulse moves rightward), then returns to 0 cm and stays flat through point $P$ (marked with a dot on the axis) and continues flat for a stretch, then dips down into a triangular pulse reaching $-4$ cm (labeled "Speed = 1 unit/second" with an arrow pointing left, indicating this pulse moves leftward), then returns to flat at 0 cm on the far right. A horizontal double-headed arrow below the axis marks "1 unit" as the width scale.]
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 with a speed of one unit per second in the direction indicated.
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.
[Graph grid titled "Velocity Versus Time": y-axis "Velocity of String at Point $P$ (cm/s)" with gridlines at $-4,-3,-2,-1,0,1,2,3,4$; x-axis "$t$ (s)" labeled $O,1,2,3,4,5$. Blank grid for the student to plot on.]
At $t=5$ s, the pulses completely overlap. On the grid provided below, sketch the shape of the entire string at $t=5$ s.
Note: Do any scratch (practice) work on the grids on the following page. You will only be graded for the sketch made on the grid on this page.
[Graph grid: y-axis in cm with gridlines at $-4,-2,0,2,4$ (cm), point $P$ marked at $0$ cm; blank grid for the student to sketch on. Below this, two additional identical blank grids are provided, explicitly labeled as scratch-work grids that will NOT be graded.]