Learn Extracted exam questions AP Physics 1 2015 Free Response
2015 Free Response
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[Figure: Two blocks connected by a string over two pulleys mounted on a frame above a table. Block 1 (mass $m_1$) hangs on the left side, Block 2 (mass $m_2$) hangs on the right side. Note: Figure not drawn to scale.]
Two blocks are connected by a string of negligible mass that passes over massless pulleys that turn with negligible friction, as shown in the figure above. The mass $m_2$ of block 2 is greater than the mass $m_1$ of block 1. The blocks are released from rest.
The dots below represent the two blocks. Draw free-body diagrams showing and labeling the forces (not components) exerted on each block. Draw the relative lengths of all vectors to reflect the relative magnitudes of all the forces.
[Two blank labeled diagrams, each showing a single dot on a set of horizontal dashed reference lines, for the student to draw force vectors on: one labeled "Block 1", one labeled "Block 2".]
Derive the magnitude of the acceleration of block 2. Express your answer in terms of $m_1$, $m_2$, and $g$.
Block 3 of mass $m_3$ is added to the system, as shown below. There is no friction between block 3 and the table.
[Figure: Block 3 (mass $m_3$) now sits on top of the table, connected by strings over the same two pulleys to Block 1 (mass $m_1$) hanging on the left and Block 2 (mass $m_2$) hanging on the right. Note: Figure not drawn to scale.]
Indicate whether the magnitude of the acceleration of block 2 is now larger, smaller, or the same as in the original two-block system. Explain how you arrived at your answer.
Some students want to know what gets used up in an incandescent lightbulb when it is in series with a resistor: current, energy, or both. They come up with the following two questions.
(1) In one second, do fewer electrons leave the bulb than enter the bulb? (2) Does the electric potential energy of electrons change while inside the bulb?
The students have an adjustable power source, insulated wire, lightbulbs, resistors, switches, voltmeters, ammeters, and other standard lab equipment. Assume that the power supply and voltmeters are marked in $0.1\text{ V}$ increments and the ammeters are marked in $0.01\text{ A}$ increments.
Describe an experimental procedure that could be used to answer questions (1) and (2) above. In your description, state the measurements you would make and how you would use the equipment to make them. Include a neat, labeled diagram of your setup.
Explain how data from the experiment you described can be used to answer question (1) above.
Explain how data from the experiment you described can be used to answer question (2) above.
A lightbulb is nonohmic if its resistance changes as a function of current. Your setup from part (a) is to be used or modified to determine whether the lightbulb is nonohmic.
How, if at all, does the setup need to be modified?
What additional data, if any, would need to be collected?
How would you analyze the data to determine whether the bulb is nonohmic? Include a discussion of how the uncertainties in the voltmeters and ammeters would affect your argument for concluding whether the resistor is nonohmic.
[Figure: A block is held against a spring of negligible mass attached to a wall, on a frictionless surface, at position $x=-D$. Position $x=0$ marks the end of the frictionless surface and the start of a rough (shaded) track extending to the right. A dashed box near $x=0$ and another dashed box further right (near $x=3D$) mark reference positions. The $x$-axis is labeled with $-D$, $0$, and $3D$.]
A block is initially at position $x = 0$ and in contact with an uncompressed spring of negligible mass. The block is pushed back along a frictionless surface from position $x = 0$ to $x = -D$, as shown above, compressing the spring by an amount $\Delta x = D$. The block is then released. At $x = 0$ the block enters a rough part of the track and eventually comes to rest at position $x = 3D$. The coefficient of kinetic friction between the block and the rough track is $\mu$.
On the axes below, sketch and label graphs of the following two quantities as a function of the position of the block between $x = -D$ and $x = 3D$. You do not need to calculate values for the vertical axis, but the same vertical scale should be used for both quantities.
i. The kinetic energy $K$ of the block
ii. The potential energy $U$ of the block-spring system
[Blank grid: vertical axis labeled "Energy" (unmarked scale), horizontal axis labeled $x$ with gridlines/tick labels at $-D$, $O$, $D$, $2D$, $3D$, for the student to sketch the two graphs on.]
The spring is now compressed twice as much, to $\Delta x = 2D$. A student is asked to predict whether the final position of the block will be twice as far at $x = 6D$. The student reasons that since the spring will be compressed twice as much as before, the block will have more energy when it leaves the spring, so it will slide farther along the track before stopping at position $x = 6D$.
Which aspects of the student's reasoning, if any, are correct? Explain how you arrived at your answer.
Which aspects of the student's reasoning, if any, are incorrect? Explain how you arrived at your answer.
Use quantitative reasoning, including equations as needed, to develop an expression for the new final position of the block. Express your answer in terms of $D$.
Explain how any correct aspects of the student's reasoning identified in part (b) are expressed by your mathematical relationships in part (c). Explain how your relationships in part (c) correct any incorrect aspects of the student's reasoning identified in part (b). Refer to the relationships you wrote in part (c), not just the final answer you obtained by manipulating those relationships.
[Figure: A raised platform (table) with two spheres, Sphere A and Sphere B, resting at the same height $H$ above the lower ground level. Sphere A is positioned at the edge of the upper level and drops straight down (dashed vertical line to a position on the lower ground directly below). Sphere B is positioned slightly to the right, launched horizontally, and follows a dashed parabolic trajectory landing a horizontal distance $D$ from the point directly below its release point. The height $H$ is marked as the vertical drop from the upper level to the lower ground, and $D$ is marked as the horizontal distance from directly below Sphere B's start to its landing point.]
Two identical spheres are released from a device at time $t = 0$ from the same height $H$, as shown above. Sphere $A$ has no initial velocity and falls straight down. Sphere $B$ is given an initial horizontal velocity of magnitude $v_0$ and travels a horizontal distance $D$ before it reaches the ground. The spheres reach the ground at the same time $t_f$, even though sphere $B$ has more distance to cover before landing. Air resistance is negligible.
The dots below represent spheres $A$ and $B$. Draw a free-body diagram showing and labeling the forces (not components) exerted on each sphere at time $\dfrac{t_f}{2}$.
[Two blank labeled diagrams, each showing a single dot on a set of horizontal dashed reference lines, for the student to draw force vectors on: one labeled "Sphere A", one labeled "Sphere B".]
On the axes below, sketch and label a graph of the horizontal component of the velocity of sphere $A$ and of sphere $B$ as a function of time.
[Blank grid: vertical axis labeled "Horizontal Component of Velocity" (unmarked scale), horizontal axis labeled "Time" starting at $O$, for the student to sketch both graphs on.]
In a clear, coherent, paragraph-length response, explain why the spheres reach the ground at the same time even though they travel different distances. Include references to your answers to parts (a) and (b).
[Figure: Side view of a string with one end attached to an oscillator and the other end attached to a block, with the string passing over a pulley mounted at the edge of a table. The distance between the oscillator and the pulley is labeled $L$. The block (mass $M$) hangs below the pulley.]
The figure above shows a string with one end attached to an oscillator and the other end attached to a block. The string passes over a massless pulley that turns with negligible friction. Four such strings, $A$, $B$, $C$, and $D$, are set up side by side, as shown in the diagram below. Each oscillator is adjusted to vibrate the string at its fundamental frequency $f$. The distance between each oscillator and pulley $L$ is the same, and the mass $M$ of each block is the same. However, the fundamental frequency of each string is different.
[Figure: Top view of the four parallel string setups, each spanning the same distance $L$ from its oscillator to its pulley, each with a hanging block of mass $M$. Labeled fundamental frequencies: $f_A = 400\text{ Hz}$, $f_B = 382\text{ Hz}$, $f_C = 364\text{ Hz}$, $f_D = 350\text{ Hz}$.]
The equation for the velocity $v$ of a wave on a string is $v = \sqrt{\dfrac{F_T}{m/L}}$, where $F_T$ is the tension of the string and $m/L$ is the mass per unit length (linear mass density) of the string.
What is different about the four strings shown above that would result in their having different fundamental frequencies? Explain how you arrived at your answer.
A student graphs frequency as a function of the inverse of the linear mass density. Will the graph be linear? Explain how you arrived at your answer.
The frequency of the oscillator connected to string $D$ is changed so that the string vibrates in its second harmonic. On the side view of string $D$ below, mark and label the points on the string that have the greatest average vertical speed.
[Figure: Side view of string $D$, now labeled $f_D = 700\text{ Hz}$, drawn taut between the oscillator and the pulley with a dashed pattern of evenly spaced vertical tick marks along its length, for the student to mark the antinode points on. Block hangs below the pulley as before.]