Learn Extracted exam questions AP Physics 1 2018 Free Response
2018 Free Response
Source PDF on the left, extracted YAML on the right. Compare numbering, marks, options and text.
A spacecraft of mass $m$ is in a clockwise circular orbit of radius $R$ around Earth, as shown in the figure above. The mass of Earth is $M_E$.
[Figure: Earth (a solid grey circle, labeled "Earth") at the center, with a dashed circular orbit of radius $R$ around it; a spacecraft icon sits on the orbit path, labeled "Spacecraft", indicating clockwise motion. Note: Figure not drawn to scale.]
In the figure below, draw and label the forces (not components) that act on the spacecraft. Each force must be represented by a distinct arrow starting on, and pointing away from, the spacecraft.
[Figure: Earth shown at upper left with the spacecraft positioned on a dashed arc representing part of its orbit, provided blank for the student to draw and label force arrows. Note: Figure not drawn to scale.]
Derive an equation for the orbital period $T$ of the spacecraft in terms of $m$, $M_E$, $R$, and physical constants, as appropriate. If you need to draw anything other than what you have shown in part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).
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?
____ Greater than ____ Less than ____ Equal to
Briefly explain your reasoning.
The first spacecraft is moved into a new circular orbit that has a radius greater than $R$, as shown in the figure below.
[Figure: Earth with the original dashed orbit of radius $R$ shown alongside a larger, concentric dashed orbit labeled "New Orbit"; the spacecraft is shown on this larger new orbit. Note: Figure not drawn to scale.]
Is the speed of the spacecraft in the new orbit greater than, less than, or equal to the original speed?
____ Greater than ____ Less than ____ Equal to
Briefly explain your reasoning.
A group of students prepare a large batch of conductive dough (a soft substance that can conduct electricity) and then mold the dough into several cylinders with various cross-sectional areas $A$ and lengths $\ell$. Each student applies a potential difference $\Delta V$ 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.
[Table — "Dough Cylinder" | $A$ (m$^2$) | $\ell$ (m) | $\Delta V$ (V) | $R$ ($\Omega$) | (two extra blank columns provided for student-added quantities): 1 | 0.00049 | 0.030 | 1.02 | 23.6 2 | 0.00049 | 0.050 | 2.34 | 31.5 3 | 0.00053 | 0.080 | 3.58 | 61.2 4 | 0.00057 | 0.150 | 6.21 | 105]
The students want to determine the resistivity of the dough cylinders.
Indicate below which quantities could be graphed to determine a value for the resistivity of the dough cylinders. You may use the remaining columns in the table above, as needed, to record any quantities (including units) that are not already in the table.
Vertical Axis: ________________________ Horizontal Axis: ________________________
On the grid below, plot the appropriate quantities to determine the resistivity of the dough cylinders. Clearly scale and label all axes, including units as appropriate.
[Figure: a blank grid (graph paper) for plotting.]
Use the above graph to estimate a value for the resistivity of the dough cylinders.
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?
____ Yes ____ No
Briefly justify your reasoning.
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.
The disk shown above spins about the axle at its center. A student's experiments reveal that, while the disk is spinning, friction between the axle and the disk exerts a constant torque on the disk.
[Figure: a thin horizontal disk mounted on a vertical axle through its center, shown in a simple side-view sketch.]
At time $t = 0$ the disk has an initial counterclockwise (positive) angular velocity $\omega_0$. The disk later comes to rest at time $t = t_1$.
On the grid at left below, sketch a graph that could represent the disk's angular velocity as a function of time $t$ from $t = 0$ until the disk comes to rest at time $t = t_1$.
[Figure: a blank graph grid, vertical axis "Angular Velocity" marked from $-\omega_0$ to $\omega_0$ (with $0$ in the middle), horizontal axis $t$ marked $0$ and $t_1$, dotted gridlines, for the student to sketch a curve.]
On the grid at right below, sketch the disk's angular acceleration as a function of time $t$ from $t = 0$ until the disk comes to rest at time $t = t_1$.
[Figure: a blank graph grid, vertical axis "Angular Acceleration", horizontal axis $t$ marked $0$ and $t_1$, dotted gridlines, for the student to sketch a curve.]
The magnitude of the frictional torque exerted on the disk is $\tau_0$. Derive an equation for the rotational inertia $I$ of the disk in terms of $\tau_0$, $\omega_0$, $t_1$, and physical constants, as appropriate.
In another experiment, the disk again has an initial positive angular velocity $\omega_0$ at time $t = 0$. At time $t = \frac{1}{2}t_1$, 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 that contact surface, reducing the friction even further.
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 $t = t_1$, which is the time at which the disk came to rest in part (a).
[Figure: a blank graph grid like part (a)'s left grid, vertical axis "Angular Velocity" (from $-\omega_0$ to $\omega_0$), horizontal axis $t$ marked $0$, $\frac{1}{2}t_1$, and $t_1$.]
On the grid at right below, sketch the disk's angular acceleration as a function of time from $t = 0$ to $t = t_1$.
[Figure: a blank graph grid like part (a)'s right grid, vertical axis "Angular Acceleration", horizontal axis $t$ marked $0$, $\frac{1}{2}t_1$, and $t_1$.]
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 times $t > \frac{1}{2}t_1$. The student writes down the following two equations, each of which includes a positive constant ($C_1$ or $C_2$) with appropriate units.
(1) $\tau = C_1\left(t - \frac{1}{2}t_1\right)$ (for $t > \frac{1}{2}t_1$)
(2) $\tau = \dfrac{C_2}{\left(t + \frac{1}{2}t_1\right)}$ (for $t > \frac{1}{2}t_1$)
Which equation better mathematically models this experiment?
____ Equation (1) ____ Equation (2)
Briefly explain why the equation you selected is plausible and why the other equation is not plausible.
A transverse wave travels to the right along a string.
Two dots have been painted on the string. In the diagrams below, those dots are labeled P and Q.
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 the dot.
[Figure: a transverse wave on a string (drawn with cross-hatching to show the string), moving right ("Direction of Wave" arrow shown above); dot P is marked at a trough of the wave (maximum displacement from equilibrium) and dot Q is marked at a zero-crossing point on the curve (zero displacement).]
The figure below shows the string at the same instant as 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 the dot.
[Figure: the same transverse wave snapshot repeated, moving right ("Direction of Wave" arrow shown above), with dot P at the trough and dot Q at the zero-crossing point, provided for the student to draw acceleration-direction arrows.]
The figure below represents the string at time $t = 0$, the same instant as shown in part (a) when dot P is at its maximum displacement from equilibrium. For simplicity, dot Q is not shown.
[Figure: a graph of $y$ (cm) vs $x$ (cm) showing a sinusoidal wave of amplitude 8 cm and wavelength 24 cm, with a "Direction of Wave" arrow pointing in the $+x$ direction; dot P is marked on the curve at $x = 12$ cm, $y = 0$.]
On the grid below, draw the string at a later time $t = T/4$, where $T$ is the period of the wave.
[Figure: a blank $y$ (cm) vs $x$ (cm) grid, same scale as above (−8 to 8 cm vertical, 0 to 48 cm horizontal) with a "Direction of Wave" arrow, provided for the student to sketch the string's new shape.]
Note: Do any scratch (practice) work on the grid at the bottom of the page. Only the sketch made on the grid immediately below will be graded.
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.
Now consider the wave at time $t = T$. Determine the distance traveled (not the displacement) by dot P between times $t = 0$ and $t = T$.
Block P of mass $m$ is on a horizontal, frictionless surface and is attached to a spring with spring constant $k$. The block is oscillating with period $T_P$ and amplitude $A_P$ about the spring's equilibrium position $x_0$. 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 $T_{PQ}$ and amplitude $A_{PQ}$.
[Figure: block P (mass $m$) resting on a horizontal frictionless surface, connected on its left side to a fixed wall by a spring (spring constant $k$); block Q (mass $2m$) is shown directly above block P with a downward arrow, about to be dropped onto it; a dashed vertical line from block P down to the surface marks the equilibrium position $x_0$.]
Determine the numerical value of the ratio $T_{PQ}/T_P$.
The figure is reproduced above.
[Figure: the same setup as above — block P (mass $m$) on a horizontal frictionless surface attached to a spring, at equilibrium position $x_0$; block Q (mass $2m$) shown above block P with a downward arrow, about to drop onto it.]
How does the amplitude of oscillation $A_{PQ}$ of the two-block system compare with the original amplitude $A_P$ of block P alone?
____ $A_{PQ} < A_P$ ____ $A_{PQ} = A_P$ ____ $A_{PQ} > A_P$
In a clear, coherent paragraph-length response that may also contain diagrams and/or equations, explain your reasoning.