Learn Extracted exam questions AP Physics 2 2024 Free Response
2024 Free Response
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In each trial of a photoelectric experiment, a scientist uses a device to shine light of a single frequency on two different metals, 1 and 2. The device can emit light with frequency $f_A$, $f_B$, or $f_C$. Each frequency of light is used to test both metals.
The scientist determines the minimum de Broglie wavelength $\lambda_e$ of the electrons ejected from the metal in each trial of the experiment. The following table summarizes the results of the experiment. For each trial, the scientist analyzes only the electrons with the minimum de Broglie wavelength.
| Trial | Frequency of Light | Metal Tested | $\lambda_e$ ($\times 10^{-10}$ m) |
|---|---|---|---|
| 1 | $f_A$ | Metal 1 | 6.9 |
| 2 | $f_A$ | Metal 2 | 9.4 |
| 3 | $f_B$ | Metal 1 | No electrons ejected |
| 4 | $f_B$ | Metal 2 | No electrons ejected |
| 5 | $f_C$ | Metal 1 | 5.3 |
| 6 | $f_C$ | Metal 2 | 6.3 |
In a coherent, paragraph-length response, indicate which frequency, $f_A$, $f_B$, or $f_C$, is greatest and which frequency is least. Justify your answer using physics principles.
Calculate the maximum kinetic energy of the electrons ejected from Metal 1 in Trial 1. Assume that the momentum $p$ of an ejected electron can be described by the classical definition $p = mv$.
Indicate whether the work function of Metal 1 is greater than, less than, or equal to the work function of Metal 2. Justify your answer by referring to the table of results.
[Figure 1: A rectangular sealed chamber labeled "Chamber" with thin, rigid walls. Inside are many small dots labeled "Gas Molecule" scattered throughout the interior. On the left wall is a component labeled "Heater". On the right wall are two circular components labeled "Sensors". Note: Figure not drawn to scale.]
In Experiment 1, shown in Figure 1, a sample of an ideal gas is contained in an insulated, sealed chamber with thin, rigid walls. The chamber contains a heater and sensors that measure the temperature and pressure of the gas. A student is asked to design an experiment to determine the number $N$ of molecules of the gas contained in the chamber.
Describe a procedure for collecting data that would allow the student to determine an experimental value for $N$. Provide enough detail so that a student could replicate the experiment, including any steps necessary to reduce experimental uncertainty.
On the following axes, sketch a curve or line to represent the expected relationship between the pressure $P$ and volume $V$ of the gas while the heater is on. Draw an arrow on the curve or line to represent the direction of the resulting thermal process.
[Graph with vertical axis $P$ and horizontal axis $V$, both starting at origin $O$; empty dashed gridded axes for the student to sketch on.]
On the following axes, sketch a curve or line to represent the expected relationship between the internal energy $U$ and the volume $V$ of the gas while the heater is on. Draw an arrow on the curve or line to represent the direction of the resulting thermal process.
[Graph with vertical axis $U$ and horizontal axis $V$, both starting at origin $O$; empty dashed gridded axes for the student to sketch on.]
Briefly justify why the curve or line drawn in part (b)(ii) has the shape that you sketched.
[Figure 2: The same rectangular sealed chamber, labeled "Chamber", with "Gas Molecule" dots scattered throughout. On the left wall is "Heater". On the right wall are two "Sensors". Inside the chamber is a smaller rectangular "Container" that is completely wrapped, holding a "Material" layer and a "Liquid" layer inside it. Note: Figure not drawn to scale.]
In Experiment 2, shown in Figure 2, a liquid-filled container that is completely wrapped with a material of uniform thickness 0.01 m is inside the sealed chamber that is filled with an ideal gas. The material has a total area of 0.06 m$^2$ in contact with the gas. The heater is turned on. As the temperature $T_G$ of the gas increases, the following data for the temperature $T_L$ of the liquid and the rate $\dfrac{Q}{\Delta t}$ of energy transfer are collected.
| $T_G$ (K) | $T_L$ (K) | $\dfrac{Q}{\Delta t}$ (J/s) | ||
|---|---|---|---|---|
| 295 | 295 | 0.0 | ||
| 371 | 303 | 26.3 | ||
| 425 | 308 | 43.1 | ||
| 475 | 313 | 60.0 | ||
| 528 | 323 | 75.0 |
The student is asked to determine an experimental value of the thermal conductivity $k$ of the material used to wrap the container inside the sealed chamber.
Indicate what measured and/or calculated quantities could be graphed to yield a straight line that could be used to calculate an experimental value for the thermal conductivity $k$ of the material. Use the blank columns in the table to list any calculated quantities you graph in addition to the data provided.
Vertical Axis: ________________ Horizontal Axis: ________________
Plot the data points for the quantities indicated in part (c)(i) on the graph provided. Clearly scale and label all axes, including units, as appropriate.
[Empty gridded graph with axes to be scaled and labeled by the student, with tick marks along both axes for plotting data points.]
Draw the best-fit line for the data graphed in part (c)(ii).
Using the best-fit line, calculate an experimental value for $k$.
[Figure 1: A circuit diagram. An ideal battery of emf $\mathcal{E}$ is connected on the left. From the top of the battery, a wire goes right through resistor $R_1$ to a node. From that node, resistor $R_2$ branches down in parallel back to the bottom rail. Also from that same node, a wire continues right to another node, from which resistors $R_3$ (upper) and $R_4$ (lower) branch down in parallel, both returning to the bottom rail, which connects back to the battery.]
A circuit consists of an ideal battery of emf $\mathcal{E}$ and four identical resistors $R_1$, $R_2$, $R_3$, and $R_4$, each of resistance $R$, as shown in Figure 1.
For parts (a)(i) and (a)(ii), express your answers in terms of numerical values, $\mathcal{E}$, and $R$ only.
Derive an expression for the current $I_1$ in Resistor $R_1$.
Derive an expression for the current $I_3$ in Resistor $R_3$.
[Figure 2: A partially completed bar chart. The vertical axis is labeled $|\Delta V|$ with a horizontal dashed reference line marked $\mathcal{E}$ near the top. The horizontal axis lists categories "Battery", $R_1$, $R_2$, $R_3$, $R_4$. A single shaded bar is drawn above "Battery" reaching up to the $\mathcal{E}$ line; the bars for $R_1$, $R_2$, $R_3$, $R_4$ are blank for the student to draw.]
The partially completed bar chart in Figure 2 shows a bar that represents the absolute value $|\Delta V|$ of the potential difference across the ideal battery.
- In Figure 2, draw a bar to represent $|\Delta V|$ across each resistor, relative to the emf $\mathcal{E}$ of the ideal battery.
- The height of each bar should be proportional to the value of $|\Delta V|$ represented by that bar. If $|\Delta V|$ is zero, write a "0" in that column.
A student claims that the rate at which energy is dissipated (power) by the circuit can be expressed as $P = \dfrac{3\mathcal{E}^2}{5R}$.
State whether the expression for $P$ is correct or incorrect. Justify your answer by referring to the derivations from part (a) or the bar chart from part (b).
[Figure 3: The same circuit as Figure 1, but the ideal battery is replaced by a nonideal battery, drawn as an emf $\mathcal{E}$ in series with an internal resistance $r$ enclosed in a dashed box. The rest of the circuit (resistors $R_1$, $R_2$, $R_3$, $R_4$ in the same configuration) is unchanged.]
When the ideal battery is connected in the original circuit, the rate at which energy is dissipated by Resistor $R_1$ is $P_{original}$. The ideal battery is now replaced with a nonideal battery of emf $\mathcal{E}$ and internal resistance $r$ to form the new circuit shown in Figure 3. The rate at which energy is dissipated by Resistor $R_1$ in the new circuit is $P_{new}$.
Indicate whether $P_{new}$ is greater than, less than, or equal to $P_{original}$.
____ $P_{new} > P_{original}$ ____ $P_{new} < P_{original}$ ____ $P_{new} = P_{original}$
Briefly justify your answer.
Two particles, 1 and 2, have different mass and charge as described by the following.
- Particle 1 has mass $M$ and negative charge $-Q$.
- Particle 2 has mass $\dfrac{M}{2}$ and positive charge $+2Q$.
In separate trials, a device is used to accelerate each particle in the $-y$-direction from rest through a potential difference of absolute value $|\Delta V|$. The polarity of the potential difference can be adjusted so that a particle with either positive charge or negative charge can be accelerated in the $-y$-direction by the device. Gravitational effects are negligible.
After moving through the potential difference, particles 1 and 2 exit the device with kinetic energies $K_1$ and $K_2$, respectively.
Calculate the ratio $\dfrac{K_2}{K_1}$.
[Figure 1: A diagram showing a "Region of Constant Uniform Magnetic Field" as a grid of dots (indicating a field directed out of the page, in the $+z$-direction) bounded above by a dashed horizontal line. Above the region, a "Particle" (circle with dot) is shown with a downward arrow into the region. A small coordinate axis in the upper right shows $+y$ up, $+x$ right, and $+z$ out of the page (toward viewer). The field magnitude is labeled $B_0$ within the dotted region.]
After exiting the device, the particles enter a large region of constant uniform magnetic field of magnitude $B_0$ that is directed in the $+z$-direction (out of the page), as shown in Figure 1. Each particle is moving in the $-y$-direction when entering the region, and each particle is moving in the $+y$-direction when exiting the region.
Determine an expression for the speed of Particle 2 in the region. Express your answer in terms of $M$, $K_2$, and physical constants, as appropriate.
Derive an expression for the horizontal distance $\Delta x$ between the locations where Particle 2 enters and leaves the region. Express your answer in terms of $M$, $Q$, $K_2$, $B_0$, and physical constants, as appropriate.
[Figure 2: The same diagram as Figure 1 — a "Region of Constant Uniform Magnetic Field" shown as a grid of dots bounded above by a dashed horizontal line, with a "Particle" (circle with dot) above the region and a downward arrow into it, and the coordinate axis ($+y$ up, $+x$ right, $+z$ out of page) shown in the upper right, field magnitude $B_0$ labeled within the region. This copy is provided blank for the student to sketch on.]
On the following diagram in Figure 2, sketch and clearly label the paths of both particles 1 and 2 in the region.
A uniform electric field is added to the region such that Particle 1 of negative charge $-Q$ travels with constant speed in a straight line through the region. Determine the direction of the electric field.