2024 AP Physics 2: Algebra-Based Free-Response Questions

Directions: Questions 1 and 4 are short free-response questions that require about 20 minutes each to answer and are worth 10 points each. Questions 2 and 3 are long free-response questions that require about 25 minutes each to answer and are worth 12 points each. Show your work for each part in the space provided after that part. 1. (10 points, suggested time 20 minutes) 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 $f_{\mathrm{A}}$, $f_{\mathrm{B}}$, or $f_{\mathrm{C}}$. 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 | $f_{\mathrm{A}}$ | Metal 1 | 6.9 | | 2 | $f_{\mathrm{A}}$ | Metal 2 | 9.4 | | 3 | $f_{\mathrm{B}}$ | Metal 1 | No electrons ejected | | 4 | $f_{\mathrm{B}}$ | Metal 2 | No electrons ejected | | 5 | $f_{\mathrm{C}}$ | Metal 1 | 5.3 | | 6 | $f_{\mathrm{C}}$ | Metal 2 | 6.3 | (a) In a coherent, paragraph-length response, indicate which frequency, $f_{\mathrm{A}}$, $f_{\mathrm{B}}$, or $f_{\mathrm{C}}$, is greatest and which frequency is least. Justify your answer using physics principles. (b) 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 $p = mv$. (c) 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.

Begin your response to QUESTION 2 on this page. Note: Figure not drawn to scale. Figure 1 2. (12 points, suggested time 25 minutes) 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. (a) 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. Continue your response to QUESTION 2 on this page. (b) i. On the following axes, sketch a curve or line to represent the expected relationship between the pressure P 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. ii. 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. iii. Briefly justify why the curve or line drawn in part (b)(ii) has the shape that you sketched. Continue your response to QUESTION 2 on this page. Note: Figure not drawn to scale. Figure 2 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 m² 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 Q/Δt of energy transfer are collected. | | T_G (K) | T_L (K) | Q/Δt (J/s) | | | | 295 | 295 | 0.0 | | | | 371 | 303 | 26.3 | | | | 425 | 308 | 43.1 | | | | 475 | 313 | 60.0 | | | | 528 | 323 | 75.0 | | (c) 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. Continue your response to QUESTION 2 on this page. i. 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: _______________ ii. 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. iii. Draw the best-fit line for the data graphed in part (c)(ii). (d) Using the best-fit line, calculate an experimental value for k.

Begin your response to QUESTION 3 on this page. Figure 1 3. (12 points, suggested time 25 minutes) A circuit consists of an ideal battery of emf $\mathcal{E}$ and four identical resistors $\mathrm{R}_{1}, \mathrm{R}_{2}, \mathrm{R}_{3},$ and $\mathrm{R}_{4}$, each of resistance $R$, as shown in Figure 1. (a) For parts (a)(i) and (a)(ii), express your answers in terms of numerical values, $\mathcal{E}$, and $R$ only. i. Derive an expression for the current $I_{1}$ in Resistor $\mathrm{R}_{1}$. ii. Derive an expression for the current $I_{3}$ in Resistor $\mathrm{R}_{3}$. Continue your response to QUESTION 3 on this page. (b) 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. Figure 2 A student claims that the rate at which energy is dissipated (power) by the circuit can be expressed as $P=\frac{3\mathcal{E}^{2}}{5R}$. (c) 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). Continue your response to QUESTION 3 on this page. Figure 3 When the ideal battery is connected in the original circuit, the rate at which energy is dissipated by Resistor $\mathrm{R}_{1}$ is $P_{\mathrm{original}}$. 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 $\mathrm{R}_{1}$ in the new circuit is $P_{\mathrm{new}}$. (d) Indicate whether $P_{\mathrm{new}}$ is greater than, less than, or equal to $P_{\mathrm{original}}$. ___ $P_{\mathrm{new}} > P_{\mathrm{original}}$ ___ $P_{\mathrm{new}} < P_{\mathrm{original}}$ ___ $P_{\mathrm{new}} = P_{\mathrm{original}}$ Briefly justify your answer.

4. (10 points, suggested time 20 minutes) 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 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 |ΔV|. 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 K₁ and K₂, respectively. (a) Calculate the ratio K₂/K₁. After exiting the device, the particles enter a large region of constant uniform magnetic field of magnitude B₀ 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. (b) i. Determine an expression for the speed of Particle 2 in the region. Express your answer in terms of M, K₂, and physical constants, as appropriate. ii. Derive an expression for the horizontal distance Δx between the locations where Particle 2 enters and leaves the region. Express your answer in terms of M, Q, K₂, B₀, and physical constants, as appropriate. (c) On the following diagram in Figure 2, sketch and clearly label the paths of both particles 1 and 2 in the region. (d) 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.