2025 AP AP Physics 2: Algebra-Based Practice Paper with Answers

A very long, straight wire is fixed along the line \(y = 0\) in the \(xy\)-plane and carries a steady current \(I_0\) in the \(+x\)-direction. A particle with positive charge \(+q\) and mass \(m\) is located at point \(S\) with coordinates \((0, -d)\) and is initially moving with speed \(v_0\) in the \(+x\)-direction. The surrounding medium is a vacuum.

A.

i. Indicate the direction of each of the following quantities at point \(S\). Choose from: Into the page, Out of the page, *\(+x\)-direction*, *\(-x\)-direction*, *\(+y\)-direction*, or *\(-y\)-direction*.
- The direction of the magnetic field \(\vec{B}\) produced by the wire at point \(S\).
- The direction of the magnetic force \(\vec{F}_B\) exerted on the charged particle by the magnetic field at point \(S\).

ii. An external uniform electric field \(\vec{E}\) is applied in the region so that the net force on the charged particle at point \(S\) is zero.
Derive an expression for the magnitude of the required electric field \(E\) in terms of \(I_0\), \(q\), \(m\), \(d\), \(v_0\), and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Also, state the direction of the electric field \(\vec{E}\).

B.

The electric field is removed and the particle is removed. A small circular conducting loop of radius \(r_0\) and resistance \(R\) is placed at rest in the \(xy\)-plane with its center at \((0, -2d)\). The current in the long wire now decreases steadily over time.

Indicate whether the induced current in the circular loop is clockwise, counterclockwise, or zero.

____ Clockwise

____ Counterclockwise

____ There is no induced current in the loop.

Justify your answer using physics principles such as Faraday's law and Lenz's law.

A sample of a monatomic ideal gas is sealed inside a thermally conducting vertical cylinder of cross-sectional area \(A\) by a movable, frictionless piston of mass \(M_p\). The top of the piston is open to the atmosphere at pressure \(P_{\text{atm}}\). A light vertical string is attached to the center of the top of the piston, runs over an ideal frictionless pulley, and supports a suspended counterweight of mass \(m_c\), where \(m_c < M_p\). The cylinder is immersed in a large water bath maintained at a constant temperature \(T_0\). The system is in thermal and mechanical equilibrium, the piston is at rest, and the gas occupies volume \(V_0\).

A. On the dot shown below representing the piston, draw and label the forces exerted on the piston. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.

$$\bullet$$

B. Derive an expression for the internal energy \(U\) of the gas in terms of \(M_p\), \(m_c\), \(A\), \(V_0\), \(P_{\text{atm}}\), and fundamental constants. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

C. The string attached to the counterweight is cut, and the piston slowly moves downward while the container remains in the water bath at constant temperature \(T_0\). The piston comes to rest at a new equilibrium state at time \(t_f\).
On the axes provided below, sketch the expected relationship between the pressure \(P\) and volume \(V\) of the gas for the thermodynamic process that the gas undergoes during this compression. Draw an arrow on your sketch to represent the direction of the thermodynamic process.

$$\begin{array}{r|l}
P & \\
\uparrow & \\
& \\
& \\
0 & \hline \longrightarrow V
\end{array}$$

D. With the string still severed, the temperature of the water bath is changed to a new constant temperature \(T_{\text{new}}\). When the gas reaches thermal equilibrium with the bath, it expands until it once again occupies the original volume \(V_0\).
Indicate whether \(T_{\text{new}}\) is greater than, less than, or equal to \(T_0\).

______ \(T_{\text{new}} > T_0\)

______ \(T_{\text{new}} < T_0\)

______ \(T_{\text{new}} = T_0\)

Briefly justify your answer by referencing at least one feature of your answers to parts A, B, or C.

In Experiment 1, a student is given a spool of thin, uniform cylindrical metal wire of unknown resistivity \(\rho\). The student is tasked with designing an experiment to determine the resistivity \(\rho\) of the metal. The student has access to a variable DC power supply, a switch, an ammeter, a voltmeter, a meterstick, a micrometer caliper, and connecting wires of negligible resistance.

A. Describe a procedure for collecting data that would allow the student to determine the resistivity \(\rho\) of the metal wire. In your description, include the specific measurements to be made and any steps necessary to reduce experimental uncertainty.

B. Describe how the collected data could be analyzed to determine the resistivity \(\rho\). Include references to appropriate equations and to relationships between measured and known quantities.

C. In Experiment 2, the student uses a micrometer caliper to measure the diameter of a different cylindrical wire sample to be \(D = 0.40\text{ mm}\) (giving a cross-sectional area of \(A \approx 1.26 \times 10^{-7}\text{ m}^2\)). The student cuts five segments of this wire with various lengths \(L\), and measures the electrical resistance \(R\) of each segment. The data collected are recorded in Table 1 below.

Table 1
Length \(L\text{ (m)}\)Resistance \(R\text{ (}\Omega\text{)}\)0.403.30.806.51.209.41.6012.92.0015.8
i. Indicate two quantities, either measured quantities from Table 1 or calculated quantities, that could be graphed on the vertical and horizontal axes to produce a straight line that could be used to determine \(\rho\).
Vertical axis: _______________      Horizontal axis: _______________

ii. On a grid, create a graph of the quantities indicated in part C (i). Clearly label the axes, including units and scales as appropriate, and plot the data points.

iii. Draw a best-fit line for the data graphed in part C (ii).

D. Using the best-fit line that you drew in part C (iii), calculate an experimental value for the resistivity \(\rho\) of the metal.

Monochromatic light of frequency \( f \) is incident on a clean metal emitter inside an evacuated phototube. The work function of the metal is \( \Phi \), where \( hf > \Phi \). An adjustable electric potential difference is established between the emitter and collector to determine the stopping potential \( \Delta V_s \) required to reduce the photocurrent to zero.

A student makes the following claim:
*"If the frequency of the incident light is doubled to \( 2f \), the stopping potential \( \Delta V_s \) needed to stop the photoelectrons will also be exactly doubled."*

A. Indicate whether the student's claim is correct or incorrect. Without manipulating equations, justify your answer by describing how the energy of each incident photon and the maximum kinetic energy of the emitted photoelectrons change when the frequency is doubled.

B. Derive an expression for the stopping potential \( \Delta V_s \) in terms of \( f \), \( \Phi \), and fundamental physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. Then, determine an algebraic expression for the stopping potential \( \Delta V_s' \) when light of frequency \( 2f \) is used.

C. Indicate whether the algebraic expression derived in part B is or is not consistent with your qualitative answer from part A. Briefly justify your answer using your derived expression.