2025 AP Physics C: Mechanics Free-Response Questions

1. Two blocks, 1 and 2, slide toward each other on a horizontal surface. Block 1 has mass m and slides in the +x-direction with constant speed 2v₀. Block 2 has mass 6m and slides in the −x-direction with constant speed v₀, as shown in Figure 1. The blocks then collide and stick together. The collision occurs from time t = 0 to t = t_c. After the collision, where t > t_c, the blocks move together with the same constant speed. [Figure 1 shows Block 1 of mass m moving in the +x-direction at speed 2v₀ and Block 2 of mass 6m moving in the −x-direction at speed v₀.] A. The diagrams in Figure 2 can be used to represent the momentum of blocks 1 and 2 before and after the collision. The momentum vector diagram for Block 1 before the collision is shown. i. Draw arrows on the grids to represent the momentum vectors of Block 2 before the collision and the two-block system before and after the collision. • Arrows should start at the zero-momentum line. • The length of the arrows should be proportional to the relative magnitudes of the vectors. • Represent an arrow of zero length by drawing a dot at zero. [Figure 2: A momentum-vector grid with columns labeled “Momentum Before Collision” and “Momentum After Collision,” and rows labeled “Block 1,” “Block 2,” and “Two-Block System.” The Block 1 before-collision grid shows a right-pointing arrow; the other indicated grids are provided for drawing the requested vectors.] ii. During the time interval 0 ≤ t ≤ t_c, a force F is exerted on Block 2 by Block 1 along the x-direction as a function of t that is modeled by F(t) = F_max sin(At), where A is a positive constant and F_max is the magnitude of the maximum force exerted on Block 2 by Block 1 during the collision. Derive an expression for F_max. Express your answer in terms of m, v₀, A, t_c, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. B. Consider a new scenario where Block 1 initially slides in the +x-direction with a new constant speed v₁ and Block 2 again initially slides in the −x-direction with constant speed v₀. The blocks collide and stick together. In this new scenario, the two-block system has constant speed v₀ after the collision. Derive an expression for v₁ in terms of v₀. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.