2023 AP Physics 1: Algebra-Based Free-Response Questions

Begin your response to QUESTION 1 on this page. PHYSICS 1 SECTION II Time—1 hour and 30 minutes 5 Questions Directions: Questions 1, 4, and 5 are short free-response questions that require about 13 minutes each to answer and are worth 7 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. Figure 1 Figure 2 K (J) 1. (7 points, suggested time 13 minutes) A cart on a horizontal surface is attached to a spring. The other end of the spring is attached to a wall. The cart is initially held at rest, as shown in Figure 1. When the cart is released, the system consisting of the cart and spring oscillates between the positions x = +L and x = −L. Figure 2 shows the kinetic energy of the cart-spring system as a function of the system’s potential energy. Frictional forces are negligible. (a) On the graph of kinetic energy K versus potential energy U shown in Figure 2, the values for the x-intercept and y-intercept are the same. Briefly explain why this is true, using physics principles. Continue your response to QUESTION 1 on this page. Figure 3 When the cart is at +L and momentarily at rest, a block is dropped onto the cart, as shown in Figure 3. The block sticks to the cart, and the block-cart-spring system continues to oscillate between −L and +L. The masses of the cart and the block are m0 and 3m0, respectively. (b) The frequency of oscillation before the block is dropped onto the cart is f1. The frequency of oscillation after the block is dropped onto the cart is f2. Calculate the numerical value of the ratio f2/f1. Continue your response to QUESTION 1 on this page. (c) The dashed line in Figure 4 shows the kinetic energy K versus potential energy U of the block-cart-spring system after the block is dropped onto the cart. This graph is identical to the graph shown in Figure 2 for the cart-spring system before the block is dropped onto the cart. Figure 4 K (J) i. Briefly explain why the two graphs must be the same, using physics principles. ii. After the block is dropped onto the cart, consider a system that consists only of the cart and the spring. On Figure 4, sketch a solid line that shows the kinetic energy of the system that consists of the cart and the spring but not the block after the block is dropped onto the cart.