2024 AP Physics 1: Algebra-Based Free-Response 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. 1. (7 points, suggested time 13 minutes) A block of mass M is released from rest at Point A, a height 6R above the horizontal. After being released, the block slides down a track, as shown. When released from Point A, the block does not lose contact with the track at any point. Points B and C are located at the highest points of their respective circular loops, both of radius R. All frictional forces are negligible. Diagram A shows an energy bar chart that represents the gravitational potential energy U_g of the block-Earth system and the kinetic energy K of the block at Point A, when the block is released from rest at height 6R. (a) Draw shaded regions in Diagram B that represent the gravitational potential energy U_g and kinetic energy K of the block-Earth system when the block is located at Point B, a height 2R above the horizontal. - Shaded regions should start at the dashed line that represents zero energy. - Represent any energy that is equal to zero with a distinct line on the zero-energy line. - The relative height of each shaded region should reflect the magnitude of the respective energy consistent with the scale shown in Diagram A. (b) Starting with conservation of energy, derive an expression for the speed of the block at Point B. Express your answer in terms of R and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference book. (c) i. On the following dot that represents the block, draw and label the forces (not components) that are exerted on the block at the instant the block slides through Point C. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot. ii. A student claims that 4R is the minimum height of Point A, such that the block can slide through Point C without losing contact with the track after the block is released from rest. Briefly explain why this claim is incorrect.