PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A 0.30kg cart rolls on a horizontal, frictionless track toward a light spring bumper that is rigidly attached to a massive wall anchored to Earth. Just before contact, the cart’s speed is 1.5ms−1 toward the wall. During the 0.040s collision, the spring compresses and then re-expands, reversing the cart’s velocity.
Assume any motion of Earth is imperceptible.
(a) Treating the cart alone as the system, identify all horizontal forces that act on that system during the 0.040s collision. State whether horizontal momentum of the cart alone is conserved, and justify your answer.
(b) Now treat the cart–spring–wall–Earth combination as the system. Explain why horizontal momentum of this larger system is conserved during the collision, even though a large force acts between the cart and spring.
(c) Using the system from part (b), determine the cart’s speed immediately after it rebounds from the spring, assuming the spring bumper and wall remain at rest after the collision.
(d) Briefly discuss how your answer in part (c) would change, if at all, were the track to exert a constant 0.05N kinetic-friction force on the cart throughout the 0.040s collision interval. Justify your reasoning without detailed calculation.