PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Three carts R, S, and T move along a straight, frictionless track. The carts have different masses but the same kinetic energy K at a particular instant:
• Cart R has mass m.
• Cart S has mass 2m.
• Cart T has mass 4m.
All carts move in the +x direction.
(a) Derive an algebraic expression for the magnitude of each cart’s linear momentum in terms of m and K.
(b) Using your expressions from part (a), rank the carts according to the magnitude of their momentum from greatest to least.
(c) Show algebraically that the ratio of the largest to the smallest momentum equals 2.
(d) Suppose another cart U has mass 2m but still possesses kinetic energy K. Using your result from part (a), determine where cart U would fit into the ranking obtained in part (b) and justify your answer.