PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Three identical low-friction carts, each of mass 1.5kg, are aligned on a horizontal air track and can move only along the x-axis. Cart 1 moves rightward at +2.0ms−1 and collides elastically with stationary Cart 2. Immediately after that collision, Cart 2 collides perfectly inelastically with stationary Cart 3 and the two stick together. Neglect the short time intervals of contact so that external impulses are absent during each collision process.
(a) Calculate the velocity of the center of mass of the three-cart system before any collisions occur.
(b) Determine the velocity of the center of mass immediately after the elastic collision between Carts 1 and 2 but before Cart 2 reaches Cart 3.
(c) Find the velocity of the center of mass immediately after Carts 2 and 3 stick together.
(d) Suppose that, after the series of collisions, a brief external horizontal impulse J is applied to Cart 1 only, bringing the CM of the three-cart system instantaneously to rest. Derive an expression for the magnitude and sign of J in terms of any velocities you have already calculated.
(e) Evaluate the numerical value of the impulse J and clearly indicate its direction along the x-axis.