PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Work Energy and Power · Work Energy and Power
Problem
Two identical carts, each of mass m, rest on a horizontal, frictionless track. A light spring of negligible mass is compressed between them and held in place by a string. The center of the spring is initially midway between the carts. At time t=0 the string is burned, allowing the spring to push the carts apart. The spring regains its relaxed length and no longer exerts force after fully expanding. Neglect air resistance.
(a) Treat both carts and the spring together as one system. Identify every external force acting on this system while the spring is expanding, and state whether the net external force is zero or non-zero. Justify your answer.
(b) Using your conclusion from part (a), derive an algebraic expression for the speed v of each cart immediately after the spring finishes expanding. Express your result in terms of the spring’s stored energy U and the mass m.
(c) Now choose a system consisting of only one cart. Explain whether mechanical energy is conserved for this new system during the expansion, and identify the form of any energy transfer across its boundary.
(d) With the one-cart system of part (c), write a work-energy equation for the cart as the spring expands. Show that this equation leads to the same numerical value of v you obtained in part (b).