PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
Two carts, A and B, of masses m1=0.40kg and m2=0.60kg respectively, are initially at rest on a horizontal, frictionless track. The carts are held together by a compressed, light spring that stores 3.6J of potential energy. A pin holding the carts together is suddenly removed, allowing the spring to expand completely and then detach so that it exerts no further force on either cart.
Neglect air resistance and any rotational motion of the carts.
(a) Identify a convenient system boundary for which the total mechanical energy remains constant throughout the process. Justify why external work is negligible for this system.
(b) For the system you chose in part (a), derive algebraic expressions for the final speeds v1 and v2 of carts A and B, respectively, in terms of m1, m2, and the spring’s stored energy Es.
(c) Suppose an observer instead considers only cart A to be the system. Explain why mechanical energy is not conserved for that system during the process, and identify the interaction responsible for the energy transfer across the system boundary.
(d) Using the given numerical values, calculate the final speeds of both carts.