Question

A spring is mounted horizontally on a flat table. A cart with frictionless bearings compresses the spring and is released at time t = 0. The spring pushes the cart, and the cart goes across the table before leaving the table. The cart is about to touch the floor at time t = T. Let C, S, CE, CS, and CSE be the mechanical energies of the cart, spring, cart-Earth, cart-spring, and cart-Earth-spring systems. Explain how each energy changes from t = 0 to t = T.  

Answer 1

ANSWER

Considering Earth as the reference level

At t =0 ( CSE )Spring is pushed by the cart. ( Elastic Potential Energy of the cart + Gravitational potential energy of the spring and the cart ). Neglecting gravitational potential energy it can be considered as spring energy ( S )

At t > 0, but just before falling down ( Cart Energy ). The spring energy is converted into kinetic energy of the cart.

At t > 0 and just falling, ( Cart Earth ) system. Kinetic energy of the cart + gravitational potential energy of the cart due to earth.

At t = T, ( just before touching the ground. ( Cart Energy ). Kinetic Energy of the cart