Two identical \(0.50-\mathrm{kg}\) carts, each \(0.10 \mathrm{~m}\) long, are at rest on a low-friction track and are connected by a spring that is initially at its relaxed length of \(0.50 \mathrm{~m}\) and is of negligible inertia. You give the cart on the left a push to the right (that is, toward the other cart), exerting a constant \(5.0-\mathrm{N}\) force. You stop pushing at the instant when the cart has moved \(0.40 \mathrm{~m}\). At this instant, the relative velocity of the two carts is zero and the spring is compressed to a length of \(0.30 \mathrm{~m}\). A locking mechanism keeps the spring compressed, and the two carts continuc moving to the right.

(a) What is the work done by you on the two-cart system?

(b) How far does the system's center of mass move while you are pushing the left cart?

(c) By what amount do you change the system's kinetic energy?