Two 0.50-kg carts resting on a low-friction track and connected by a spring are pushed toward each other. The left cart is pushed with a force of 10 N over a distance of 0.10 m, and the right cart is pushed with a force of 5 N over a distance of 0.04 m. Assume the spring has negligible inertia. You can convince yourself that the center of mass moved to the right by 0.03 m. Calculate the change in center of mass kinetic energy of the system consisting of the two carts and the spring.

The work-energy theorem states that the work done on the system is equal to its change of kinetic energy: [tex]W=\Delta K[/tex]. This refers to the center of mass in the case of a system of particles. To calculate this work, we need to use the net Force on the system and the displacement of its center of mass:

[tex]\Delta K=W=F_{net}d_{cm}=(10N-5N)(0.03m)=0.15J[/tex]

Answer Link