Final answer:
To determine the mass of a cart after a spring is released, the conservation of energy principle is used. Each cart receives half of the total energy worked by the spring, assuming no external forces act upon them.
Step-by-step explanation:
To find the mass of the cart on the right hand side, when two carts are at rest with a spring in between them and the spring is released, we apply the principle of conservation of energy. Assuming no external forces are acting on the carts, the work done by the spring is transformed into kinetic energy of the carts. When the spring is released, each cart will have an equal amount of kinetic energy due to the center of mass remaining stationary.
Since the carts have equal masses and the spring does 10 J of work, dividing the total kinetic energy by two gives us the kinetic energy for each cart, which is 5.0 J. This means that each cart has 5.0 J of kinetic energy.