Final answer:
The work done on a two-object system in linear motion will change the kinetic energy of the center of mass of the system.
Step-by-step explanation:
The work-energy theorem states that the net work done on a system is equal to the change in kinetic energy of the system. In the case of a two-object system in linear motion, the work done on the system will change the kinetic energy of the center of mass of the system. This means that the two objects will gain or lose kinetic energy depending on the work done on them. For example, if a compressed spring applies a force on two latched carts, doing work on them, the kinetic energy of the center of mass of the two-cart system will change. This change in kinetic energy can be calculated using the work-energy theorem, by determining the net work done on the system and equating it to the change in kinetic energy. Therefore, by applying the work-energy theorem, we can analyze and quantify how work done on a two-object system in linear motion affects the kinetic energy of the center of mass of the system.