Which of these is always conserved in a collision in a closed system?

a) momentum and energy
b) momentum and mechanical energy
c) energy only
d) momentum and kinetic energy

B) momentum and mechanical energy

Explanation:

In classical physics, a closed system is a system that does not exchange any matter with the surrounding, and on which there are no external forces acting on it.

Due to this definition, we have the following consequences:

- In a collision in a closed system, momentum is always conserved. This is because there is exchange of matter with the surroundings (so, no mass can be lost), and also because there are no external forces acting on the objects inside the system. In fact, the variation of the total momentum of the system is related to the net force acting on the system:

but since the net force F is zero, then the variation of momentum, , is also zero, therefore the momentum is constant.

- Also, mechanical energy is conserved. Mechanical energy is the sum of potential energy and kinetic energy of the system: again, since there are no external forces acting on the system, energy cannot be dissipated, so the total energy of the system cannot change.