Question

Must the total energy of a system be conserved whenever its momentum is conserved? Explain why or why not.

a) Yes, total energy is always conserved with conserved momentum.
b) No, total energy is independent of conserved momentum.
c) Total energy conservation depends on external forces.
d) Momentum conservation does not affect total energy.

Answer 1

No, the total energy of a system does not have to be conserved whenever its momentum is conserved. The conservation of momentum does not necessarily guarantee the conservation of total energy in a system. Hence, option (b) is correct.

Step-by-step explanation:

No, the total energy of a system does not have to be conserved whenever its momentum is conserved. This is because the total energy of a system is the sum of both kinetic energy and potential energy. While momentum is conserved in collisions and interactions, the total energy of a system may change due to the conversion of kinetic energy to potential energy or vice versa.

For example, in an elastic collision where two objects collide and kinetic energy is conserved, the total energy of the system remains constant. However, in an inelastic collision where objects stick together and kinetic energy is not conserved, the total energy of the system decreases due to the loss of kinetic energy.

Therefore, the conservation of momentum does not necessarily guarantee the conservation of total energy in a system.