Momentum is conserved in closed systems, while mechanical energy may not be, particularly in inelastic collisions. For instance, when two clay balls collide and stick together, momentum remains constant, but mechanical energy is lost. An external force can alter the mechanical energy without affecting momentum, illustrating that mechanical energy can be constant while momentum is not. Additionally, when considering systems like a ball thrown upwards, momentum can be zero at its apex, yet mechanical energy remains constant. Overall, momentum conservation is contingent on the absence of external forces or torques, while mechanical energy can fluctuate independently.