Final answer:
In a collision between two objects, momentum is conserved but mechanical energy may not be conserved. On the other hand, in a system where kinetic energy is conserved but momentum is not, we can consider an explosion.
Step-by-step explanation:
In a collision between two objects, momentum is conserved but mechanical energy may not be conserved. A common example is an inelastic collision, where two objects stick together after colliding. The momentum of the system is conserved because the total initial momentum is equal to the total final momentum. However, the mechanical energy is not conserved because some of the initial kinetic energy is converted into other forms of energy, such as heat or sound.
On the other hand, in a system where kinetic energy is conserved but momentum is not, we can consider an explosion. When an explosive device detonates, the fragments move away from each other with high velocities. Although the individual momenta of the fragments may not cancel out to zero, the total kinetic energy of the system is conserved as long as no external forces are present.