Final answer:
The total mechanical energy is not always conserved when two objects collide in the absence of external forces. Momentum is conserved, but kinetic energy is not necessarily conserved, particularly in inelastic collisions where internal energy changes.
Step-by-step explanation:
When two objects collide in the absence of external forces, is the total mechanical energy always conserved? The answer is No. Inelastic collisions, where objects may stick together after impact, do not conserve kinetic energy even though momentum is conserved. Considering a scenario with two objects of equal mass, where one object initially moves and the other is at rest, and after collision, the moving object comes to rest while the other object moves with some unknown velocity, we can conclude the following:
- Momentum is conserved since there are no external forces acting on the system.
- Kinetic energy is not conserved if, after the collision, the objects stick together or there's a change in the internal energy.
For instance, if two equal-mass objects collide and come to rest, momentum is not conserved because of the net external force acting on the system. This type of collision would be inelastic because the internal kinetic energy is not conserved, meaning it has been transformed into other forms of energy, such as heat or sound. This contrasts with an elastic collision, where both momentum and kinetic energy are conserved. Therefore, not every collision where momentum is conserved will also conserve the total mechanical energy.