Question of Conservation of Momentum

Question

I think I understand the concept of conservation of momentum in an inelastic collision. However, what if two objects, one being more massive than the other, started out together and then separated (via a mechanism), wouldn't the object of smaller mass gain velocity after the separation due to conservation of momentum?

Examples I can think of are:

1. A skateboarder riding on a frictionless surface and he jumps up off the skateboard.
2. A rocket dropping a stage that is heavier(even after all the fuel is spent) than the next stage.
3. An astronaut is holding onto an object more massive than himself in outer space. He then simply lets go of the larger object, not applying any force to the object.

Answer 1

These are 'superelastic' collisions - where energy is released.

Yes the smaller mass would gain velocity due to conservation of momentum, but only provided the energy released in the separation pushed the smaller mass 'forwards' in the same direction as the motion

If, for example, the skateboarder jumps forwards off the skate board he (the heavier body) can go forwards at a higher velocity and either slow down, stop, or force the skateboard to go backwards in the opposite direction depending on how hard he pushes back on the skateboard as he jumps.

As pointed out by Sofia in comment, momentum is conserved, but in these cases the total kinetic energy of the bodies increases.

I suppose strictly speaking these events are not collisions - more dissociations - but the are definitely superelastic

Answer 2

Two important points:

1. You must apply Conservation of Momentum to a system, and that system must remain the same throughout the event in question;

   2. The system must be free of external forces.

In the case of the skateboarder, the system is the skateboarder plus skateboard. If the skateboard has good quality wheels, and the surface is level, then there are no external horizontal forces, and the horizontal momentum is conserved. If the skateboarder jumps off, then the jumping force is internal and the momentum of the system is conserved. The skateboard may well shoot ahead, with more momentum, but the skateboarder will correspondingly slow down, with an exactly matching decrease in momentum.

In the case of a rocket separating from a lower stage, there will not be any dropping unless air friction (an outside force) or on board thrusters act to separate the two objects...