Can internal forces do work onto object(s) in a system?

Question

I know that internal forces can't do work on a system but can it do work on the bodies in a system? For example, for a ball-earth system, even though gravitational force is internal, it still did work onto the ball. So, i'm assuming that internal forces are able to do work onto an object/objects in a system?

Answer 1

Yes. As long as $\int\mathbf F\cdot\text d\mathbf x\neq0$ the force has done work.

Answer 2

Internal forces can most definitely do work on a system too. Just imagine two bodies getting attracted under gravitational force, with no outside forces in play. The kinetic energy of both bodies, and hence the system, would increase, which means that an internal force did work on both individual bodies as well as the system.

Answer 3

So, i'm assuming that internal forces are able to do work onto an object/objects in a system?

Yes, as already pointed out in the other answers internal forces can do work on components of the system.

In your ball/earth system example, not only does the gravitational force of the earth do work on the ball, the gravitational force of the ball does work on the earth, albeit much less work than that done on the ball.

But the gravitational force between them does no work on the ball/earth system as a whole since gravity is internal to the system. For external work to have been done on the ball/earth system it must add energy to the system. In this case, no energy is added. Gravitational potential energy is converted to kinetic energy.

Hope this helps.