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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?

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3 Answers 3

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

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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.

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  • $\begingroup$ In your example what is the work done on the center of mass of the system? $\endgroup$
    – Bob D
    May 16, 2021 at 17:22
  • $\begingroup$ The centre of mass doesn't displace at all, so work done on it is zero, but that hardly matters. Work is done on the system with respect to the centre of mass. $\endgroup$ May 16, 2021 at 19:14
  • $\begingroup$ So, since Work done in ground frame=Work done in CM frame + Work done on CM, hence my claim. $\endgroup$ May 16, 2021 at 19:25
  • $\begingroup$ My point is if the system is the two bodies (ball-earth system in the OP) no external work is done since no energy has been added to or removed from the system. All that has happened is gravitational potential energy of the two body system is converted to kinetic energy. $\endgroup$
    – Bob D
    May 16, 2021 at 20:35
  • $\begingroup$ No no, I'm pretty sure I am correct. Even in the case of a ball freely falling in a gravitational field, the PE of the ball is converted to KE. From energy conservation, we can say that no energy is being added. But that does not mean that gravity doesn't do work on the falling ball. Work is defined as the change in kinetic energy, not the change in total energy. $\endgroup$ May 16, 2021 at 20:42
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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.

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