# Internal forces and the work done by them

Kaushik
My book states that, '∑Finternal=0∑Finternal=0. But the work done by them may or may not be zero.
Why is this true?
Edit: How can the work ≠ 0 sometimes?

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Summary: My book states that, '##\sum F_{internal} = 0##. But the work done by them may or may not be zero.

My book states that, '##\sum F_{internal} = 0##. But the work done by them may or may not be zero.
Why is this true?

Newton's third law.

Kaushik
Newton's third law.
If net internal force = 0, then how can they do work?

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If net internal force = 0, then how can they do work?

Can you think of an example where a) internal forces do work and b) internal forces do no work?

Hint: think about orbits and trajectories under gravity.

• Kaushik
Kaushik
a) internal forces do work
Setup:- A compressed spring between two blocks on a horizontal plane
System:- spring + 2 blocks
Spring force acts on the blocks. The blocks move even though there is no external force that contributes to its acceleration.
Am I correct? Is this example valid or am I misinterpreting something?

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Setup:- A compressed spring between two blocks on a horizontal plane
System:- spring + 2 blocks
Spring force acts on the blocks. The blocks move even though there is no external force that contributes to its acceleration.
Am I correct? Is this example valid or am I misinterpreting something?

In the simplest terms, you are really just looking for an example where the kinetic energy of the system changes. Certainly, if two blocks are connected by a spring, then they may oscillate, hence the internal forces are doing alternately positive and negative work.

A simpler example, perhaps, is just an object falling under gravity; or, two charged particles attracting or repelling each other.

• Kaushik
Kaushik
an object falling under gravity
In this the system is Earth + object, isn't?

Kaushik
So there is work being done because there is a force(internal) that is not perpendicular to the displacement and it does not matter if the force contributes to that displacement or not. Isn't?

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In this the system is Earth + object, isn't?

Yes. If the Earth isn't part of the system then , technically, gravity is an external force.

• Kaushik
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So there is work being done because there is a force(internal) that is not perpendicular to the displacement and it does not matter if the force contributes to that displacement or not. Isn't?

I'm not sure I understand that. The point about the force being perpendicular to displacement is a good one. That's the key to getting a example where no work is done.

Another example is simply the forces within a solid object. The individual particles may be oscillating but the total kinetic energy is a measure of the temperature of the object. And, if the temperature is constant then the nett work done by all the internal forces is zero (at least approximately).

• Kaushik
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How can the work ≠ 0 sometimes?
I am not convinced about this claim of the book. For the spring + 2 blocks the increased KE of the blocks is the same magnitude of the decreased PE of the spring, so the energy is constant and the work is 0. For gravity the gravitational field serves the role of the spring so the increased KE again corresponds to a decreases PE for no net work done on the system.

Perhaps the book is only considering changes in KE and not changes in PE. That seems like a poor description to me, but as long as they are clear it would be ok.