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I have heard that an isolated system is where no energy and no mass is exchanged with outside the system. Does that imply that no external force can be applied to an isolated system? Why?

For example, there is a block at rest in a system and an external force is applied to move the block and provide kinetic energy. This contradicts the conservation of energy. Is it because a force is applied hence the system is not isolated?

Sorry for asking a silly question, just being confused.

abouttostart
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2 Answers2

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It all depends on how you look at you situation. If by your system only mean the block, then yes energy in that system is not conserved. However, usually when people talk about energy conservation in a case like yours they do one of two options:
1. Either you include the force in your system and hey presto, the kinetic energy gained in the block comes from the work done by the force and energy is conserved.
2. Or you think of the external force, $\vec{F}$, as the result of a potential energy field, $V$, through the relation $\vec{F}=-\nabla V$. By that reasoning, the kinetic energy gained by the block comes from the block's initial potential energy, and again energy has been conserved.

A word of warning though: for energy to be conserved the potential field, $V$, must not have any explicit time dependence. Basically, the potential energy of every point in your space has to be the same at all times, for energy conservation to be valid. For the more advanced of you, this is a result of Noether's theorem, which basically states that any conservation law stems from a symmetry of your system. For the case of energy conservation, the symmetry I question is time symmetry. (The word "symmetry" might sound a bit weird since it is not related to say mirror symmetry of geometric shapes. Rather, "time symmetry" refers to that the system should behave the same regardless of when in time you start your system, either at $t=0$ or at any other time $t=t'$. Minute physics has a video on this.)

Andréas Sundström
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You’re correct that an isolated system is by definition one that cannot exchange mass nor any form of energy with its surroundings.

But a force is not a form of energy. You can apply a force to an isolated system as long as it does no work on the system.

So as long as a force applied to your box does not cause it to move from rest the box is still considered an isolated system.

Hope this helps

Bob D
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