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Assuming that I defined a block as my system, due to certain factors (assumingly friction), when I exerted a force on the block, the block doesn't move.

Since the block (the system) didn't accelerate,

  1. Does that mean the force I exerted is internal?

  2. Can I still consider the force to be external since it didn't cause the centre of mass of the system to accelerate?

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The block will not move if and only if the net sum of all external forces acting on it is zero. This may mean that there are no external forces. Or it may mean that there are two or more external forces which sum to zero.

If you exert a force on the block then, considering the block as a system, that is an external force. So there must be some other external force (or combination of forces) acting on the block too, so that the net external force on the block is zero. Other external forces acting on the block could include gravity, friction and normal force from whatever the block is resting on.

Internal forces are forces which one part of a system exerts on another part of the same system. If the block is the system, then internal forces will include the forces between the individual molecules of the block which keep the block in one piece

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