Areteem: AP physics 1 practice test question

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AP physics 1 practice test question

I have a question with this problem

I understand that the correct answers are B and C by elimination, but I don't understand why A is false. Does Earth move at all as the block slides down?

Let's think in terms of the block-Earth system. The only outside force is friction, which is opposing motion is is NOT responsible for any change in momentum. Hence, momentum should be conserved in the system.

Therefore, a change in the momentum of the block (due to gravity) must be balanced out by a change in momentum of the Earth, meaning that (A) and (C) are contradictory answer choices. So since the momentum of the block increases (C) is true, so (A) must be false.

Note: I think the confusion here is that we typically ignore the Earth moving in situations like this. We can do so because the Earth is SO massive the speed is too tiny to be relevant. If you're curious, this old blog post (click here) has a rough calculation of Earth's speed if EVERYONE on Earth jumped at once (in the same place) to show that even then, it's basically nothing.

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I understand that A is false by contradiction, but why isn't friction responsible for change in momentum?

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Here is the better explanation. In terms of the block-Earth system, both gravity AND friction should be thought of as internal forces, as both are forces between the block and Earth.

Typically we don't think of friction this way because it is non-conservative (no associated potential energy with it) but for this system that is the easiest way to consider things.

Note: I also think it's useful to consider the case of NO friction here. For many conceptual problems like this, the "edge cases" can help, as "no friction" is approximately the same scenario as "very little friction", so the answers should not change much. In the no friction case, I think it's fairly clear that (by conservation of momentum), the Earth's momentum is NOT constant. In fact, this scenario might be simple enough to go back to very basic principles. By Newton's 3rd Law (or just definition of force of gravity) the force of gravity on the block is equal and opposite to the force of gravity on the Earth. Hence, both objects are accelerating so both objects have a change in momentum.

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