Question 10

[quadalpha]

There seems to be a slight problem with this question (and the premise of the passage) if the answer is as given. There is no way for a force acting on m_1 to accelerate either m_2 (frictionless) or m_3. What's going to happen is that m_1 accelerates and hits m_3, which has no component of its own acceleration in the horizontal direction. Once m_1 hits m_3, then there can be force acting on both m_1 and m_3 in the horizontal direction, but it's doesn't seem to be a way for said force to act on m_2.

This seems to bear some relation to the "airplane taking off on a treadmill" scenario.

[emilie.maz5603]

When the force F acts on m1, it accelerates it forward, acceleration = a.

But, thanks to no friction between m2 and m1, m1 doesn’t take m2 along, so m2 slips relatively to m1.

That is m2 stays where it is and m1 moves forward, so relative to m1, m2 moves behind.
BUT, m2 is connected to m3, which has force acting on it, as we saw in the diagram and question.

So m3 exerts a force on m2 via a string, in which it develops a tension due to its weight.
The force is just right to keep m2 from slipping backwards, or to pull it towards itself and down, and like the question says, and the net result is that m3 doesn’t move up or down, m2 stays at rest relative to m1, moving along with it.

[quadalpha]

[mcat_premed3832]

The fact that you have remained on the case shows that you are diligent and you will likely do very well on the real test!

But for this question, let's break down your reasoning which is essentially based on the following premise:

[quadalpha]

Sorry, I took the test and disappeared. But back to the question:

I think the problem is in the pulley. There is a physical connection via the pulley, but because the pulley is just a string bent around a disc, the only force it can exert is tension, i.e., the only direction the string can move m3 in is up. Your example with the pulley shows that it can move things up. So when m1 moves, the only thing that will move m3 horizontally (before m1 crashes into it) is the restoring force from the movement of the pulley, as in a pendulum. Now, that restoring force is always going to be less than the force of gravity that drags it down, since it is a component of F_g. Does that make more sense now?