# Help with Pulley Problem

Okay, so I’ve been looking at this problem for quite some time now and I’m still a little confused. I looked online and the answers had stated that m1 has twice as much as acceleration as m2. It doesn’t really make sense to me how, cause I thought acceleration and distance remains the same in a pulley system because the string is always the same length. I’m also questioning if you can do the question without the hint given. Any help will be appreciated. Image above ^

My work so far

m1: Fnet =T1

m2: Fnet =Fg-2T1

• Voting to reopen. This is clearly a question about underlying principles of the pulley system, not about specific computations. Commented Sep 28, 2023 at 16:19

The rope supporting $$m_2$$ is doubled up. Consider pulling $$m_1$$ all the way to the left as far as it will go, for rope length $$L$$. Now let $$m_2$$ fall as far as it can - since the rope is doubled up on itself, $$m_2$$ can only fall to length $$L/2$$, not length $$L$$. As rope moves from the horizontal to the vertical section, half the length gets distributed to each vertical section of rope.

This is the principle behind what's called a "block and tackle" system of pulleys. It allows you to lift weight several times what you could normally, at the cost of applying the force over a longer distance.

• Thank you so much Commented Sep 28, 2023 at 18:35

I thought acceleration and distance remains the same in a pulley system because the string is always the same length.

The string is always the same length, but the amount of string between $$m_1$$ and $$m_2$$ is not constant because of the pulley on the top of $$m_2$$. If $$m_1$$ moves a distance $$d$$ to the right then $$m_2$$ only moves down by a distance $$\frac d 2$$, because the amount $$d$$ of string has to be split between the two parts of the string attached to the pulley on the top of $$m_2$$. So both the speed and the acceleration of $$m_1$$ are twice that of $$m_2$$.

I’m also questioning if you can do the question without the hint given.

You have to know the configuration of the pulleys, which is equivalent to being given the hint. If the system had a different configuration - for example, if there were no pulley on top of $$m_2$$ and $$m_1$$ and $$m_2$$ were just linked by a piece of rope with constant length - then the answer would be different.

• Thank you I understand now Commented Sep 28, 2023 at 18:35