Distance the lower pulley moves all 3 ropes

[Magos]

Consider this pulley:
http://67.18.37.18/1014/142/upload/p1957458.png

There has been some discussion at a forum whether this pulley reduces the necessary force to 1/2 or to 1/3 of a "non-pullied" rope. I'm strongly for 1/3 basically since for each distance the lower pulley moves all 3 ropes are moved = 3 times the distance = 3 times less force. I'm just posting this here to get a more accurate answer since, well, it's a physics forum :).

 

[russ_watters]

You are correct. Sometimes there is confusion about whether a pulley actuall provides a mechanical advantage or is just re-directing the force. Since line from the lower pulley is straight up, that pulley does give a mechanical advantage.

 

[Gokul43201]

I'll second russ' opinion on that and yours on the M.A = 3 statement.

The easiest way to show this is by drawing and labeling all the tension vectors in the different sections of string. On the lower pulley, there are three upward forces, all equal in magnitude to T, the tension. So, in equilibrium, you have 3T = W or T = W/3. But clearly F = T, at the end of the rope. So, W/F = M.A = 3