# 2 masses and 2 pulleys

1. Sep 22, 2013

### ashrafi

In the figure below, the pulleys and the cord are light, all surfaces are frictionless, and the cord does not stretch.

http://awesomescreenshot.com/0301qqz07c

How does the acceleration of block 1 compare with the acceleration of block 2? (Use the following as necessary: m1, m2, and a2.)

I know that a_1 should be 2a_2 but I have no idea why. Can someone please explain in details why its like that?

Last edited: Sep 22, 2013
2. Sep 22, 2013

### Staff: Mentor

This is strictly a kinematics problem. Let the initial lengths of the 3 sections of cord be l1, l2, and l3, where
l1 is the initial distance between m1 and the first pulley
l2 is the distance of the first pulley above the second pulley
l3 is the distance of the second pulley below the ceiling

Let m1 move to the right by δ1 and let m2 (and the lower pulley) move down by δ2. Now, the new lengths of the 3 sections of cord are l11, l2 + δ2, l3 + δ2. The total length of cord doesn't change, so

(l11)+(l2 + δ2)+(l3 + δ2) = l1+l2+l3

So, δ1=2δ2