How Does Block 1's Acceleration Compare to Block 2's in a Dual Pulley System?

[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.)

Explain your answer.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?

 

[Chestermiller]

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 l₁-δ₁, l₂ + δ₂, l₃ + δ₂. The total length of cord doesn't change, so

(l₁-δ₁)+(l₂ + δ₂)+(l₃ + δ₂) = l₁+l₂+l₃

So, δ₁=2δ₂