Two objects connected by a cord over a pulley

[chudd88]

Homework Statement

Two objects with masses 5.00 kg and 2.00 kg hang 0.600 m above the floor from the ends of a cord 6.0 m long passing over a frictionless pulley. Both objects start from rest. Find the maximum height reached by the 2.00-kg object.

Homework Equations

I'm baffled. I don't see a way to apply any equations, which is the main problem.

The Attempt at a Solution

I'm having a very difficult time visualizing this problem, I guess. I'm hoping someone can explain simply what's wrong with the image I have in my head when reading this problem.

So, I picture a 6-m long cord with a 5-kg weight on one end, and a 2-kg weight on the other end. This cord is placed over a pulley such that the two weights are both 0.600 m above the ground. So, there is an equal amount of cord on both sides of the pulley (left and right). When the weights start to move, the 5-kg weight will drop, and the 2-kg weight will ascend.

So, given that the 5-kg weight is 0.600 m above the ground, the most it can descend is 0.600m. It seems to me that this should mean that the other weight will be lifted 0.600 m above its starting position, for a final height of 1.20m. My book give a different, higher value.

For a cord passing over a pulley, regardless of the diameter of the pulley, it seems that however much I pull down on one end of the cord, the other end will go up by the same amount. Since there's only 0.600m between the 5-kg weight and the floor, how could the other weight possibly move up more than 0.600m in response to the 5-kg weight moving?

Can someone please explain what I'm doing wrong here? I can't see any way to apply any of Newton's laws to this one.

Thanks.

 

[ehild]

Drawing a picture always help.

You release the bodies, they start to move, and at the end the 5kg-mass body reaches the ground. The other body is at 1.2 m height in that instant, but it has some velocity and the cord has no resistance against its motions. It will continue to move upward for some more height.

ehild

 

[chudd88]

Perfect. Thank you. That should have been obvious.