Two objects connected by a cord over a pulley

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Two objects with masses of 5.00 kg and 2.00 kg are connected by a cord over a frictionless pulley, starting from rest at a height of 0.600 m. The confusion arises regarding the maximum height the 2.00 kg object can reach when the 5.00 kg object descends. Initially, it seems that the 2.00 kg object can only rise 0.600 m, but it can actually ascend higher due to the momentum gained from the falling 5.00 kg weight. As the 5.00 kg weight reaches the ground, the 2.00 kg weight continues to rise, resulting in a final height greater than 1.20 m. Visualizing the motion and understanding the dynamics involved clarifies the solution.
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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.
 
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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
 
Perfect. Thank you. That should have been obvious.
 

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