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Old Jul 29th 2012, 04:53 AM   #1
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Momentum problem

A skater with a mass of 60 Kg is on a skateboard with a mass of 3 kg. The skater holds in his hands two weights each of them with a mass of 5 kg. The system is at rest and at some moment the skater throws horizontaly one of the weights so that it's velocity in respect to the skater is 8 m/s. After some more time he throws the second weight in the same direction.

What is the velocity of the skater after the second throw?

Well from conservation of momentum you get that for the first throw the momentum of the skater+skateboard after the throw minus the momentum of the first weight after the throw equals to 0. But why is it so clear that the skater and the skateboard will move in the same velocity? They don't say anything about any friction between the skater and the skateboard and if there's no friction then when the skater throws the weight he should move to the other direction in respect to the ground and to the skateboard. The skateboard should stay put because there is no horizontal force acting upon him. Am I wrong?

Also - isn't there something missing about the velocity of the second weight in order to solve the question?
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Old Jul 30th 2012, 10:35 AM   #2
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Originally Posted by assaftolko View Post
Well from conservation of momentum you get that for the first throw the momentum of the skater+skateboard after the throw minus the momentum of the first weight after the throw equals to 0.
Don't forget that after the first throw he's still holding the 2nd weight, so: momentum of (man + skateboard + weight2) - momentum of weight1 = 0.

Originally Posted by assaftolko View Post
...if there's no friction then when the skater throws the weight he should move to the other direction in respect to the ground and to the skateboard. The skateboard should stay put because there is no horizontal force acting upon him. Am I wrong?
No you're not wrong, but it seems pretty clear that the intent here is that the man and the skateboard travel together. The reason the skateboard is mentioned is so that you can ignore friction between the man+skateboard and the ground. Otherwise what allows the man to slide without friction across the ground?

Originally Posted by assaftolko View Post
Also - isn't there something missing about the velocity of the second weight in order to solve the question?
Yes - it's critical that you know the relative velocity of the second throw. If that data isn't provided I suggest that your answer be given in general form for v_weight2, and then add a note that says something like "If we assume v_weight2 = v_weight1 then the final velocity v_skater is ..."

Last edited by ChipB; Jul 30th 2012 at 10:38 AM.
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Old Jul 30th 2012, 10:18 PM   #3
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Ok thank you very much!
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