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Question: A bungee jumper jumps from a bridge. The length of the loose rope is 30 m. When the jumper reach the lowest point possible, the rope stretches 10 m. What is the final stretch of the rope, when the oscillation of the rope stops? Mechanical energy loss is null. Hook law applies for the elastic.

I think this problem is unsolvable, because we need mass or the coefficient of the rope?

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What is this "coefficient of the rope"? In such problems mass of rope is neglected normally. –  Georg Nov 15 '11 at 11:20
    
Elastic coefficient, F = k*x => k. –  Matt Nov 15 '11 at 11:22
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The problem is solvable. There are two equations: the energy balance for the lowest point after jump and the force balance at the final rest point. This allows to solve the question,. BTW, ""...when the oscillation of the rope stops? Mechanical energy loss is null. "" is of course a funny wording. If loss is zero, the oscillation will never stop. :=) –  Georg Nov 15 '11 at 11:55
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If all energy loss is null the oscillations will never stop. Is that what you intended in your question? Is there at least air resistance? Can the mass of the rope be ignored as insignificant? –  FrankH Nov 15 '11 at 11:57
    
Haven't heard from you so I assume the oscillation will stop eventually and that the weight of the rope is negligible. Since this is homework, I will give you a clue to get you started: Consider the total kinetic + potential energy when the rope just starts to stretch compared to the same total energy when the person is stopped at the bottom. You should be able to figure it out from there... –  FrankH Nov 16 '11 at 0:54
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