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# Maximum Tension in a Rope watch

1. Bungee-jumper has mass of 80kg, attached to one end of a 20m rubber rope, rope is 2.5cm in diameter, other end attached to a bridge 28m above river.

Assuming rope obeys Hooke's Law; use energy calculation to find maximum tension in rope.
It's a simple question - I know, but I feel like it's going over my head.
Thanks.
2. I think you'll need to assume the jumper will just barely get dipped into the river... Then you're able to use the extension of the bungee and the change in height from the bridge deck for energy calculations.
3. (Original post by Prudator)
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(Original post by Joinedup)
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I think it would be incorrect to make the assumption Joinedup stated i.e. assuming that the bungee jumper dangles barely above the river at their lowest point of their jump.

By considering the total energy in the system, the lowest position in the bungee jumper's descent can be determined - which is unlikely to be coincidentally at the altitude of the river.

For the initial conditions, the energy in the system is purely gravitational potential.

You should consider that at the point of maximum tension in the rope, the rope will be at its greatest elongation. At this point, the jumper will have descended 20m (the length of the rope) plus the elongation.

You can determine the elongation by assuming that the initial gravitational potential energy is all converted into the strain energy of the rope - remember to include the loss in gravitational potential energy as the jumper descends 20m plus the elongation.

Once you have determined the elongation, you can simply use Hooke's law to determine the maximum tension in the rope.

You can determine the elongation by assuming that the initial gravitational potential energy is all converted into the strain energy of the rope - remember to include the loss in gravitational potential energy as the jumper descends 20m plus the elongation.

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but you don't know k yet - afaict you have to assume the jumper gets their hair wet or you won't have enough to work with.
5. (Original post by Joinedup)
but you don't know k yet - afaict you have to assume the jumper gets their hair wet or you won't have enough to work with.
I agree.
Actually what really bother me about the question is that it asks for max tension.
6. (Original post by Prudator)
Bungee-jumper has mass of 80kg, attached to one end of a 20m rubber rope, rope is 2.5cm in diameter, other end attached to a bridge 28m above river.

Assuming rope obeys Hooke's Law; use energy calculation to find maximum tension in rope.
It's a simple question - I know, but I feel like it's going over my head.
Thanks.
When the rope is taught energy is converted to tension and this happens 8m above the water 28-20. So KE = 1/2(u+gt)^2*80 at this point. Or 80*9.81*20 is the KE maximum. The extended length when tension is maximum assuming the system is closed is KEmax/80*9.81=h as the velocity is zero when the jumper is fully extended on the rope and has no horizontal motion. Hope this helps you should find the extended height by adding 20 to the final value of h found by the above process.

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