The problem states that a bungee jumper is jumping from a bridge 50 metres above a river. He has a mass of 80 kg and is using an elastic rope of unstretched length 30 m. When he jumps, at the bottom of his fall he is only a few milimetres above the surface of the water.

The question then asks for the force constant of the rope, i.e. how much force is required to stretch the rope by one metre?

To solve this problem, I suppose the first thing you need to do is to determine the elastic potential energy of the rope at the bottom of his fall. Would I be correct in assuming that this would be equal to his loss in gravitational potential energy?

If yes, then the problem is easy. And I've already done it. I had my working all typed out, but realised it was irrelevant.

Originally posted by AD1
The problem states that a bungee jumper is jumping from a bridge 50 metres above a river. He has a mass of 80 kg and is using an elastic rope of unstretched length 30 m. When he jumps, at the bottom of his fall he is only a few milimetres above the surface of the water.


Amazingly, I just a few hous ago tutored a physics student on that exact same problem (same numbers and everything).


To solve this problem, I suppose the first thing you need to do is to determine the elastic potential energy of the rope at the bottom of his fall. Would I be correct in assuming that this would be equal to his loss in gravitational potential energy?


Yes, since you are not given enough info to account for nonconservative forces such as air resistance.

I believe the problem is a past A-level exam question here in England. Thanks for the help, Tom.

I get the force constant to be 20g newtons per metre (that's 196.2 N/m using 9.81 m/s^2 as the value for g), that what you got?

Originally posted by AD1
I believe the problem is a past A-level exam question here in England. Thanks for the help, Tom.


That makes it even more amazing, because I teach at a school in the US!


I get the force constant to be 20g newtons per metre (that's 196.2 N/m using 9.81 m/s^2 as the value for g), that what you got?


Yes. Unlike my student, you remembered to subtract the relaxed length of the cord from the height of the bridge when calculating the potential energy stored in the cord. Good job!