# Rock Climbing Energy Conservation (further help)

1. Sep 8, 2011

### JJB11

1. The problem statement, all variables and given/known data

I know that this question has been dealt with on this forum before, however it is part (b) that is new and that I need help with. I have re-written part (a) for clarity.

Question: The greatest instantaneous acceleration a person can survive is 25g, where g is the acceleration of free fall. A climber's rope should be selected such that, if the climber falls when the rope is attached to a fixed point on a vertical rock, the fall will be survived.

A climber of mass m is attached to a rope which is attached firmly to a rock face at B. When at a point A, a distance L above B, the climber falls.

a) Assuming the rope obeys Hooke's Law up to breaking, use the principle of conservation of energy and the condition for greatest instantaneous acceleration to show the the part AB of the rope (of unstretched length L) must be able to stretch by more than without breaking for the climber to survive.

b) A particular rope has a breaking strength of 25 times the weight of the climber, and obeys Hooke's law until breaking, when it has stretched by 20% of its length. Determine whether this rope is suitable.

2. Relevant equations

3. The attempt at a solution

(a) I've got the answer to this question.

I said that for the climber to survive:

1/2Fx > (2L+x)mg

as I figured the max distance the climber could fall before the rope became taut would be 2L (ie L below B) and then it would extend, thus losing more GPE. As F=ma+mg=26mg, substitute and get x must be greater than or equal to L/6.

(b) I know that the given breaking strength is insufficient to decelerate the climber beyond 25g so this is okay. However I can't work out whether the string will break or not as I'm not sure which energy balance equation I can use to find the rope extension.