By how much does a 65.0-kg mountain climber stretch her 0.800-cm diameter nylon rope when she hangs 35.0 m below a rock outcropping?

Question

 i know which formula to use but i am not getting the right answer

Answer 1

Look up Young's modulus (E) for nylon.  For an elongation ΔL and an unstretched length L, the longitudinal stress (σ) in the rope is 

 

σ = (ΔL/L)E

 

But σ must equal the weight of the climber per unit cross sectional area of rope.  Given the diameter d,

 

A = πd²/4

 

σ = mg/A = mg/(πd²/4) = 4mg/(πd²)

 

(ΔL/L)E = 4mg/(πd²)

 

ΔL = 4mgL / (πd²E)

 

You know m, g, d, and L (assuming the giving length of rope is the unstretched length).  Look up E and plug in the numbers. Be careful with the units.