An 77.4-kg climber is scaling thevertical wall of a mountain. His safety rope is

Question

An 77.4-kg climber is scaling thevertical wall of a mountain. His safety rope is made of nylon that,when stretched, behaves like a spring with a spring constant of1.21 x 103N/m. He accidentally slips and falls freely for 0.815 m before the rope runs out of slack. Howmuch is the rope stretched when it breaks his fall and momentarilybrings him to rest?
m
Thank you for your help! An 77.4-kg climber is scaling thevertical wall of a mountain. His safety rope is made of nylon that,when stretched, behaves like a spring with a spring constant of1.21 x 103N/m. He accidentally slips and falls freely for 0.815 m before the rope runs out of slack. Howmuch is the rope stretched when it breaks his fall and momentarilybrings him to rest?
m
Thank you for your help!

Explanation / Answer

m g h + m g x = k x2 / 2 Potential energy lost by climber equals potential energy ofstretched rope k x2 - 2 m g x - 2 m g h = 0 Solve the quadratic for x the distance the ropestretches

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