A rock climber is rappelling down the face of a cliff when hishold slips and he

Question

A rock climber is rappelling down the face of a cliff when hishold slips and he slides down over the rock face, supported only bythe bungee cord he attached to the top of the cliff. Thecliff face is in the form of a smooth quarter-cylinder with height(and radius) H = 300 m (picture below). Treat thebungee cord as a spring with force constant k = 5.00 N/mand unstressed length L = 60.0m. The climber's massis 85.0 kg. (a) Using a spreadsheet program, make a graph of therock climber's potential energy as a function of s, hisdistance from the top of the cliff measured along the curvedsurface. Use values of s between 60.0 m and 200m. (can ignore this spreadsheet part if youwant) (b) His fall began when he was a distancesi = 60.0 m from the top of the cliff, andended when he was a distance sf = 110 m fromthe top. Determine how much energy is dissipated by frictionbetween the time he initially slipped and the time when he came toa stop.

Explanation / Answer

as the energy dissipated by the friction is stored in the bungeecord energy of the bungee cord as the climber slips -------------------------------------------- when he stop the distance from the ground=190m now horizontal distance=190cos horizontal distance from the figure=300*300-110*110=279.10m=279m hence energy=1/2k(change inlength)2=0.5*5*(279-60)=547.5J

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