A bungee cord is 30.0 long and, when stretched a distance , it exerts a restorin

Question

A bungee cord is 30.0 long and, when stretched a distance , it exerts a restoring force of magnitude . Your father-in-law (mass 94.0 ) stands on a platform 45.0 above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 before the cord stops him. You had several bungee cords to select from, and you tested them by stretching them out, tying one end to a tree, and pulling on the other end with a force of 400 .

Explanation / Answer

See energy stored in bungee cord is given by 1/2kx^2, now when father in law is at 45m above ground its potential energy is mgh = 94*9.8*45 = 41454J, and when at 4m from ground is 94*9.8*4 = 3684.8J, now change in energy will be converted to 1/2kx^2. so 1/2kx^2 = 41454 - 3684.8 = 37769.2J. but x = change in length of cord = 41 - 30 =11m. so equation becomes 1/2k*(11)^2 = 37769.2, so k = 624.28, now when tested with 400N , 400 = kx, so x = 400/624.28 = 0.64metres.

ans: cord should strech 0.64metres on applying force of 400N

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