Bungee Jump. A bungee cord is 30.0 m long and, when stretched a distance x, it exerts a restoring force of magnitude ?kx?. Your father-in-law (mass 95.0 kg) stands on a platform 45.0 m 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 m 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 380.0 N. When you do this, what distance will the bungee cord that you should select have stretched?
Solution 51P Step 1: Data given Length of cord x = 30.0 m 1 Distance stretched x Restoring force of the cord kx Mass m = 95.0 kg Height h = 45.0 m Force exerted F = 380 .0 N We need to find the distance at which the cord stretches Let us find the stretch coefficient of the cord F = kx Consider the equation 2 mg = 1/2 kx Substitute values we get 2 95 kg × 9.8 = (1/2) × k × (1.71 m) Solving for k we get 95 kg ×9.8×2 k = (1.71.0 m) k = 1862 2.95 k = 631.1 Using this value of k we can obtain distance x F = kx Substitute 380 N = 631.1 × x x = 380 N /631.1 x = 0.602 m Hence we get the streched distance as 0.602 m
