Conservation of energy. A daring friend of yours talks you into bungee jumping f

Question

Conservation of energy. A daring friend of yours talks you into bungee jumping from the Royal Gorge Bridge, in Colorado. Starting from the bridge (at rest), you launch off and fall first to the unstretched length of the bungee, 153 m. The bungee then stretches until you reach the final drop distance of 321 m. For this problem, approximate your mass as 65 kg. a. There is some air resistance (drag) acting on you, which slows your initial drop speed slightly. If you reach a speed of 53.0 m/s in the first (153 m) part of the drop, what is the work done by drag? b. The bungee starts to stretch at this point, at 153 m, when you are traveling at 53.0 m/s. Ignoring the small effect of air resistance that you explored in part a, what is the ?effective spring constant? of the bungee if it brings you to a stop when you have fallen a total distance of 321 m? (In other words, the stretch of the bungee is the initial drop subtracted from the total distance.)

Explanation / Answer

Given that,

unstreched length of bungee = L = 153 m

streched legth (final) = D = 321 m

your mass = 65 kg and velocity = v 53 m/s

Part (a)

The KE at a speed of 53 m/s will be

KE = 1/2 m v2 = 1/2 x 65 x (53)2

KE = 91292.5 Joules

PE at the drop of 153 m

PE = m g h = 65 x 9.8 x 153 = 97461

Work done by drag will be =   97461 - 91292.5 = 6168.5 Joules

Part(b)Let it be k

F(spring) = F (gravty)

k ( D - L ) = m g

k = mg / (D - L) = 65 x 9.8 / (321 - 153) = 637 / 168= 3.79

Hence K = 3.79 N/m

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