As part of a fundraiser, you want the new dean to bungee jump from a crane. The

Question

As part of a fundraiser, you want the new dean to bungee jump from a crane. The jump will be made from 44 m above a 2.5m deep pool of Jello. A 30 m long bungee cord would be attached to the dean?s ankle. You must convince the dean that your plan is safe for a person of his mass, 70 kg. As the bungee cord stretches, it will exert a force with the same properties as the force exerted by a spring. Your plan has the dean stepping off a platform and being in free fall for the 30 m before the cord begins to stretch. You must determine the elastic constant of the bungee cord so that it stretches only 12m, which will keep the 2m-tall dean?s head just out of the Jello.

Explanation / Answer

Total length of bungee cord untill it stretces,

h = L + x

h = 30 + 12 = 42 m

strech in the cord, x = 12 m

mass of person, m = 70 kg

From conservation of energy,

mgh = (1/2)kx^2

70*9.8*42 = (1/2)*k*12^2

k = 400 N/m

elastic constant of the bungee cord, k = 400 N/m

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