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 99.0 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 420 N. When you do this, what distance will the bungee cord that you should select have stretched?

Explanation:

The extra fall by bungee during which the cord stretched x = 41-30

= 11 m .

work done by elasticity of cord = 1/2 k x²

x = 11 m

work done = 1/2 x k x 11 x 11

= 60.5 k

loss of potential energy by Bungee

= mgh

= 99 x 9.8 x 41

= 39778.2 J

According to low of conservation of mechanical energy

60.5 k = 39778.2

k = 657.5 N /m

When this bungee cord is stretched by force 420 N

amount of stretch = force / Force constant (k )

= 420 / 657.5

= .6387 m

63.87 cm .

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