A bungee cord has length L0 = 24 m when unstretched; when it’s stretched to L >

ID: 1725625 • Letter: A

Question

A bungee cord has length L0 = 24 m when

unstretched; when it’s stretched to L > L0,

the cord’s tension obeys Hooke’s law with

“spring” constant 69 N/m. To test thecord’s

reliability, one end is tied to a high bridge of

height 69 m above the surface of a river) and

the other end is tied to a steel ball of mass

97 kg. The ball is dropped off the bridge with

zero initial speed.

Fortunately, the cord works and the ball

stops in the air a few meters before it hits the

water — and then the cord pulls it back up.

The acceleration of gravity is 9.8 m/s2 .

Calculate the ball’s height above the wa-

ter’s surface at this lowest point of its trajec-

tory.

Answer in units of m.

L0 = 24 m, k = 69 N/m. H = 69 m, m = 97 kg. find theball’s height h above the water’s surface at thislowest point.

initial energy = mgH

at the lowest point, energy = mgh + k(L - L0)2/2

where L = H - h

energy conservation:

mgH = mgh + k(H - h - L0)2/2

H = h + k(H - h - L0)2/(2mg)

69 = h + 0.0363(45 - h)2

let 45 - h = x

0.0363*x2 - x - 24 = 0

x = 42.9 m

h = 45 - x = 2.1 m

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