(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Note: A bungee cord can stretch, but it is

never compressed. When the distance be-

tween the two ends of the cord is less than

its unstretched length L0, the cord folds and

its tension is zero. For simplicity, neglect the

cord’s own weight and inertia as well as the

air drag on the ball and the cord.

A bungee cord has length L0 = 34 m when

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

the cord’s tension obeys Hooke’s law with

“spring” constant 53 N/m. To test the cord’s

reliability, one end is tied to a high bridge of

height 94 m above the surface of a river) and

the other end is tied to a steel ball of mass

98 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.

2. The attempt at a solution

At first I thought maybe this could be solved using Fg= ma and then dividing Fg by the spring constant because at the bottom point Ft should be equivalent to Fg. That didn't work, so I tried setting it up like a conservation of energy problem.

mg(94)= 1/2 k (60-h)^2 + mgh

I solved for h and got 2.3 m. This is also not right. What am I doing wrong here?

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# Homework Help: Find the height of an object when a bungee cord stops it

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