Consider a bungee cord of unstretched length Lo = 34 m. When the cord is stretched to L >Lo it behaves like a spring and obeys Hooke's law with the spring constant k=22 N/m. However, unlike a spring, the cord folds instead of becoming compressed when the distance between its ends is less than the unstreteched length: For L > Lo the cord has zero tension and zero elastic energy.
To test the cord's reliability, one end is tied to a high bridge (height H = 204 m above the surface of a river) and the other end is tied to a steel ball of weight mg = 120kg x 9.8 m/s^2. The ball is dropped off the bridge with zero initial speed. Fortunately, the cord works an the ball stops in the air before it hits the water --and then the cord pulls it back up.
Calculate the ball's height hbot at the lowerst point of its trajectory.
Conservation of Energy.
Before dropping, the ball has only PE due to gravity. At its max. stretch height, it has PE due to the spring like nature of the rope and it also has some PE due to gravity.
The final h (204 - 34 - x) can be visualized if you draw a picture.
this is the distance from the bridge it stretches to until folding back.
This distance is also equal to 36m above the ground.
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