Physics Question - Potential Energy?
The Royal Gorge bridge over the Arkansas River is 310.0 m above the river. A 60.0-kg bungee jumper has an elastic cord with an unstressed length of 64.0 m attached to her feet. Assume that, like an ideal spring, the cord is massless and provides a linear restoring force when stretched. The jumper leaps, and at at her lowest point she barely touches the water. After numerous ascents and descents, she comes to rest at a height h above the water. Model the jumper as a point particle and assume that any effects of air resistance are negligible.
1) (a) Find h.
2) (b) Find the maximum speed of the jumper.
I keep setting up the equations but I must be doing something wrong becaue I can't get the right answer.
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Verified answer
(a) initial E = mgh = 60kg * 9.8m/s² * 310m = 182 280 J
This is converted entirely into spring energy at water level, and the spring has stretched
x = 310m - 64m = 246 m, so
182280 J = U = ½kx² = ½ * k * (246m)²
k = 6.02 N/m
Her weight, then stretches the spring such that
mg = kx
60kg * 9.8m/s² = 6.02N/m * x
x = 97.6 m
Then the height above the river is
h = 310m - 97.6m - 64m = 148 m
(b) The maximum speed will be attained when the force in the spring changes from being less than her body weight to being more than her body weight, which we already found to correspond to spring stretch x = 97.6 m
and height h = 148 m.
At that point, the kinetic energy is
KE = 182280J - 60kg * 9.8m/s² * 148m - ½ * 6.02N/m * (97.6m)² = 66 332 J
KE = ½mv² = ½ * 60kg * v² = 66 332 J
v = 47 m/s