A bungee jumper leaps from a bridge and undergoes a series of oscillations. Assu

Question

A bungee jumper leaps from a bridge and undergoes a series of oscillations.
Assume g = 9.78 m/s^2. If a 64.0 kg jumper uses a bungee cord that has an un-stretched length of 32.5 m and she jumps from a height of 41.0 m above a river, coming to rest just above the water surface on the first downward descent, assuming no damping what is the period of the oscillations?
If there is some damping and the oscillations settle how far is the rope stretched from the original length?

Please give an explanation with your calculations. Thank you.

Explanation / Answer

A bungee jumper leaps from a bridge and undergoes a series ofoscillations. If a 64.0 kg jumper uses a bungee cord that has anunstretched length of 32.50 m and she jumps from a height of 41 mabove a river

1/2 k (41 - 32.5)^2 = potential energy stored inbungee cord
PEB = 36.125 k
m g h = 64 * 9.78 * 41 = 25662.72 J potential energyof jumper (to be stored in bungee cord)

k = 710.386 N/m

2f=(k/m)

f = 0.530

T = 1.8859 s = period of the oscillations

in case of damping the oscillations cease and the person comes to rest

s0 m*g = k*x

so x = 0.8829 m

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