Question

A bungee jumper with mass 70.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 42.0 s. He finally comes to rest 28.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.

Answer 1

given,

mass of jumper = 70 Kg

height when he is at rest = 28 m

time = 42 s

Time period, T =
`(42)/(8)`

T = 5.25 s

now,

`T = 2\pi\sqrt{(m)/(k)}`

`5.25= 2\pi\sqrt{(70)/(k)}`

`(70)/(k)=0.698`

k = 100.26 N/m

extension of the chord

`x = (mg)/(k)`

`x = (70* 9.8)/(100.26)`

x = 6.84 m

un stretched length of the bungee cord

L = 28 - 6.84

L = 21.16 m