A bungee jumper with mass 60.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 49.0 s. He finally comes to rest 30.0 m below the level of the bridge.
1) Calculate the spring constant of the bungee cord.2) Calculate the unstretched length of the bungee cord.

a) Spring constant,k = 63.09 N/m

b) Unstretched length = 20.68 m          

Explanation:

a) Mass of the bungee jumper, M = 60 kg

time for complete oscillation, t = 49 s

Number of oscillations, n = 8

The period of oscillation, T = t/n

T = 49/8

T = 6.125 s

To calculate the spring constant of the bungee cord, use the formula:

Spring constant,k = 63.09 N/m

b) The extension in the spring is given by the formula:

x = mg / K

x = (60*9.8)/63.09

x = 9.32 m

extension, x = final length - original length

Original length = Final length - extension

Original length = 30 - 9.32

Original length = 20.68m                                

Unstretched length = 20.68 m            

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