A bungee jumper with mass 65.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. After many oscillations, he finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.

The spring stiffness constant is 116.7 N/m and the the unstretched length of the bungee cord is 19.54 m.

The given parameters;

The period of oscillation of the bungee jumper is calculated as follows;

The spring stiffness constant is calculated as follows;

The extension of the cord is calculated as follows;

The unstretched length of the bungee cord is calculated as;

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Explanation:

It is given that,

Mass of a bungee jumper is 65 kg

The time period of the oscillation is 38 s, hitting a low point eight more times.It means its time period is

After many oscillations, he finally comes to rest 25.0 m below the level of the bridge.

For an oscillating object, the time period is given by :

k = spring stiffness constant

So,

When the cord is in air,

mg=kx

x = the extension in the cord

So, the unstretched length of the bungee cord is equal to 25 m - 5.6 m = 19.4 m

and 1and 1

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