A bungee jumper with a mass 66kg jumps from a high bridge. After reaching his lo

Question

A bungee jumper with a mass 66kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 35.3 seconds. He finally comes to rest 22 meters below the level of the bridge. Calculate the spring stiffness constant of the bungee cord. Calculate the unstretched length of the bungee cord A bungee jumper with a mass 66kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 35.3 seconds. He finally comes to rest 22 meters below the level of the bridge. Calculate the spring stiffness constant of the bungee cord. Calculate the unstretched length of the bungee cord

Explanation / Answer

The period of the spring is how long it takes an object to go from peak to peak in an oscillation. And since we know that the jumper peaked 8 times in 35.3 seconds, we can simply divide 35.3 s by 8 to figure out about how long it takes the jumper to go from low-point to low-point. So:
(35.3 s)/(8) = 4.4125 s = T

Now we can take all of out information and solve for k:
T = (2)*sqrt(m/k)
(4.4125 s) = (2)*sqrt((66 kg)/k)
Dividing both sides by (2) and then squaring both sides gives:
((4.4125 s)/(2))^2 = (sqrt((66 kg)/k))^2
(.49318 s^2/m^2) = (66 kg)/k
k = 133.82 N/m = spring constant of bungee cord

Now that we have our spring constant, we can easily find the unstretched length of the bungee cord.
To do this, the stretch of the cord can be solved by setting the force of the jumper pulling down on the cord equal to the force of the spring pulling up on the jumper. So:
mg = kd
Where m is the mass of the jumper, g is the gravitational acceleration, k is the spring constant, and d is the change in distance of the bungee cord (with vs without the jumper attached to it)
Plugging in what we know:
(66 kg)(9.81 m/s^2) = (133.824 N/m)(d)
Simplifying and dividing both side by (133.824 N/m) gives:
4.838 m = d
Since this is the change in equilibrium point with vs. without the jumper, we can simply subtract this value from 22 meters, which is the equilibrium point the cord experiences when the jumper is still attached to it. So:
(22 m) - (4.838 m) = 17.162 m
This is the length of the unstretched bungee cord

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