Calculate the spring constant of the bungee cord

[physicsss]

A bungee jumper with mass 200.0 kg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 30 s. He finally comes to rest 20.0 m below the level of the bridge. Calculate the spring constant of the bungee cord and the unstretched length of the bungee cord.

How do I approach this problem?

 

[aviv87]

Well, you know that T = 30/8 = 3.75
And $$T=2\cdot\pi\cdot\sqrt{\frac{m}{k}}$$ => k = 561.47[N/m]
You also know that 20m under the bridge a=0
$$\Sigma \vec{F} = 0$$
$$mg=k\Delta L$$
Now you just need to get $$\Delta L$$.

HTH

 

[wais]

To calculate the spring constant of the bungee cord, we can use the formula k = (mg)/x, where k is the spring constant, m is the mass of the bungee jumper, g is the acceleration due to gravity (9.8 m/s^2), and x is the displacement of the bungee cord.

First, we need to calculate the displacement of the bungee cord. Since the bungee jumper reaches a low point eight more times in 30 s, we can divide 30 s by 9 to get the time for one oscillation, which is approximately 3.3 s. This means that the bungee cord oscillates 8 times in 3.3 s, so the total number of oscillations is 8 x 9 = 72.

Next, we can use the equation d = (1/2)at^2 to calculate the displacement of the bungee cord. We know that the final displacement is 20.0 m below the bridge, and the initial displacement is 0 since the bungee cord is unstretched at the beginning. So, we have:

20.0 m = (1/2)(9.8 m/s^2)(3.3 s)^2
20.0 m = 54.3 m

Now, we can substitute the values into the formula for spring constant:

k = (mg)/x
k = (200.0 kg)(9.8 m/s^2)/54.3 m
k = 36.8 N/m

Therefore, the spring constant of the bungee cord is 36.8 N/m.

To find the unstretched length of the bungee cord, we can use the formula L = (m + k)/k, where L is the unstretched length, m is the mass of the bungee jumper, and k is the spring constant.

L = (200.0 kg + 36.8 N/m)/(36.8 N/m)
L = 200.0 kg/36.8 N/m + 1
L = 5.43 m

So, the unstretched length of the bungee cord is 5.43 m.

In summary, the spring constant of the bungee cord is 36.8 N/m and the unstretched length is 5.43 m. These calculations can help ensure the safety and