Calculating Spring Constant of Bungee Cord

[HHippo]

Homework Statement

A bungee jumper with a mass of 77.0kg, jumps from a high bridge. He just touches the water in the river below and after reaching this lowest point, he oscillates up and down, hitting the lowest point another 8 times in 48.0 seconds. Calculate the spring constant of the bungee cord.

Homework Equations

F = -kx
T = 2π√(m/k)

The Attempt at a Solution

I thought the period was 6 (48/8) and then used those two equations to solve for k. Got 8.94 but I am not sure if I did it right...

 

[rl.bhat]

Hi HHippo, welcome to PH.
Will you please show your calculations?

 

[RTW69]

You know the period and mass you can solve for the spring constant directly from the period equation. Check your math.

 

[ashishsinghal]

method seems correct show your calculations

 

[rwisz]

I would approach this problem by first clarifying some information. Is the bungee cord assumed to be ideal, meaning it has no mass and does not stretch? Also, what is the initial length of the bungee cord and how much does it stretch when the jumper reaches the lowest point? These details are important in accurately calculating the spring constant.

Assuming that the bungee cord is ideal and has an initial length of 0, we can use the formula T = 2π√(m/k) to calculate the spring constant. In this equation, T represents the period, which is the time it takes for the jumper to complete one full oscillation up and down. In this case, the period is 6 seconds (48 seconds/8 times), so we can plug in the values and solve for k.

6 = 2π√(77/k)
6/2π = √(77/k)
(6/2π)^2 = 77/k
k = 77/(6/2π)^2 = 2.62 N/m

Therefore, the spring constant of the bungee cord is 2.62 N/m. It is important to note that this is an ideal calculation and in reality, the spring constant may vary depending on the actual length and properties of the bungee cord. Additionally, the mass of the jumper may also affect the spring constant. Further experimentation and analysis would be needed to determine the exact value of the spring constant in a real-world scenario.