Spring Constant [Please Check Work]

[BuGzlToOnl]

Homework Statement

A bungee jumper, whose mass is 98 kg, jumps from a tall building. After reaching his lowest point, he continues to oscillate up and down, reaching the low point two more times in 9.3 s. Ignoring air resistance and assuming that the bungee cord is an ideal spring, determine its spring constant.

Homework Equations

[tex]\omega[/tex]=[tex]\sqrt{k/m}[/tex]

[tex]\omega[/tex]=2[tex]\pi[/tex]/T

The Attempt at a Solution

2[tex]\pi[/tex]/9.3s = [tex]\sqrt{k/98kg}[/tex]

k = 44.732N/m [?]

I rewrote the equations so I can try to obtain.

The answer I got 44.732N/m, but that seems way to low, can anyone verify if its right/wrong and where I went wrong

EDIT: Well I think I'm wrong because I never used the fact that he reached the lowest point 3 times and didn't incorporate gravity. Not sure on how to approach this so any help would be appreciated.

 

[alphysicist]

Hi BuGzlToOnl,

Homework Statement

A bungee jumper, whose mass is 98 kg, jumps from a tall building. After reaching his lowest point, he continues to oscillate up and down, reaching the low point two more times in 9.3 s. Ignoring air resistance and assuming that the bungee cord is an ideal spring, determine its spring constant.

Homework Equations

[tex]\omega[/tex]=[tex]\sqrt{k/m}[/tex]

[tex]\omega[/tex]=2[tex]\pi[/tex]/T

The Attempt at a Solution

2[tex]\pi[/tex]/9.3s = [tex]\sqrt{k/98kg}[/tex]

I don't believe the period is 9.3 seconds. Do you see what it needs to be?

 

[thomate1]

Your approach is correct, but you forgot to include the acceleration due to gravity in the equation. The correct equation should be:

\omega=\sqrt{(k/m) + (g/m)}

Where g is the acceleration due to gravity (9.8 m/s^2). This will give you a slightly higher value for the spring constant, which makes sense since the bungee cord needs to be strong enough to support the jumper's weight and the force of gravity acting on them.

Using this equation, the spring constant would be:

k = 45.25 N/m

This is a more accurate value for the spring constant and makes more sense for a bungee cord. Keep in mind that this is an ideal case and does not take into account factors such as the elasticity of the bungee cord and air resistance, which would affect the actual spring constant in a real-world scenario.