Which Elasticity Formula Should You Use for Bungee Jumping?

[brayrbob]

Just to let you all know I really appreciate your help.

Problem
A person is doing bungee jumping from a 100m platform. Let's say that the rubber cord's coefficient is k = 6500 g/s^2. Would a 60 kg person hit the ground when jumping using that rubber cord?
The two equations that are given to use are Force - -(spring constant)(elongation) and Hanging mass *gravity = spring constant * elongation.
I'm not really sure which formula to use. I think the spring constant is k=6500 and I have done this 60*980 = 58800 but have drawn a blank.

 

[zwtipp05]

Have you been given the equation for spring potential energy? It is E= .5 k x^2
I would calculate the gravitational potential energy and see how far the bungee would stretch. Also, does your problem say how long the cord itself is? I think you would need to know that to solve the problem.

If you do have the length of the bungee, calculate how much the cord stretches and see if that is larger than 100 m. If it is...*splat*

 

[brayrbob]

No that equation is not in this lab and the question doesn't say what the length of the bungee is. Somehow I'm supposed to find the stretch distance in problem two.
Would a 70kg person hit the ground when jumping? Use g= 980cm/s^2 Hint: find the stretch distance and compare with 100 meters or 10,000cm. I think I'm tired because this problem makes no sense to me.

 

[zwtipp05]

Hmm..I guess you're just supposed to set the force of the cord equal to the force of gravity and solve for x. But I'd think there should be more stuff involved here (i.e. energy, rather than just forces). I'd approach this as a conservation of energy problem, so I'm not sure if I can help you here. Maybe someone else on the board can get you going in the right direction. Sorry

 

[brayrbob]

Well here is the equation for elongation
elongation * constant = mass * gravity to solve for elongation I have to change the equation to elongation = mass * gravity/constant So instead of using 60kg for the mass I used 60,000g since the other info has grams as their units.
60,000 * 980/6500 = 9046.153846 So the elongation of the cord is 9046.15 compared to 10,000 cm platform that leaves about 953.85 cm of clearance if I've figured this right

 

[zwtipp05]

Yep looks like you did it right.

 

[brayrbob]

Thank goodness,
Now I have to solve the second problem which is would a 70kg (70,000g or 154lbs) person hit the ground when jumping? Use g = 980 cm/s^2. The hint is to find the stretch distance and compare with 100 meters or 10,000cm.
My question is the stretch distance and elongation basically the same thing? If it is then I can use the coefficient k = 6500 g.s^2 of the previous problem.

 

[mathmike]

how long is the cord

 

[brayrbob]

The question doesn't say how long the cord is.I used the coefficient from the previous prpblem.