Find the Function of a Bungee Cord for Egg Drop

[larso5]

Homework Statement

For my Calc based Physics class we will be given an egg, a required height and a bungee cord (non-linear). We're to have already come up with a formula for this bungee cord to compute the required length so that we'll be able to drop the egg from the height and come as close to the ground as possible without the egg breaking.

The problem is that Hooke's Law does not apply since the bungee cord is a non-linear spring. I assume we'll have to expirement to find the function of the bungee cord.

We attempted this by running the cord horizontally on a track with a frictionless cart attached, and used a force-meter and motion detector to measure force versus position. Using a computer program we then attempted to plot the graph and find the equation. However the one we got was incorrect. We had a quintic equation, and I'm not sure that this is the right power...

Any help would be appreciated.

 

[nvn]

Perhaps try thread https://www.physicsforums.com/showthread.php?t=316822". I don't know if it will help; but maybe it will give you a few ideas. Maybe it will help a little.

 

[larso5]

That did help a little.

I was mostly looking for an experimental way to find the function f(x) that would describe the elasticity of the cord. Like the one you got for "P(x)" in that thread.

Like I said we had a cart on a horizontal track, with a bungee cord connected to it and to force meter. At the opposite end of the track was a motion detector (to read position). We pulled the cart along the track measuring the force applied and used the motion detector to measure the distance we pulled. We then graphed Force vs. Position and got a curve. This was a quintic curve. However, after integrating the function and doing the algebra involved in U_i + K_i = U_f + K_f + W_bungee (integral of f(x)) to find a velocity. The solution we arrived at was different from that which we got after running an experiment of pulling back a certain distance to find a certain velocity.

I know that might be confusing, but I don't have the exact data on me... If you can help any more I'd appreciate. I really think that if we knew how to find the function f(x) for the elasticity of the bungee we'd be all set, but I'm not sure how to do that...

Again, thank you!

 

[nvn]

larso5: Somehow, somewhere along the way, it appears someone did something wrong. With no data and no work shown, we don't know who did what wrong. However, keep trying. If you do the regression correctly, and work the problem correctly, as explained in my post in the thread I cited above, and perform the integral as explained therein, it works fine. And the integral, regardless of how complicated, is easy to solve numerically. Show your work, and then someone might check your math.