Determining the Length of Bungee Cord Needed for an Egg Drop Experiment

[lccstuednt]

Homework Statement

Find how long of a cord needed to drop an egg from 14m to come within 5cm of the ground
We have determined a force deflection ratio for the cord given a .5m sample.

Homework Equations

what is x supposed to be here. Is it a number as I have or is it the mass or the height of the drop?

The Attempt at a Solution

if I plug this into the energy conservation equation I get a solution of x = .8440104689 I have no idea what this means if it is even what I am supposed to do at this point.

the PE for the cord is as follows, determined from integrating the force deflection equation.
25.04714286*x^7+122.3833333*x^6-206.5000000*x^5+123.8475000*x^4-37.43333333*x^3+7.890000000*x^2+.2133000000*x

4. Additional comments.
I am supposed to have a working model for class on Monday, but when I use the value for x I get an increasing length of cord for increasing mass, assuming the total mass of the egg and bag is going to be 70~100grams.

 

[berkeman]

Homework Statement

Find how long of a cord needed to drop an egg from 14m to come within 5cm of the ground
We have determined a force deflection ratio for the cord given a .5m sample.

Homework Equations

what is x supposed to be here. Is it a number as I have or is it the mass or the height of the drop?

The Attempt at a Solution

if I plug this into the energy conservation equation I get a solution of x = .8440104689 I have no idea what this means if it is even what I am supposed to do at this point.

the PE for the cord is as follows, determined from integrating the force deflection equation.
25.04714286*x^7+122.3833333*x^6-206.5000000*x^5+123.8475000*x^4-37.43333333*x^3+7.890000000*x^2+.2133000000*x

4. Additional comments.
I am supposed to have a working model for class on Monday, but when I use the value for x I get an increasing length of cord for increasing mass, assuming the total mass of the egg and bag is going to be 70~100grams.

To a first approximation, can you not treat the cord as a light lossles spring? Or is its mass to large for that approximation?

 

[lccstuednt]

I believe we are considering it a light loss-less spring because we have only been told to account for the mass of the egg and bag.

 

[berkeman]

I believe we are considering it a light loss-less spring because we have only been told to account for the mass of the egg and bag.

Okay, then why the long equation? You already alluded to using energy considerations... The egg has initial PE, and the spring has final stored energy at full extension...

 

[lccstuednt]

The long equation comes from our data on finding a force deflection curve for the sample cord. We then integrated that function to get the PE for it. But maybe I am confusing what you are saying with something else, this problem has me so twisted it's not even funny.

 

[berkeman]

The long equation comes from our data on finding a force deflection curve for the sample cord. We then integrated that function to get the PE for it. But maybe I am confusing what you are saying with something else, this problem has me so twisted it's not even funny.

So when you experimentally tried to fit F = kx to the bungee cord, it did not match, and you had to go to several higher powers of delta-x to get a reasonable match? Then the bungee cord is much more complicated than a massless spring I guess? (Certainly could be true. I would think that there is significant loss associated with the bungee cord, which is not part of a lossless, massless spring equation)

 

[lccstuednt]

Right the simplest equation we could fit was of degree 6 with R^2=.998 so that's the one we chose to work with and I am lost as to what x needs to be although it did just occur to me that it maybe should be the amount of stretch that is going to happen during the fall...

 

[berkeman]

Right the simplest equation we could fit was of degree 6 with R^2=.998 so that's the one we chose to work with and I am lost as to what x needs to be although it did just occur to me that it maybe should be the amount of stretch that is going to happen during the fall...

Well, unstretched length plus the stretch.

I'd start with the first order approximation, and see what that gives you. Then the 2nd order approximation, and so on. Hopefully you can develop some intuitive feel for the higher order terms, and what they mean in practical terms in terms of the stretch length.

 

[lccstuednt]

Right, thanks for your help. I apologize for any confusion I gave you.

 

[berkeman]

Right, thanks for your help. I apologize for any confusion I gave you.

No worries. I'd also look at the mass of the bungee cord, since it really isn't negligible compared to the payload. Putting it all together into one model will give you a more accurate estimate of the final stretched length.

Have fun with the lab project!