How to calculate the distance that a bungee will extend....

[Siddhartha]

Hi. So let me put the situation in context. At school we are doing a lab where there is a bungee and a barbie connected to the bungee. We will drop the barbie from a height of 4.94 meters and need to make it reach a point that is 5 cm off the ground give or take 5 cm. The bungee will not extend the entire 4.94 meters. Non-stretchy string is provided that will provide the extra needed distance. So, how can one do this?

So far I have tried this, but my teacher says it is wrong. I do not understand why. I said the mgh is equal to the energy at the top of the 4.94 meters. It was around 6.5 J. Then I took the height of the classroom and then found a mass that would essentially simulate the same extension. My teacher says this is wrong. Can someone please explain why. I then dropped thee barbie with that mass and then found the length of the bungee and then found the length of the non stretchy string.

Also, my teacher made the note that the bungee is not exactly a spring. The k value is not constant and the graph of elongation vs mass is not linear.

Thanks!

 

[mfb]

Then I took the height of the classroom and then found a mass that would essentially simulate the same extension.

What exactly did you do?

The barbie will fall down without getting slowed down initially - to stop it before it reaches the ground, you'll need a force stronger than its gravitational force. This extends the bungee cord more than an equivalent mass just hanging statically.