Bungee Survivor Question

flouran · 2009-05-29, 01:05

Hi,
So I have a final lab in my college physics class. And the lab procedure is as follows:

Quote:

Originally Posted by Procedure

Make or use a bungee cord by tying ten or eleven #19 latex rubber bands end-to-end. Attach the upper end high enough so that when 200 grams (0.2 kg) is hung from its lower end, it will almost touch the floor. Begin with a weight of about 0.2 N (0.0204082 kg) and measure the extension of the bungee cord as a function of the applied force up to a maximum extension of 1 to 12 meters. Also hang the Super Hero on the bungee cord and measure the resulting extension. The purpose is to predict, given a particular bungee cord, the minimum height above the floor necessary to ensure (or insure

) that the jumper comes within 5-10 centimeters (0.05 to 0.1 meters) of the floor.

Note: The measured mass of the Bungee jumper is 0.25837 kilograms (258.37 grams).
I have attached my data as a text file (I can't upload Excel files apparently):
AP Physics Post Lab.txt.
My question is, what formula does k follow (it is most definitely not linear)?
Thus, once I find k, it should hopefully be easy to compute this minimum height using energy considerations (please let me know if I am somehow wrong):
$U_i + K_i = U_f + K_f$ ,
Since the object is released from rest,
$mg(h_{min}-{L_0}) = mg(0.05)+0.5k(h_{min}-0.05-L_0)^2$ ,
where $h_{min}$ is the minimum height (the thing I need to calculate), m is the mass of the jumper = 0.25837 kg. $L_0$ is the initial length of the bungee which I measured to be 0.395 meters.

flouran · 2009-05-29, 01:11

I have also attached a graph of the empirical computation of k (y-axis) versus the attached mass in kilograms (x-axis). As you can see, k asymptotically approaches 4 N/m, but is non-linear. I estimate k to be around 7 N/m if the bungee jumper is attached.

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flouran · 2009-05-29, 20:46

Well, we did the experiment. And my computations were correct! Yay!

davieddy · 2009-05-30, 02:07

Rubber bands also exhibit considerable hysteresis:
the height attained after the initial descent is nowhere
near the starting point.

2009-05-29, 20:46	#3
flouran Dec 2008 7²×17 Posts	Well, we did the experiment. And my computations were correct! Yay! Last fiddled with by flouran on 2009-05-29 at 20:47 Reason: Grammar Error. I initially posted: "And I my computations were correct!" as opposed to "And my computations were correct!"

2009-05-30, 02:07	#4
davieddy "Lucan" Dec 2006 England 6474₁₀ Posts	Rubber bands also exhibit considerable hysteresis: the height attained after the initial descent is nowhere near the starting point. Last fiddled with by davieddy on 2009-05-30 at 02:08

2009-05-29, 01:11	#2
flouran Dec 2008 7²×17 Posts	I have also attached a graph of the empirical computation of k (y-axis) versus the attached mass in kilograms (x-axis). As you can see, k asymptotically approaches 4 N/m, but is non-linear. I estimate k to be around 7 N/m if the bungee jumper is attached.