# Bungee Jumper Physics Lab Question

1. May 28, 2009

### flouran

1. The problem statement, all variables and given/known data
Hi,
So I have a final lab in my college physics class. And the lab procedure is as follows:
Note: The measured mass of the Bungee jumper is 0.25837 kilograms (258.37 grams).
I have attached my data as an Excel file:
View attachment AP Physics Post Lab.xls .
My question is, what formula does k follow (it is most definitely not linear)?

2. Relevant equations
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.

3. The attempt at a solution
In the attached Excel file I included 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.

Last edited: May 28, 2009
2. Jun 8, 2009

### nvn

flouran: I don't think I would bother with computing k, for the main calculations, although k is informative (for information only).

Your empirical data, although extremely coarse, suggests that a better regression would be P(x) = 17.24*x/(1 + 4.786*x - 1.886*x^2), where P(x) = applied force (N) as a function of x, and x = deflection (m). Thus, U11 + K1 = U12 + K2 + U22, where U1 = potential energy, and U2 = strain energy. Therefore,

m*g*h1 + 0 = m*g*h3 + 0 + integral[P(x)*dx],

where h1 = jumper initial height above ground, h3 = jumper final height above ground, and the integral is integrated from 0 to h2 - h3, where h2 = height of unstretched bungee cord lower end above ground (the unknown). Unless you can find an analytic solution to the above integral, which I did not attempt, you could solve the problem numerically, by trial and error, if you wish.