# Bungee Jumper Physics Lab Question

## Homework Statement

Hi,
So I have a final lab in my college physics class. And the lab procedure is as follows:
Procedure said:
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 :razz:) 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 an Excel file:
View attachment AP Physics Post Lab.xls.
My question is, what formula does k follow (it is most definitely not linear)?

## Homework 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.

## 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.

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