Question

An audacious physics student weighing 130 pounds attaches herself to the free end of a securely anchored bungee cord that is 110 feet long when un-stretched, and has a force constant of k = 540 Newtons/meter. Then she jumps from a bridge 150 feet above the floor of a canyon. Will she make it? What are the important safety considerations? Show your reasoning.

Answer 1

The free body diagram is:

And the sum of forces when the string is stretched is: sigma F = F_R - W = 0 F_R = W - kx = mg x = mg/k x = (58.97kg)(9.8m /s^2)/540N/m x = 1.07 m = 32.61 ft this is the length that the string stretched. Now, we sum this with the length of the string unstreched if it passes the value of the fall: L = 110 ft + 32.61 ft L = 142.61 ft Answer: she makes it by a little. The important thing to see here is that the string is almost the length of the fall, and to do this is important to know how is the maximum stretching to avoid accidents

And the sum of forces when the string is streched is:

$\sum F = F_{R} - W = 0$

$x = \frac{mg}{k}$

$x = \frac{(58.97kg)(9.8m/s^{2})}{540N/m}$

This is the length that the string streched. Now, we sum this with the length of the string unstreched to see if it passes the value of the fall:

ANSWER: she makes it by a little. The important thing to see here is that the string is almost the length of the fall, and to do this it is important to know how is the maximum streching to avoid accidents.

I hope it helps!!