Bungee Jumping.

A bungee jumper jumps from a tall bridge attached to a light elastic cord (bungee cord) of unstretched
length L. The cord first straightens and then extends as the jumper falls. This prevents
her from hitting the water! Suppose that the bungee cord behaves like a spring with spring constant
k = 100 N/m. The bridge is h = 100 m high and the jumper’s mass is m = 50 kg.
a) What is the maximum allowed length L of the unstretched bungee cord to keep the jumper
alive? (Assume that the spring constant doesn’t depend on L).
b) Before jumping, our jumper verified the spring constant of the cord. She low

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a) To find the maximum length of the unstretched bungee cord, we need to consider the forces acting on the jumper as they fall. At the maximum allowed length, the spring force from the bungee cord should be able to counterbalance the gravitational force pulling down on the jumper.

The gravitational force acting on the jumper is given by the equation F_gravity = m * g, where m is the mass of the jumper (50 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).

The spring force acting on the jumper is given by the equation F_spring = k * x, where k is the spring constant (100 N/m) and x is the extension of the bungee cord.

At the maximum allowed length, the spring force should be equal to the gravitational force. Therefore, we can set up the equation F_spring = F_gravity:

k * x = m * g

We can rearrange the equation to solve for x:

x = (m * g) / k

Plugging in the given values, we get:

x = (50 kg * 9.8 m/s^2) / 100 N/m

Simplifying the equation, we find:

x = 4.9 m

Therefore, the maximum allowed length L of the unstretched bungee cord to keep the jumper alive is 4.9 meters.

b) The spring constant is determined by the characteristics of the bungee cord. In this case, the spring constant is given as k = 100 N/m, which means that for each meter of extension, the bungee cord will generate a spring force of 100 N.

To verify the spring constant, the jumper can conduct experiments by attaching different weights to the bungee cord and measuring the extension. By measuring the extension and the corresponding force applied, she can calculate the spring constant.

The experiment can be done by attaching a known weight to the bungee cord and measuring the extension of the cord. This step can be repeated with different weights to create a set of data. By plotting a graph of force applied versus extension, the slope of the graph will give the spring constant. The jumper can then compare this experimental value with the given value of k = 100 N/m to verify if they are consistent.