Simple Harmonic Motion - bungee jumping

AI Thread Summary
The discussion focuses on a bungee jumping problem involving a 50 kg woman attached to a spring-like elastic rope. The key equations for solving the problem involve the balance of forces and energy conservation, specifically relating gravitational force to elastic force. A common misconception is equating forces to find when acceleration is zero, rather than determining when the jumper's velocity becomes zero at the lowest point of the fall. The correct approach involves using energy conservation to find the maximum stretch of the rope, which leads to a solution of 27.2 m below the bridge. Understanding the distinction between zero acceleration and zero velocity is crucial for solving this type of problem.
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Homework Statement


A woman bungee-jumper of mass 50 kg is attached to an elastic rope of natural length 15 m. The rope behaves like a spring of spring constant k = 220 N/m. The other end of the spring is attached to a high bridge. The woman jumps from the bridge.

a) Determine how far below the bridge she falls, before she instantaneously comes to rest.

Homework Equations


Fe = -kx, Fg= m*g... Fg=Fe, -kx=m*g
OR
1/2kx^2=mgh

The Attempt at a Solution


Okay, so this is a question that appears in the Tsokos book and although I am aware of the solution and how to acquire it (through the use of the conservation of energy; equating the potential energy and elastic energy) by using the formula above, I would like to know why the task cannot be solved through the conventional equating of forces. Since the woman is in free fall, the only other force that could cause her to stop is the restoring force of elastic rope, hence the formula above: Fg=Fe. Through using this formula, however I have gotten that x=17.2 m and the answer seems to be 27.2 m and I do not know why I cannot solve it through equations of force.

Please, help.

Thanks.
 
Physics news on Phys.org
By equating the weight of the bungee jumper with the restoring force, you are creating the condition that the acceleration is zero.

In this problem you are not interested in when the acceleration is zero, you are interested in when the velocity is zero.
 

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