Simple Harmonic Motion - bungee jumping

In summary: In order to solve for that, you need to use the conservation of energy, where the potential energy at the top of the jump is equal to the potential energy at the bottom of the jump plus the elastic potential energy stored in the rope. This will give you the correct answer of 27.2 m. In summary, the problem of determining how far a bungee jumper falls before coming to rest cannot be solved by equating forces, as the goal is to find the distance when the velocity is zero, not the acceleration. Instead, the conservation of energy must be used to equate the potential energy at the top and bottom of the jump, plus the elastic potential energy stored in the rope. This yields the correct answer of 27
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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.
 
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  • #2
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.
 

1. What is simple harmonic motion in the context of bungee jumping?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a repeating pattern. In the context of bungee jumping, this refers to the motion of the bungee cord as it stretches and recoils, causing the jumper to oscillate up and down.

2. How does the length of the bungee cord affect the simple harmonic motion during a jump?

The length of the bungee cord affects the frequency and amplitude of the simple harmonic motion during a jump. A longer cord will result in a lower frequency and larger amplitude, while a shorter cord will result in a higher frequency and smaller amplitude.

3. What factors can affect the period of the simple harmonic motion in bungee jumping?

The mass of the jumper, the length and elasticity of the bungee cord, and the height of the jump can all affect the period of the simple harmonic motion in bungee jumping. These factors can also impact the safety and comfort of the jump.

4. How is the energy transferred between the jumper and the bungee cord during simple harmonic motion?

During the jump, the potential energy of the jumper is converted into kinetic energy as they fall, and then back into potential energy as the bungee cord stretches. This process continues, with the energy being transferred between the jumper and the bungee cord until the jumper comes to a stop.

5. Can the simple harmonic motion in bungee jumping be modeled mathematically?

Yes, the simple harmonic motion of bungee jumping can be modeled using mathematical equations such as Hooke's Law and the equation for simple harmonic motion. This allows for the prediction and analysis of the motion, as well as the design of safe and effective bungee jumping experiences.

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