Max Acceleration of a Bungee Jumper

In summary, the problem involves a bungee jumper of mass m kg jumping from 20 meters. The bungee cord's spring constant is k N/m and the point of maximum acceleration is y = -17. The question asks for the value of the maximum acceleration, which is not equal to gravity. The method to solve this problem involves using the equation a = (ky - mg)/m, with F = net force, k = spring constant, x = distance cord is stretched, m = mass of person, and g = 9.81 m/s^2. The correct distance used in the equation is 17m, not 37m.
  • #1
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Homework Statement



A bungee jumper of mass m kg jumps from 20 meters. The bungie cord's spring constant is k N/m. Let y = 0 be the point where the bungee cord begins to become taught, and let y = 20 be the jump point.

It is known that the point of maximum acceleration is y = -17.

Question: What is the value of the maximum acceleration?

Hint: The acceleration is not equal to gravity.

2. The attempt at a solution

F = ky - mg = ma
a = (ky - mg)/m [FAILS!]
 
Last edited:
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  • #2
Thanks, but that didn't work.
 
  • #3
The problem is a bit unclear about the altitudes used.
It says a jump from 20 m, but then they say that the cord only starts to become taught
at 20 m below the jump point, and the point of maximum acceleration (hence maximum length of the cord) is 17m below that. I hope the jump is from an altitude of at least 37m.

The method of you and anti-meson is correct. a = F/m = (kx - mg)/m, with
F = net force on person
k = spring constant = 100N/m
x = distance cord is stretched = 17m.
m = mass of person = 60 kg.
g = 9.81 m/s^2

only the distance should be 17m and not 37m

I don't see how you got 9.81, -9.81, 6, or -6 as none of them is the answer comes
from the equation with either 17 or 37 m.
 

Related to Max Acceleration of a Bungee Jumper

What is the maximum acceleration of a bungee jumper?

The maximum acceleration of a bungee jumper depends on various factors such as the length and elasticity of the bungee cord, the weight of the jumper, and the initial height from which they jump. Generally, the maximum acceleration can range from 2 to 5 g-forces.

How is the maximum acceleration of a bungee jumper calculated?

The maximum acceleration of a bungee jumper can be calculated using the formula a = (2L)/t^2, where a is the acceleration, L is the length of the bungee cord, and t is the time taken for the bungee cord to stretch and rebound.

What are the safety precautions taken to ensure the maximum acceleration of a bungee jumper is not exceeded?

Before a bungee jump, the length and elasticity of the bungee cord are carefully calculated to ensure that the maximum acceleration does not exceed a safe range. The equipment is also regularly inspected and tested to ensure its strength and durability. In addition, bungee jumping is only allowed under the supervision of trained professionals.

Can the maximum acceleration of a bungee jumper be controlled?

Yes, the maximum acceleration of a bungee jumper can be controlled by adjusting the length and elasticity of the bungee cord. A shorter and less elastic cord will result in a higher maximum acceleration, while a longer and more elastic cord will result in a lower maximum acceleration.

What are the potential risks associated with the maximum acceleration of a bungee jumper?

The potential risks of bungee jumping include neck and back injuries, whiplash, and loss of consciousness due to the sudden deceleration and rebound. However, these risks can be minimized by following proper safety measures and using high-quality equipment.

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