Spring constant and bungee jumping.

In summary, a 68kg bungee jumper standing on a 46m platform will have a speed of 13.3 m/s after falling 9m and the spring constant of 66N/m will factor in for calculating the speed after falling 31m. The position-time graph would be a parabola only if there is constant acceleration, which needs to be determined in this situation.
  • #1
anotherperson
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0

Homework Statement



68kg bungee jumper standing on a 46m platform above the ground. The bungee cord has no effect for 9m(ie natural cord length is 9m)

when the bungee jumper is more than 9m away the spring constant is k=66N/m

a)what is his speed after falling 9m from the platform?
b)what is his speed after falling 31m from the platform?
c) sketch the position-time graph.

Homework Equations





The Attempt at a Solution



a) vf^2=0^2 + (2x9.8x9)
=13.3 m/s

b) for b I'm not sure how to factor in the spring constant. and i don't know if i should factor it in from the start or after 9m, I am assuming after 9m. i think it relates to Usp=.5kx^2

c) for the graph it would just be a parabola right? no need to draw one for me.
 
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  • #2
anotherperson said:
b) for b I'm not sure how to factor in the spring constant. and i don't know if i should factor it in from the start or after 9m, I am assuming after 9m. i think it relates to Usp=.5kx^2
It does relate to the elastic energy. Energy is conserved, so that's a good way to start.

c) for the graph it would just be a parabola right? no need to draw one for me.
Only for constant acceleration. Is it in this situation? :wink:
 

What is the spring constant in the context of bungee jumping?

The spring constant, also known as the stiffness constant, is a measure of the elasticity of a spring. In the context of bungee jumping, it refers to the resistance of the bungee cord to stretching as the person jumps off a platform.

How is the spring constant related to the bungee cord's length and material?

The spring constant is directly related to the bungee cord's length and material. A longer and/or stiffer bungee cord will have a higher spring constant, meaning it will require more force to stretch it a certain distance.

What role does the spring constant play in determining the safe height for bungee jumping?

The spring constant is a crucial factor in determining the safe height for bungee jumping. It must be carefully calculated to ensure that the bungee cord will not stretch too much and cause the jumper to hit the ground. A higher spring constant will allow for a lower safe jumping height.

Can the spring constant be adjusted for different body weights of bungee jumpers?

Yes, the spring constant can be adjusted for different body weights of bungee jumpers. The bungee cord used for a heavier person will have a higher spring constant to maintain the same level of safety as a bungee cord used for a lighter person.

Is there a maximum spring constant that can be used for bungee jumping?

Yes, there is a maximum spring constant that can be used for bungee jumping. It is important to find a balance between safety and the thrill of the jump. A bungee cord with too high of a spring constant can be dangerous, while one with too low of a spring constant may not provide enough resistance for a satisfying jump.

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