Physics Problem: Bungy Jump Calculation for Maximum Acceleration | Matt (44kg)

[Tollehej]

Homework Statement

Matt(44kg) was going to do a bungy jump(spring constant=105N/m) that is 30m long when it's unstreched.The rope is attached to a platform 65m above the ground.What is the maximum acceleration closes to the ground.
Sorry for my bad english, i was trying to translate my homework from swedish to english.

Homework Equations

Don't know

The Attempt at a Solution

I'm using the conservation of engery rule thing.
Ep+Ek+Es=E2p+E2k+E2s
There is no kinetical energy or spring energy in the beginning, and no potential or kinetical energy in the end => Ep=E2s => mgh=1/2*k*x^2
and we don't know the total length => mg(h+x)=1/2*k*x^2
and then i solve x and i get that x= about 20m
so the total length when the string is attached is 20+30=50m
And then i can solve the force of the spring, F=k*x F=105N/m*50m F=5250N
And then i use ƩF=m*a => G-F=m*a => (G-F)/m=a
=> (44kg*9,81m/s^2-5250N)/44kg=-109,508 m/s^2
And this can't be true!
Any ideas?

 

[Tollehej]

Is this in the right section? I'm new here.

 

[PhanthomJay]

During the first 30 m, the cord is slack and has no potential energy at the beginning or end.. But the jumper is in free fall, so the jumper has Kinetic Energy at 30m. Use this 30 m drop as the starting point for your energy equation

 

[Tollehej]

Sorry but I don't understand why it would be so.. But later when i was trying to solve it i got an answer that is 37 m/s^2, when the person accelerates upward from the ground. I can send my equations later, if u can take a look at them?

 

[PhanthomJay]

Your answer looks about right, i thought you had made an incorrect assumption when your answer was so far off, but you initial equation looks OK if h =30, and then you made a typo using x =50 when you should have used x = 20. Looks like you've corrected that.

Note that the person does not accelerate upward from the ground. The jumper never reaches it, he comes to a halt at 50 m, or at about 15 m above ground, where his upward acceleration is highest.

 

[Tollehej]

Yupp, the problem was when i was going to solve the Force of the spring F=k*x
and then i took the total length of the spring when it was streched but i was suppose to only the length that was streched which is kinda obvious! But thank you for your help!

 

[stef6987]

use the 30m drop as your starting point, easiest option.