Bungee jump height/spring energy

[Matt123456789]

Homework Statement

Imagine that you have been given the job of desiging a new bungee jumping platform. Customers of mass 53.0 kg will step off a platform, attached to a rope of unstretched length 52.6 m and spring constant 17.0 n/m.

How far below the platform will the end of end of the rope get during a jump? This is the lowest point it will ever reach, not where it settles down.

You may assume that g=9.8 m s-2.

Homework Equations

PE=mgh
KE=0.5mv^2
Spring energy=0.5kd^2

The Attempt at a Solution

- Set the distance from platform to when rope first goes taut as H, distance from H to to lowest point as L
- rearranged equations to get mgh=0.5kL^2-mgL
- also tried mgh=0.5kd^2 and solve for d
- got 90.6 and 91.5, both wrong, no idea what to do now

 

[Suraj M]

mgh=0.5kL^2-mgL

I think you're on the right track.
What is answer that is given, which makes you think you're answer is wrong?

 

[ehild]

The Attempt at a Solution

- Set the distance from platform to when rope first goes taut as H, distance from H to to lowest point as L
- rearranged equations to get mgh=0.5kL^2-mgL

You explained the meaning of H and L, but what are h and d?

 

[Matt123456789]

The answer i submit is checked and I am told if I am wrong or right, but not what the actual answer is.

h is the total height, and d i think is meant to be L

 

[ehild]

The answer i submit is checked and I am told if I am wrong or right, but not what the actual answer is.

h is the total height, and d i think is meant to be L

In this case, your first equation is wrong, and there are too many unknowns in the second equation.

If you count the potential energy zero at the height of the platform, what is the PE at the deepest position, at depth h? How much is the rope stretched then? What is the elastic energy? What is the speed?

 

[Suraj M]

h is the total height,

Do you mean the length of the rope?
If so I don't see why your 1st equation could be wrong.

 

[ehild]

Do you mean the length of the rope?
If so I don't see why your 1st equation could be wrong.

The OP said that h was the total (stretched ) length of the rope, that is, h=H+L:. The equation

mgh=0.5kL^2-mgL

is wrong.

 

[Suraj M]

The OP said that h was the total (stretched ) length of the rope

oh! I thought he said it was the length of the rope,thats why i put the condition

Do you mean the length of the rope?
If so ...

I misunderstood, sorry