Solving Bungee Jump Problem with No Air Resistance or Damping

[dopey9]

a bungee jumper stnd on a bridge of 100m above the floor of a valley.
She is attached to a bungee rope of length 25m and has a mass of 60kg. and i have taken g to be 10

there's no: air resistance
damping in the bungee rope
and the weight of the bungee rope is negliable

i need to find the minimum required value for the spring constant k if she is to avoid hiting the valley floor

im using 1/2kx^2=mgh...but I am getting confused in what I am doing i don't know where to go next..i was wondering if i am doing it right n what i should do next ?...thankz

 

[Hootenanny]

im using 1/2kx^2=mgh...

Your on the right track, but what happens when the binjee jumper falls the first 25m? Will the rope be storing potential energy then? What is the maximum extension the rope can undergoe without the jumper hitting the floor?

 

[dopey9]

confused

Your on the right track, but what happens when the binjee jumper falls the first 25m? Will the rope be storing potential energy then? What is the maximum extension the rope can undergoe without the jumper hitting the floor?

sorry I am really confused?

 

[arildno]

Remember that for the first 25 meters of falling, the rope is SLACK and there is no tension in it.

 

[dopey9]

my calculation

this is what i did

mgh= 0.5*k*(h-l)^2

60*10*100=0.5*k*(100-25)^2

k= 21.3

this is what i did and got k as ...have i done it right because I am so confused

 

[arildno]

Okay, for clarity I'll take this step by step:
Consider the moment when the jumper has fallen $h=25$ meters.
Then, obviously, the kinetic energy gain equals the loss of potential energy:
$$\frac{1}{2}mv_{0}^{2}=mgh$$

We now look at conservation of mechanical energy during the phase where the rope stretches, and where L is the maximal length the rope stretches:
$$\frac{1}{2}mv_{0}^{2}=\frac{1}{2}kL^{2}-mgL$$
which can be rewritten as
$$mg(h+L)=\frac{1}{2}kL^{2}$$
with h=25, L=75, you get your own equation, so yes, you did the problem right!

 

[dopey9]

thankz

Okay, for clarity I'll take this step by step:
Consider the moment when the jumper has fallen $h=25$ meters.
Then, obviously, the kinetic energy gain equals the loss of potential energy:
$$\frac{1}{2}mv_{0}^{2}=mgh$$

We now look at conservation of mechanical energy during the phase where the rope stretches, and where L is the maximal length the rope stretches:
$$\frac{1}{2}mv_{0}^{2}=\frac{1}{2}kL^{2}-mgL$$
which can be rewritten as
$$mg(h+L)=\frac{1}{2}kL^{2}$$
with h=25, L=75, you get your own equation, so yes, you did the problem right!

Thankz .