# Bungee jumping

1. Aug 18, 2009

### glugger

we've been studying te physics involved in bungee jumping. We went to a bungee site, and recorded data, such as length of rope, weight of jumper, distance to fall, etc.

With the data we collected, I've been able to determine spring constant, equilibrium point, force exerted etc.

But I've been having trouble to work out the height the jumper will bounce back up to after reaching the lowest point.

Here's an example:
k= 50 N/m
x= 50 m (this includes the length of cord)
length of cord= 10m

so f=k(x-L)
=50 x 40
= 2000 N

and that his elastic potential energy at the bottom = E grav potential at top
m= 80kg

mgx=.5k(x-L)^2
Eep=40000 J

But using this how do i find the height the jumper will bounce to? I'm pretty sure he wouldn't reach the same height he fell from, due to gravity.

Last edited: Aug 18, 2009
2. Aug 18, 2009

### mgb_phys

Assuming they stop at the bottom of the bungee then they have no kinetic energy, so all the spring energy goes into the potential energy they have at the top of the bounce.
so 1/2 k x^2 = m g h
where x is the spring extention and h is the height (above the lowest point)

3. Aug 18, 2009

### glugger

1/2 k x^2 = m g h

h= 40000/ 800
= 50m

and this would not be correct.

Last edited: Aug 18, 2009
4. Aug 18, 2009

### Staff: Mentor

Not affected by gravity. Affected by losses to air resistance and losses into the rope (it's a lossy spring)

5. Aug 18, 2009

### glugger

so without these losses, the rope would be in constant motion, and never stop?

6. Aug 18, 2009

### Staff: Mentor

Not exactly. Without losses, the system is basically a mass on a spring. The mass oscillates up and down, and the spring goes with it.

http://en.wikipedia.org/wiki/Simple_harmonic_motion

.

7. Aug 18, 2009

### glugger

yes, but it would never stop without these losses?

8. Aug 18, 2009

### rcgldr

9. Aug 18, 2009

### Phrak

I'm sure Berkeman didn't understand what you were driving at or some subtle point. Anyway, without energy loss in the cord or through air friction, you would oscillate forever, or if you wish, return to your starting point at take-off, with everthing else being ideal.

Last edited: Aug 18, 2009
10. Aug 18, 2009

### Q_Goest

Yes... If there are no losses (no energy converted to heat) then the bungee jumper just keeps bouncing forever.

I think I'd vomit...

11. Aug 19, 2009

### glugger

ok thank you. that solved the problem....sorta.