The physics of Bungee Jumping 1

I was always taught that you can't push with a rope.
On construction sites, I have seen many times a suspended load with two taglines.
When the load has to be aligned by pulling on one of the taglines, that man on the other tagline tries to help by pushing on his rope.
This has never been successful.
Now you tell me that it is possible to push with a rope?
I'm too old for this. grin
ps; Joking aside, I may spend a lot of time trying to get my head around this.
Possibly a related effect, and possibly a way to aid in visualizing.
First investigate the physics of a vertical post, pivoted at the bottom end. Calculate the forces and acceleration as the post falls 180 degrees around the pivot.
Now take a series of fairly long members joined by pivots and let them fall similar to the chain, fastened at one end..
As each section completes its 180 degree arc its downward motion abruptly stops.
The next section of the chain of members has falling at the same speed when one end is abruptly halted.
The next section already has a lot of downward velocity and if one end is abruptly halted the inertia of the mass will act at the center of the section and the free end may be accelerated rapidly.
This will be in addition to acceleration due to gravity, The acceleration will be restrained by the free end still above, but as the free end becomes shorter, the effect and the velocity will increase.
If a link chain is used, the links will tend to bunch up and the action will not be the same.
The action of a roller chain may be closer to the action of a rope.

Did it once years ago, thought it was a blast.

TLDR:
Bungie cords stretch under their own weight.

MintJulep said:

Bungie cords stretch under their own weight.

Click to expand...

Another factor.
Thanks Mint.
Would that add to the acceleration?

(I will have to put old boring reruns on TV tonight and bore myself to sleep.
Else I will be awake all night trying to figure this out.

Nite all.

waross said:

Would that add to the acceleration?

Click to expand...

Sure,

As a near-analogy:
Consider a horizontal Bungie anchored to a mass at one end and you at the other.
Walk away from the mass to stretch the Bungie.
Take one more step - onto a skateboard.
As soon as you stop being able to resist the force in the Bungie, the Bungie accelerates you.

Taking that to the actual Bungie jumping case, stepping onto the skateboard = stepping off the platform.

Very interesting. Thanks for sharing.

ot sure if they actually covered it, but I guess as the jumper starts to descend, the bungee inflexion point is also moving faster than a rigid chain or rope as the suspended mass of the cors increases and hence the elongation of that section of the cord increase. Though is this not taken account of by the fact that the bit attached to the jumper is shortening??? hmmmm.

SO it looks like the extra mass of the bungee, plus some effects of the cord stretching under its own weight increase force on the jumper.

Interesting.

Never done one myself - too close to the ground for this ex skydiver....

The energy argument is rather neat, if an over estimate. L=length of bungee S is the distance the suicidal body has fallen, B is the mass of the bungee, M is the mass of the man . So initially the CG of the bungee is 1/4L below the platform.PE_S=0=g*(0*M-B*L/4) KE=0

When the bungee is just taut, and hence stationary

PE_S=L=g*(-L*M-B*L/2) KE=1/2*M*v^2=g*(-L*M-B*L/2)-g*(-B*L/4)=g*(-L*M-B*L/4)

which if we ignore the sign convention I've used to confuse myself is obviously bigger than just g*L*M if you forgot to clip onto the bungee (it has happened).

I love energy arguments, they cut through all the pesky details.

The energy argument is used incorrectly IMO.
Take an inextensible chain suspended at one end, as in the bungee, falling under its own weight. When the chain is fully down there is no kinetic energy in the system (except for some pendulum oscillations): this means that all the initial potential energy, temporarily transformed into kinetic, is completely consumed by internal friction in the chain.
This should mean that the cord does not add any actual energy to the mass of the jumper, so the acceleration can't be higher than g (which is BTW evident per se).
I would like to analyze this scenario with Lagrangian mechanics, but of course g is the maximum acceleration for a freely falling mass on earth's surface.

Looking forward to your explanation of MEASURED acceleration>1g

Greg, read their conclusions, and you'll see that they are (were) not positive on the demonstration of the calculated accelerations by the tests.

prex said:

When the chain is fully down there is no kinetic energy in the system (except for some pendulum oscillations): this means that all the initial potential energy, temporarily transformed into kinetic, is completely consumed by internal friction in the chain.

Click to expand...

prex said:

The energy argument is used incorrectly IMO.
Take an inextensible chain suspended at one end, as in the bungee, falling under its own weight. When the chain is fully down there is no kinetic energy in the system (except for some pendulum oscillations): this means that all the initial potential energy, temporarily transformed into kinetic, is completely consumed by internal friction in the chain.
This should mean that the cord does not add any actual energy to the mass of the jumper, so the acceleration can't be higher than g (which is BTW evident per se).
I would like to analyze this scenario with Lagrangian mechanics, but of course g is the maximum acceleration for a freely falling mass on earth's surface.

Click to expand...

The chain will bounce up and down and burn up energy with air resistance and friction. A bit of a different situation.

Look at it from another perspective.
If you want the jumper to experience an acceleration greather than g, then you need to exert a force on the jumper, additional with respect to its weight. This force can't be the weight of the cord, as this one is used to accelerate the cord itself.
This additional force could come from an initial stretch of the cord, but no such stretch exists.
So g is the maximum acceleration the jumper can experience, as long as the cord is not stretched.

prex said:

If you want the jumper to experience an acceleration greather than g, then you need to exert a force on the jumper,

Click to expand...

Like, "Push with a rope"?

Which is exactly why I like energy methods. As the cord drops to its original length, it has no KE, and therefore all the PE must go into the only moving object.

As to conclusions

Prex said:
"take an inextensible chain" - no. You are arguing an infinitely stiff chain, which is not a real thing. It would be like arguing a massless chain too, a physical unreality.

At the point the real chain (or bungee) "is fully down", it has stretched from its unloaded condition, this stretch absorbs the kinetic energy of the system and stores it as potential (spring) energy, just like a real bungee cord (assuming the jumper's ankles don't just snap off). Reread Greg's energy argument, he is looking at the point where the bungee has "just gone taut", i.e. has not begun to stretch. This is the point where kinetic energy is a maximum. Poke a hole in his argument, don't add massless and infinitely stiff things to distort reality and create your own.

"This additional force could come from an initial stretch of the cord, but no such stretch exists."

Yes, it does. The cord at the extreme low point of the loop might not have any stretch, but every inch of cord, on both sides above the bottom of the loop, "sees" the weight of cord suspended below it, which creates a linearly varying tension in the cord, equal to half the cord weight at the point of attachment to the bridge and another half the cord weight at the jumper's ankle. The spring force on the ankle side is slowly unloaded as the end of the cord (and the jumper) fall...

I'd think a structural engineer would think more clearly...except civil engineers are taught not to let things move...

This is wrong, but perhaps someone can make it right. For the jumper before jump and the instant they step off the platform.

It's a complicated problem.

I think this version is less wrong. At the instant the jumper steps off the system transitions from static to dynamic.

The bungie wants to contract. Forces resisting its contraction are: its own weight and the jumper's inertia.

In the next instant (that I haven't even tried to sketch) things get even more complicated as the part of the bungie connected to the platform starts to "reel in" the extended length of the bungie. I think this is the whip effect the paper is trying to describe.

btrue, I fully respect civil engineers, but I am not one of them.

And an inextensible chain is not that unreal, we engineers should be accustomed to the concepts of nearly..., substantially... etc. In our case an actual metallic chain would behave as inextensible, because the strain that it will undergo is negligible (though still present and energy consuming) with respect to the dimensions of the problem.
But even an elastic cord behaves in the same way: if you leave it fall without a jumper, all its energy will be consumed by the internal friction forces with a little (in engineering sense) elongation.
The same happens with a jumper at the end: part of the cord goes progressively to rest, as the fall progresses, and the kinetic energy that that portion had just before going to rest, is lost. Greg, a transfer of mechanical energy from one body to another requires that forces come into play. The weight of the cord that acts on the feet of the jumper decreases during the first phase of the fall, because part of the cord becomes suspended to the portion that is attached at the top. So which force will cause the transfer of energy from the cord to the jumper?

Is the chain in question a conventional linked chin or a roller chain?