# Cutting the cord

Gold Member
Had an interesting concept in physics class today. What would happen to a bungee jumper if right at the apex of his jump (when the resultant forces are zero) someone cut the cord? Would he go splat or just hit the ground without too much damage?

For ease, lets say that at the apex he is a metre away from the ground.

I would think that the rope itself would snap back like if you stretched an elastic band then let go of one end, but I cant picture what would happen to the dude at the end.

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Doc Al
Mentor
After you cut the cord, the only force acting will be gravity. His initial speed is zero.

He will hit the ground exactly as if he had just jumped from a height of one meter. No big deal.

arildno
Homework Helper
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Dearly Missed
Apart from getting whipped by a furious piece of cord, the only effect should be that gravity is now the sole force acting upon the dude.

Gold Member

If you were standing on a piano which was dropped from a great height, and just before it hit the ground you jumped off, what would happen?

I have the opinion that you would still go splat. Am I right?

arildno
Homework Helper
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Dearly Missed
People wouldn't be able to hear your SPLAT above the CLOING of the piano

Integral
Staff Emeritus
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It is not clear how you would stand on the piano, both you and the piano are free falling, which means "weightless". You hit the ground just as hard with or with out the jump. Perhaps a split second later. Jumping does not help.

Gokul43201
Staff Emeritus
Gold Member
Integral said:
It is not clear how you would stand on the piano, both you and the piano are free falling, which means "weightless". You hit the ground just as hard with or with out the jump. Perhaps a split second later. Jumping does not help.
I disagree ! If you can exert a downward force on the piano, you will reduce your downward vertical velocity (and increase the piano's). In theory, if you can exert a large enough force, you could even make your velocity (in the ground frame) change directions. There is nothing stopping you, save the strength of the muscles in your legs. If you are capable of vertical leaps of the same height as that from which you (and the piano) fall, then you can make your landing velocity very small. It's because most people can jump only 2 feet or so upwards that this won't work for "most people".

Only the CoM velocity needs to increase at a rate of g...not each individual velocity. If a falling bomb explodes just before it hits the ground, does not shrapnell fly upwards ?

Doc Al
Mentor
jump!

Gokul43201 said:
If you can exert a downward force on the piano, you will reduce your downward vertical velocity (and increase the piano's).
I agree with that. Jump!

krab
Gokul43201 said:
In theory, if you can exert a large enough force, you could even make your velocity (in the ground frame) change directions. There is nothing stopping you, save the strength of the muscles in your legs. If you are capable of vertical leaps of the same height as that from which you (and the piano) fall, then you can make your landing velocity very small.
But if you are capable of such vertical leaps, then (running the film backwards) you can survive a fall from that height, and the presence of the piano is immaterial. So I agree with Integral. Jumping is of no benefit compared with just using the same muscles to absorb the impact.

Integral
Staff Emeritus
Gold Member
GADS! here we go again! It is still not clear to me how you manage to remain upright on a falling piano, which may will decide some where along the line that orientation you dropped it in, is not the most stable. So the question should be "would it be POSSIBLE to stand on a falling piano, or freight train, or whatever.

Tell you what, anyone who wishes to do an experiment, have at it. Let us know the results....Myself? I'll take the stairs. ...Then submit the Darwin award nomination.

Well, I suppose you could affix the piano to vertical rails and that should at least cover the orientation of the piano. Assuming that you did drop as though you would normally have it sit in a room (large, flat surface available, hopefully with the top closed), would it be safe to assume that the piano encounters more air resistance than you, enable you to remain in some sort of contact with the piano?

Those ideas being tossed around, if this is any reasonable height, say, from the top of a two story house, even with air resistance your speed should be appreciable enough for you to want to have a spare jetpack when you realize there's a reason you don't play for the NBA.

I'll follow Integral down the stairs. I'd take the elevator, but the cable might snap.

Doc Al
Mentor
krab said:
But if you are capable of such vertical leaps, then (running the film backwards) you can survive a fall from that height, and the presence of the piano is immaterial. So I agree with Integral. Jumping is of no benefit compared with just using the same muscles to absorb the impact.
While I'm not crazy about Gokul43201's example wherein one is falling a distance one could leap, I don't see why you wouldn't benefit from jumping. If I find myself in the highly improbable situation of being crouched atop a falling piano, I have a choice:
(a) Crash into the ground at full speed
(b) expend some energy to reduce my speed (by pushing off the piano), then crash into the ground at a slightly lesser speed.

Although I'm sure I'll regret the experience either way, option b seems preferable. Yes, you are using muscles (and bones and ligaments) to aborb the energy either way, but two smaller steps must be better than one big one.

Am I missing something?

krab
Doc Al said:
Am I missing something?
I look at it from an energy point of view. Ideally, you would like to absorb all the energy with the large leg muscles. You can do it in 2 steps, or in 1, but I just don't think it's any more likely either way.

Additionally, think about crouching on the piano (OK, Integral, hold yourself down with handles or something), and miss-timing the jump. You could hit the ground with legs entirely in the squatting postion, and your biggest muscles could absorb none of the impact. IOW, SPLAT.

Now think of the scenario where you've just used all the stored energy-absorbing capability in jumping and a split-second later, ask the same muscles to absorb impact. Is this enough time for the muscles to recover? I doubt it.

Now imagine your legs are strong enough to jump straight up to the height from which you fell. There is in fact no difference between jumping just before impact on one hand, and keeping your legs slightly bent and ready to absorb the impact when it occurs on the other hand. (That's the point of my previous post.)

Integral said:
GADS! here we go again! It is still not clear to me how you manage to remain upright on a falling piano, ...
How about if you were inside a falling elevator? That'd take care of the orientation issues.

In that case, yes, you should jump. but be careful. If you're strong enough to jump that powerfully, though you won't go splat against the floor, you'll bump your head on the cieling and go splat there anyway.

I tried this experiment result was many broken bones

Gza
I would think the internal force pair of piano->person, person->piano would cancel by NTL, therefore having no real effect whether you jumped or not meaning the acceleration of the piano-person system would simply be g.

Gokul43201
Staff Emeritus
Gold Member
Gza said:
I would think the internal force pair of piano->person, person->piano would cancel by NTL, therefore having no real effect whether you jumped or not meaning the acceleration of the piano-person system would simply be g.
This only means that the acceleration of the piano-person system's center of mass would remain g. However, each of the individual components of the system need not have that same acceleration. And if there are unbalanced internal forces, they won't.

Again, see example of bomb.

would not the limitation on the fall rate of the piano be the friction of the air - that prevents it from going faster.

Still it would do the 32 feet per second per second thing until it reaches this limitation.

As you jump the only resistance you would have to overcome ((as you strive for action = reaction) is that of the impeding air.

If that is all that can save you .... can you spell S P L A T ? :yuck:

DaveC426913
Gold Member
would not the limitation on the fall rate of the piano be the friction of the air - that prevents it from going faster.

Still it would do the 32 feet per second per second thing until it reaches this limitation.

As you jump the only resistance you would have to overcome ((as you strive for action = reaction) is that of the impeding air.
We're not talking about jumping away from the piano and falling beside it. We're talking about whether reducing your downward velocity by jumping straight up at the last moment will reduce your impact force.

The answer is that, while technically, you will reduce your impact force slightly (your jump is not very high), it is a distinction without a difference. In reality you are much better to forget the jumping and instead simply use that strength in your legs to absorb the full impact.

We're talking about whether reducing your downward velocity by jumping straight up at the last moment will reduce your impact force.
Yo Dave:

So was I .... I took it that he was standing on the top of the instrument as it fell - and, as in a cartoon, jumped up a second before it impacted. Did not Galilao point out that, given no resistance (as in from the air) everything falls at the same rate - so he would be about standing on the piano, but travelling at the same speed.

If he tried to jump up - the only resistance on the piano would be that supplied by the air, which as you point out, is minimal. So ... his guts and the paino innards would be intimately mixed. :yuck:

jtbell
Mentor
Just out of curiosity, what were you searching for that led you to this five and a half year old thread?

DaveC426913
Gold Member
... he would be about standing on the piano, but travelling at the same speed.
The point of the thread is that, the velocity of his jump away from the piano would reduce his overall velocity, meaning he'll hit the ground at a slightly lower velocity than the piano will.

I'll throw some arbitrary numbers into it (I'll use velocities, though accurately, they're accelerations):

The piano and man reach 80mph during their fall.
At the last moment, the man jumps up off the piano the air with a velocity (relative to the piano) of 10mph. His impact velocity is now only 70mph.

rcgldr
Homework Helper
What would happen to a bungee jumper if right at the apex of his jump (when the resultant forces are zero)
The resultant forces aren't zero. At the bottom apex, the jumper experiences maximum upwards acceleration. The velocity is zero at the apex though.

Just out of curiosity, what were you searching for that led you to this five and a half year old thread?
If that is directed toward me ... no I did not get caught in a GR times dilation .... I was on my computer at work and did not have my spectacles with me ... so did not notice the date.

It was (is) sort of a whimsical question and I am about as whimsical as you can get.