Cable that holds the elevator got disconnected

[Integral]

A key point here is that when falling at a velocity V, your body had kinetic energy mV²/2 it does not matter whether this energy is dissipated by jumping or stopping the effects on your body will be the same.

 

[Janus]

One thing that seems to be missed with all this super-human legs business. Your body would still have to absorb the forces involved in coming to a stop. It would just be spread out over the distance over how much you can bend your legs.

For instance, assuming you are trying to cancel out a falling speed of 60mph (88 ft/sec) and you maximum leg flex is 2 ft (from crouch to extended), the rest of your body would have to be able to withstand 60g. (forget about what happens later, the jumping itself would kill you.)

To survive, you would need a combination of enough leg strength and g force resistance. But if you had these, then you don't need to jump in the first place. You can just allow yourself to go from standing up to a crouch as you hit and let your legs absorb enough of the deceleration(like a shock absorber) to let you come out unharmed.

 

[outandbeyond2004]

A post considered jumping hard enough to cancel the downward speed. That is not possible if my equations in a prior post are correct. Substitute zero for v_P and solve for v_B. The result is the same as the downward speed just prior to the jump. This is possible only if the mass of the person is zero.

You can survive any value of personal KE as long as you have time to dissipate it. However, a jump certainly does not give you much time, and if you have to jump to dissipate mucho KE, that would HAVE to be a very, very brief jump. It is said that people can survive 20 Gs, but I rather doubt even Olympic-class athletes can match that by jumping. Barry Sanders, the football carrier -- nah.

So I agree that jumping will do little good, and maybe it would be better to get to the top of the elevator, if at all possible, in the hope that the elevator can cushion the impact well enough.

A racecar driver survived a 170mph crash, because the "cell" he was inside absorbed enough energy slowly enough to let him survive.

 

[UltraPi1]

Integral is fully correct. Even if you could jump, and even if there were no ceiling in the way, you would go up, and eventually land with the same velocity the elevator landed. All you could do is delay the impact slightly. You can't beat the conservation of energy.

Wrong also. When you jump - You are just transferring that potential energy from you to the elevator through the use of another energy source, and that would come from those superhuman legs.

 

[Integral]

Wrong also. When you jump - You are just transferring that potential energy from you to the elevator.

What potential energy? Potential energy is not a problem,the problem is kinetic energy.
Can you explain the difference between the elevator suddenly stopping and you jumping? If you change your velocity from -V to 0 the change in velocity is the same, Remember the old saying "Its not the fall that hurts, its the sudden stop at the end". It does not matter what causes the sudden stop the forces experienced by your body will be identical in either case.

You need to read some of the other posts.

 

[UltraPi1]

One thing that seems to be missed with all this super-human legs business. Your body would still have to absorb the forces involved in coming to a stop. It would just be spread out over the distance over how much you can bend your legs.

Not missed - Just not mentioned. Make no mistake about it. This is a job for a superhuman. But you seem to at least understand the process of being able to slow your descent to zero by taking the hit before ground zero. Some here do not.

 

[UltraPi1]

Can you explain the difference between the elevator suddenly stopping and you jumping? If you change your velocity from -V to 0 the change in velocity is the same, Remember the old saying "Its not the fall that hurts, its the sudden stop at the end". It does not matter what causes the sudden stop the forces experienced by your body will be identical in either case.

You seem to be evading the original disagreement from the content of your last few post. I'll take that as a ... yes .. I was wrong, and accept that you just don't want to say so. At any rate I'm done here.

 

[Integral]

slow your descent to zero. Some here do not.

How do you SLOW you decent. You have only mentioned how to change it SUDDENLY, it is the sudden part that causes problems.

 

[Michael D. Sewell]

Originally posted by Integral
By my estimates "dangerously fast" will be anything from about 10m/s up. 10m/s sec is equivalent to a free fall drop of 5m (This is a survivable drop...

Integral,
This is a very good estimate. You are even being a little generous. In skydiving we consider 3m/sec to be a safe rate of descent for landing; higher speeds are OK with proper technique if the jumper is in excellent physical condition.

In construction, falling two stories is considered to be survivable. Falls involving distances greater than that rapidly decrease your chances for survival. This is a well documented fact. -Mike

 

[Integral]

Michel,

Thanks for the infromation. I spent a bit of time searching for real data with no luck, finally just aked myself how far would I want to jump. In my youth I did a fair amount of jumping off rocks into water, I know that anything over about 5m takes courage (or lack of brains!).

I find it interesting that your safe landing speed is very close to the landing (and launch) velocity of a good jump.

 

[Michael D. Sewell]

You mentors take a lot of abuse, a big thank you to all of you for your contribution to the physics forums. -Mike

 

[outandbeyond2004]

Originally posted by Michael D. Sewell
You mentors take a lot of abuse, a big thank you to all of you for your contribution to the physics forums. -Mike

Amen!

 

[Cliff_J]

Agreed with above. Its more a question of if you restrict the elevators speed to a human attainible number OR if you're willing to consider a world where humans could be 2-3 orders of magnitude stronger to 'push off the elevator floor' (jump) hard enough to create a velocity with an opposite vetor component and the soft tissue could handle the loads as well). I thought it was humorous to joke about it, maybe not.

What if we change this to a problem of solving how much potential energy we need to store in a spring along with the timing and duration of energy release to push a 30Kg weight off the floor of our falling elevator that weighs 2 metric tons. While this would not be a trivial integration to solve, it seems like an equivalent problem that doesn't fall prey to human strength limitations, correct?

Cliff

 

[Gara]

im confused. are some of you saying that if i am on a surface which is falling at 60 mph, and i jump up so i am now falling at 0 mph in relation to the ground outside, i would still land at 60 mph?

even if the ground is 5 feet below me? how am i going to accelorat in a free fall to 60 mph with in the distance of 5 feet?

 

[Integral]

No we are saying that if you were falling at 60mph and jumped so your speed was 0 your body would be every bit as crushed as if you had let the ground stop you.
edit:
Forgot a bit.


Now let us suppose that the elevator is falling at a constant velocity.(I am going back to metric, just because.) Also I am going to totally neglect any superhuman feats, So the elevator is falling at a dangerously fast constant velocity, say 20m/s. If at some random time during the fall you jump up wards with an initial velocity of 2m/s your equation of motion wrt to the elevator will be given by y= 2t- gt²/2. You velocity will be given by v= 2-gt. The max height of the jump will occur when the velocity is 0 or at t= 2/g (let g=10 for easy numbers) so t~.2s. Now at the peak of your jump your velocity wrt elevator =0 at that point you begin to fall back to the floor of the elevator your velocity is still described by v=2-gt but now we have gt>2 so your velocity is negative. That is you are moving down.

Now let us superimpose the motion of the elevator on the motion of the jump. This is what an outside observer would see.

V_elevator + V_you = -20 + 2 -gt = -18-gt.

The first thing to notice that there is no value of t for which this is a positive number, so you are ALWAYS falling. For the time period (0,.2) your velocity will be less then 20m/s, at t=.2 your velocity will BE 20m/s (remember we have 0 velocity wrt to the elevator) for t > .2s you velocity will be GREATER then 20m/s as you will be accelerating in free fall motion until you reach the floor of the elevator. This would occur at t=.4s, at that time your velocity will be 22m/s.

OK, so there it is, during the period (0,.2s) you have succeeded in reducing your velocity wrt to the ground. Now, consider that you MUST be in the air when the collision occurs, the further into that initial .2s you are the faster you are falling, consider the condition of your legs at the instant you jump, they are fully extended, knees straight and perhaps locked, this looks like the way to MAXIMIZE injury, especially since you are still falling and will impact the ground before completion of the jump.


I still maintain that jumping will do no good.

 

[outandbeyond2004]

Gara, to amplify Integral's reply a bit:

If you could jump SLOWLY enough and yet attain zero velocity (something that my equations show is possible only for a person with zero mass) then ultimately you will go far above the ground. Then there is nothing left to do but a Wiley Coyote and no elevator to jump off. But nobody can jump slowly, no leg is long enough. And, if you can jump fast enough, your leg bones will tear into small bits, to say the least. Maybe death will be by internal bleeding in the thigh. Actually that is not all. Forces induced by such tremendous acceleration (exceeding 20 Gs, probably) must do a lot of havoc to other parts of the body, such as the brain; maybe it will turn into . . . well, enough.

 

[Gara]

aah i see now.

so the asnwer is,

Only if you SOMEHOW knew where the bottom was, and somehow knew how FAST the lift was falling, and knew JUST when to jump, and had SUPERHUMAN strenth, to be able to jump up at the speed of the lift is falling at a speed you do not know, and if you timed it just right, even though you don't know where the bottom is, you could slow to 0 mph, making the same G Forces as if you had just crashed, meaning you might as well just crash.

so basicly, you can only survive it by jumping, if you are able to survive it by crashing. making the jump pointless.

 

[Michael D. Sewell]

Gara,
You've just made us all very proud.

 

[AnthreX]

i am very confused with all these conclusions..

can someone tell me what the real conclusion is?

or .. is the argument still continuing ?
ta

 

[Integral]

Read Gara's last post, she sums it up nicely.

 

[Rog]

I always thought that the reason you would die in such a scenario is due to deceleration trauma i.e. when the elvator hit the ground your organy soft bits would continue and try and take up residence in your legs! So by this thinking even if you could jump at the quoted 60mph you would reduce the impact on landing however you would have experienced the deceleration trauma you were trying to avoid by the very act of jumping.

 

[Cliff_J]

Anyone of us can jump off a building and land on an airbag and live to tell about it. Same velocity/kinetic energy/etc, longer timeframe=lower G loads=survivability.

So unless your fast twitch muscle fibers are really fast, seems pretty slow in comparsion of a steel on concrete impact. So I respectfully disagree that it won't help to jump, although I think we can all agree it becomes a mere formality after a certain speed is attainted.

Cliff

 

[UltraPi1]

Cliff has it right. You would still be better off jumping. Jumping would allow you to absorb the energy of the fall over the course of say two feet, while not jumping requires you to absorb the impact in one feld swoop. Irrespective of whether you survive or not - Jumping at the right moment has a greater chance for survivability than not jumping.

 

[outandbeyond2004]

Well, there may always be borderline cases when it is better to jump. But, generally speaking . . .

 

[Integral]

The more I look into this the more convinced I am that jumping, not only will not help but may well be the formula to maximize injuries. Simply because, to reduce your fall velocity, you must jump less then about .2s before impact, this means, since you are really still falling at a pretty good rate, you will impact with your legs straight and knees locked. Not what you want. Your best bet may to to lay flat on floor and adsorb the shock with as much surface area as possible.

I am not sure what air bags and cushioned landing have to do with this discussion. If those safety features are in place then you were never in danger to begin with, so why bother jumping

 

[UltraPi1]

Your best bet may to to lay flat on floor and adsorb the shock with as much surface area as possible.

Bad idea - The main thing to protect is your head. Your legs are expendable. They can serve to absorb some shock albeit little. You might as well let someone take a full swing to your head with a baseball bat than lie on the floor. Ouch!

 

[jdavel]

Janus wrote: "To survive, you would need a combination of enough leg strength and g force resistance. But if you had these, then you don't need to jump in the first place. You can just allow yourself to go from standing up to a crouch as you hit and let your legs absorb enough of the deceleration(like a shock absorber) to let you come out unharmed."


I think you're forgetting something. If you jump you get to use the fles in your legs twice, once when you jump and once when you land. So whatever maximum deceleration the rest of your body has to absorb is cut in half. Since no one has enough leg strength to produce a lethal acceleration by jumping, any jump that has you moving away from the floor when the elevator lands will improve your chance of survival.

 

[outandbeyond2004]

In the case that the elevator is already going too fast or will, I think it would be better to flex your legs and hip at about 160-170 degrees and brace your arms straight downwards than trying to time your jump. We should not expect the person atop the elevator to be able to see the end coming well enough to time the jump, if it would help at all.

I wrote the above before seeing jdavel's post. I assume he had in mind jumping before the elevator hits. If so isn't he forgetting that any KE that is dissipated by the jump would soon be restored, and the end would be about just as bad anyway. The potential energy is the same however and when you jump. Otherwise, if you jump right at the moment the shock of the elevator's ground impact reaches just a few centimeters above the level where your feet are (or maybe 6-10 cm depending on how long your legs are), I don't think it would really be a jump. The neuromuscular-skelton system, if not badly damaged enough, would have its coordination too badly disrupted to generate much power for a jump. However, suppose it did manage a really good jump, i.e., not only did it absorb and dissipate considerable KE in heat (damages the muscles etc.) and muscle tears, you have to do it again ==> Yet more heat in already damaged and torn muscles, etc.

 

[Integral]

If you can understand the analysis I did up stream a bit you will understand why your legs will NOT be flexed for the landing following a jump. The time to reach the peak of a normal humans standing jump is roughly .2s this corresponds to an initial jump velocity of 2m/s. So if the elevator, falling at say 10m/s hits bottom shortly after your feet leave the floor, you will still be falling at a rate of about 8m/s. Let us suppose the elevator hits the ground when you your feet are 5cm off the floor. Let's run some numbers on this.

With respect to the elevator we have

y= 2t -gt² = .05

This occurs at .03s from the time you feet left the floor. At this time your velocity wrt to the elevator is 1.7m/s but, remember the elevator has just come crashing to a stop, all that remains is your velocity wrt to the outside world which is -8.3m/s, now you are .05m from the floor, your legs are still configured for the jump you just initiated. According to my numbers you are .007s from hitting the floor traveling at over 8m/s, this equivalent to a free fall from about 12.5m.

Edit:

This in incorrect it should read 3.3m

End edit


You are now in just about the WORST possible ergonomic condition for surviving such a fall. How will having your thigh bones driven into your shoulder blades protect your head? Knees? what knees?
Think about it.
Edit:
from only 3m you would probably only break your legs

End edit.

Once again, jumping is NOT the thing to do.
I think that I would prefer doing this standing on my head, It would be over with in a hurry that way.

 

[outandbeyond2004]

Warning = although this has been edited, it may still offend some people.

Some of Integral's number seem to be incorrect, and we have overlooked the effect of adrenaline ==> superhuman athletic feats.

Let me add here to the advice to get to the top if at all possible. If the elevator crumples to a pancake, you certainly don't want to be inside. One way to get to the top is to take your shoes off and fling them to the floor one at a time. However, if you have time to do that, well, good luck!

I assume Integral is correct to say that most young adults can manage jumps with an initial velocity (feet just leaving the ground) of 2 m/s. I will try 4 m/s just for fun if nothing else.

I also assume the elevator is falling at 5 m/s. I think after reading Integral and from my memory, this is survivable for most people; but the question now is, would jumping make your landing easier?

I assume you have managed to somehow climb onto the elevator's top. You time the jump just before the elevator top comes to a rest, which may be 3 m above the ground, but you are still moving at 5 m/s wrt the ground. This is just before the shock reaches your feet, not like in my last post. (The elevator top might even bounce up a little.) So, wrt the elevator top just before it comes to a stop, which after all is what you will impact with, the position of your head is maybe

y = 1.5 - t - gt^2/2

where t = 0 is the time of maximum velocity, when your legs are almost straight and your feet is still in contact with the elevator top and at zero velocity wrt the elevator. I suspect that is pessmistic, because surely the elevator top will begin to slow down shortly after the elevator bottom hits the ground.

You have been following the thread, so you know at this point that you have to immediately tense your thigh muscles to brace yourself. How much time do you really have? Just 0.2 seconds to recognize that you have successfully timed your jump and to tense your thigh muscles, according to computations from the above equation. At this point, your head would have moved down about 0.4 meters. You can't generate much power in this position in the time left till head impact, which is about 0.3 seconds, so your legs are going to bang against the elevator top. Ouch! You will hold out your hands to break your fall.

I am going to disagree somewhat with Integral. Surely survival of the head takes precedence over that of the limbs. He may have overlooked the point that the head attains maximum velocity while the feet is still in contact with the elevator. The person's center of mass might move less than the head during the jump, besides, which would make a difference in boderline cases.

So in conclusion, well, I don't know about the borderline cases. Maybe jumping will be better, and in other cases maybe not.