If You're in a Falling Elevator...!

Say you were in an elevator, in a free fall. Assuming you have the presence of mind in this situation, and assuming you get the timing right and jump so that you are up in the air when the elevator hits bottom, would you be hurt as much as if you hadn’t jumped? Thanks.
- J.K. (age 18)
University of Illinois, Urbana, IL, USA

Great question! How much you get hurt depends on the force on you when you hit the ground. Remember that force is proportional to the change in momentum and inversely proportional to the length of time over which the momentum changes.


Since momentum is mass times velocity, the faster you’re going when you hit the ground, the more force you will feel, and the more it will hurt. If the elevator has been falling for a while, then it’s probably moving very fast. If you jump up, then you’ll change your velocity just a little bit. So you’ll be going a tiny bit slower when you hit the ground. So, technically speaking, you would probably not be hurt quite as much. But this difference would probably be so small as to not be noticeable. In particular, if you’re falling so fast as to be killed in the fall, jumping would most likely not make enough of a difference to save your life.

-Tamara

p.s. If you’re like me, you might at first think that jumping up won’t do any good because you’ll just fall back down, speeding up again. In fact, Tamara is right.  Once the elevator is falling more than half as fast as the speed you get by jumping from rest, jumping reduces your energy, and will soften the fall.  If you tried jumping just as soon as the elevator started to fall, you’d actually end up falling from a greater height, and hit harder. The best time to jump is right before landing.   If you jump too early, you’ll just crash your head into the ceiling of the elevator, and get all of your original momentum back.

To anyone who might have read this during the days when I had posted an ’improved’ but wrong answer, I apologize.
(As a practical problem, jumping might not be a good idea because then you hit a fixed elevator floor, rather than having you and the elevator crash together into the shaft bottom, maybe with a more stretched-out collision.) Mike W.

(published on 10/22/2007)

You explained why jumping at the last minute won’t help you survive in a falling elevator. But, what position WOULD you want to be in to up your chances of surviving in a falling elevator? According to the book "The Worst Case Scenario" you’d want to lie flat on the ground to "spread the force" of impact. It seems to me, though, that you’d want to stand up and use your legs as imitation airbags. Who is right, if either of us are right?
- Joe (age 16)
Reading, PA

Just using common sense and elementary physics suggests that you're right. Maybe there is some tricky medical complication, but the obvious thing you'd want to do is minimize the acceleration of the most important parts of your body, especially the head. If the acceleration is uniform during stopping, its value is given by v^2/2d, where v is the initial velocity and d is the distance traveled during stopping. Obviously making d bigger reduces a. Using your legs to cushion the fall gives d of a few feet. Lying flat on the floor gives much smaller d. So I think you're right.

Mike W

(published on 10/22/2007)

On the other hand, standing forces your ankles and legs to take all the force (which is proportional to your mass) of decceleration, and you are going to break and/or dislocate bones and tear ligaments. If you lie flat, the force is spread across a wider area, so there’s less stress on your body. Also, the long bones lay perpendicular to the force vector, so ther are less likely to fail. You may break ribs and suffer soft-tissue injuries, but your going to have a easier recovery.
- Webs (age 40)
Montreal, QC, Canada

Here the question is : how bad a crash is this, and what are your goals. We tried to give the answer that seemed most likely to minimize the acceleration of the brain and other vital organs, which are themselves soft tissue. Minimizing leg trauma seemed less important.

Mike W.

Lying flat sounds like a bad idea, since the collision will be quicker and the forces stronger.  If you stand up and do not lock your knees, at least some expendable parts of you have distance and time to crumple up, absorbing some of the energy, before the vital organs hit hard surfaces.  This is standard advice for parachutists who must absorb the remaining energy of falling when they hit the ground -- even with a parachute you do not hit the ground with zero speed, and it is good to absorb it by bending legs and rolling after the impact.

Tom

(published on 10/22/2007)

for those who think jumping up right when the elevator is about to crash is the dumbest thing i have ever heard. go take a physics class before answering this question. this isn's Dragonball Z where you can expect yourself to hop off of falling rocks. Jumping in an elevator to prevent from having a greater impact is the same concept. IT CANT BE DONE.
- John (age 24)
Los Angeles, CA

I'm not sure what Dragonball is, but jumping just before the collision reduces the person's net kinetic energy. (The energy is dumped into the elevator.) In principle it could thus reduce the severity of the collision. In practice, it's unlikely to work, but that's not because of any basic conceptual error.

Mike W.

(published on 06/03/2009)

I don't think free fall will happen as the elevator will have friction with the wall. But if this does happen, I agree that we should stand up to reduce the acceleration. But we will most likely break some bones in the process (better than having brain juice). I am thinking will it be better if we stand up and at the same time use our hand to hold the bar? This way, the impact on the leg will be distributed to the upper body also?
- David (age 26)
NY

That sounds sensible.

Mike W.

(published on 09/26/2011)

I know you said that you wouldn't answer a question "you already answered," but I wasn't satisfied with your answer regarding why one shouldn't jump up in a falling elevator as a measure taken to soften the inevitable collision with the floor. You said one would just crash into the ceiling. Why is that the case when one's body would be falling at the same rate as the falling elevator(body would already be accelerating downward along with the elevator)? Wouldn't jumping up in a falling elevator have the same relationship as jumping up in a stationary elevator? Wouldn't the body still be falling rapidly along with the elevator, even while the body was jumping up? It seems to me to be just a matter of basic relativity; the jumping up would be relatively the same as when interior body and elevator were stationary. If my analysis is correct, maybe jumping up wouldn't be such a bad idea after all.
- Aaron (age 36)
Los Angeles, CA, USA

Aaron- That's a great question, and for a moment you had me convinced. Here's the problem with applying relativity that way.
Relativity says that internal events in a free-falling elevator are identical to those in an elevator in zero gravity with no forces on it. What would happen if you jumped in such an elevator? You'd acquire upward momentum (and the elevator would head downward a bit) and no subsequent force would be around to change that until you hit the ceiling.
You're implicitly comparing to the case of a stationary elevator with gravity and some other force (e.g. cable tension) to prevent falling. The presence of the cable tension in one case and its absence in the other mean that the situations are not the same internally, even though relativity says that the presence or absence of gravity is irrelevant.

Mike W.

(published on 05/16/2013)

If you were standing when the elevator started to fall, would you even be able to lie down? If you and the elevator are both in free fall, accelerating at the same rate, what force would you be able to exert that would allow you to move downward from a standing position?
- Joe (age 42)
Boston, MA

That's a great question. You're absolutely right that ordinary lying-down motions would not be able to lower your center of gravity with respect to the elevator. In fact, to the extent that you pushed on the floor, you would accelerate upward. The only way to do it would be to grab something on the sides and push yourself down. That might be quite hard.

We hadn't thought about that problem because we get so used to the ordinary Earth-surface frame that we make assumptions which wouldn't be true in other frames.

Mike W.

(published on 05/16/2013)

Suppose I am in elevator which is at 10m height above ground. Now if someone cuts the cable n elevator falls freely.And if I make a jump of 0.5m high just before hitting the ground then with what velocity I will hit the ground??
- yogesh balar (age 21)
surat,gujarat,india

If you didn't jump, your speed would be sqrt(2g*10m)=14 m/s.

Let's say that you jump just before hitting in a way that would give 0.5 m height in a non-accelerating elevator. (That may be hard to do in free-fall, but let's pretend.) That means an upward velocity (in the elevator frame) of sqrt(2g*0.5m)=3.1m/s. So you'll have reduced your velocity at that height to 10.9 m/s. 

Why is it hard to jump in free-fall? Ordinarily, you and the floor exert a force on each other equal to your weight.  You can bend your knees, and gravity will keep you in contact with the floor. Then rapidly unbending your knees exerts extra force between you and the floor, and you jump up. In free fall, if you bend your knees your feet will just pull up a bit from the floor as your upper body pulls down a bit. Unless your knees happened to be bent at the start of the free-fall you'd have to somehow stretch out to jump. That's unlikely to give a powerful jump.

Mike W.

(published on 06/02/2013)