You Can Survive a Falling Elevator...Just Not By Jumping.

[00:00:00]Now, imagine this. You're plummeting toward the ground in a broken elevator.

[00:00:05]Elevator cable snaps. And in the movie, someone always yells, "Jump right before we hit the ground." My question to you is, could that split-second leap right at the last second actually save your life? Or is it just Hollywood physics?

[00:00:23]Today, we're diving into the real science of falling elevators, human muscles, and answering the question, could you jump in a falling elevator to avoid death?

[00:00:51]Now, let's set the scene. You're in an elevator when suddenly the cables snap.

[00:00:57]Now, you're in free fall and every single second, you're falling faster and faster and faster. For instance, after just 3 seconds, you're already moving at about 67 mph. That's almost 30 m/s.

[00:01:14]Think about that. 30 m every second just after a few seconds of falling. That's highway speeds. Except, you're about to slam into the concrete at the bottom.

[00:01:25]Now, let's take a second just to unpack this part of it, right? It's very counterintuitive how fast you're moving after just a few seconds of falling.

[00:01:33]Because meters per second is a unit of velocity. You could talk in miles per hour or kilometers per hour, but let's for a minute talk about meters per second. Right? That's how many meters you were traveling per second. That's velocity. Now, acceleration is units of meters per second squared. Right? So, in gravity, we say that the Earth has a gravitational acceleration of 9.8.

[00:01:57]That's a rounded number, 9.8 m/s².

[00:02:01]That unit basically means that you're increasing your velocity every second by 9.8 m/s. So, it's like for the first second, you at the end of the first second from free fall, you're going 9.8 m/s. But, after the next second, you've increased your velocity again by another 9.8 m/s. At the end of the third second, you've increased your velocity again by 9.8 m/s again. So, when we fall and we have acceleration or in general the concept of acceleration, you're increasing your velocity every second.

[00:02:35]That's why the units are m/s² because the better way to say it, I think, is acceleration has a units of m/s per second. So, it's not telling you how fast you're moving every second, it's telling you how much velocity you're picking up every single second. m/s increasing velocity per second. That's why we call it m/s².

[00:02:58]And that's why you get to such crazy fast velocities after just a few seconds of falling. Now, as we fall in this situation, someone then shouts, "Jump!"

[00:03:08]right before we hit the bottom, like that's going to save our life. Sounds pretty logical, right? I probably would have the same thought myself. Now, if the elevator is falling down and you jump up off the bottom of the elevator, shouldn't these forces kind of cancel out and sort of save you? Here's what we need to talk about here. We need to talk about something called inertia. It's one of the most fundamental concepts of physics and it basically dominates what's going to happen in this falling elevator. Now, inertia is a fancy word that's basically the property that any mass in the universe has is a built-in resistance to changes in motion. Not motion itself, it's built-in resistance to changing the motion. For instance, you can easily push a golf ball. You can throw a golf ball really easily because it has low mass. You can accelerate it easily. Low inertia. Easy to change the speed, like when you throw a golf ball.

[00:04:03]It's much, much harder to throw a bowling ball or to pick up a car off the ground and throw that because it has more mass, more inertia, more resistance to movement, to changes in movement.

[00:04:16]Now, it's kind of confusing on the ground because we have gravity to think about, but if you take a golf ball in space and you take a car, literally an entire car in space, and you're an astronaut and you float behind the golf ball, there's there's uh we're not talking about gravity here. We're talking deep space, way away from the Earth. Throwing the golf ball is easy.

[00:04:34]Changing its velocity is easy because it has low mass. But, pushing on that car, you will be able to push it, but it'll be much harder. You'll have to really exert a lot more effort, maybe use your thrusters to get it to change its state of motion, to accelerate. That's because it has more mass, which means it has more inertia, which means it resists changing its state of motion or its velocity more. Let's look at it from another angle. Right now at the second, you're sitting still, probably, in a chair, and your body really wants to stay still. That's inertia. But, once you're moving, your body really wants to keep moving at the same speed and the same direction. Inertia is the resistance a mass has to changes in its state of motion. You probably heard of an object in rest tends to stay in rest, and an object in motion tends to stay in motion. That's kind of a phrase from physics that's made its way into the everyday language, right? That's exactly what Isaac Newton described in his first law of motion over 300 years ago, and it's about to become your biggest problem in this falling elevator. You see, here's the situation. When that elevator is falling at 67 mph after just a few seconds, You're not just inside a falling box, right? You're also falling inside the elevator at 67 mph with respect to the ground. So, what's really happening is your entire body inside the elevator, every cell in your body, every atom, every proton, right? Is racing downward at that same speed that the elevator is traveling. You and the elevator are moving together, matched perfectly in your descent towards a really bad day. Now, here's the crushing reality of the situation.

[00:06:20]To save yourself, what you need to do is cancel out the entire downward velocity that you have in just a fraction of a second. Think about what that means for just a second. If you could somehow jump upward at exactly 67 mph at the moment of impact, and this is only assuming that the elevator's been falling for a few seconds, remember. If it's falling for many more seconds than that, you're traveling much faster. But, if you could do that, you'd be briefly stationary relative to the ground. You would cancel out your downward velocity. And you may have a chance in that situation, but the question is, can human legs actually do that? Can human legs generate enough force to actually cancel out a downward velocity so high? Now, you're going to have to use your imagination with me.

[00:07:06]Here is the elevator. I've cut the front of the elevator off so we can see inside, but really it'd be closed up.

[00:07:11]Here is you. That's your head. Here's your body, right? You got to use your imagination. Let's say you're in this elevator, and we start really, really high.

[00:07:19]Suddenly, the cable snaps, right? As soon as we get a going here, you're going to be essentially in free fall inside the elevator. The elevator's moving down, but so are you. You're moving down at the same rate of the elevator because you're both accelerated by gravity. So, this is the situation.

[00:07:35]Now, as soon as the elevator hits the ground, it's going to stop, but you're going to keep moving, and you're going to slam into the bottom. So, what's actually going to happen is your the elevator will stop and you'll just continue moving in the same state of motion and you'll hit the bottom and go splat. So, here's what needs to happen.

[00:07:51]When you're in free fall like this, you need to Let's say you're standing on the bottom. You're in free fall like this and your legs are barely contacting the bottom. You need to somehow jump right at the moment so that suddenly you're not moving down anymore relative to the ground. You've canceled out that downward velocity that you had by doing what? By jumping like this and then your downward velocity relative to the ground is zero. You may still fall a little bit inside, but you've canceled out most of the downward velocity with your legs so that you don't splat whenever the elevator comes to a stop. So, it quickly comes down to biology. Let's talk about what your muscles are actually capable of. So, your leg muscles are powered by something called ATP. You may have heard about that or learned about it in biology, adenosine triphosphate. It's basically the energy currency of your cells. When you need to jump, what happens is your muscle cells break down ATP to release energy, right? And that causes the muscle fibers to contract and then push you upward. All of this is happening all the time every time you move any muscle in your body. Your legs are actually incredibly powerful.

[00:09:02]They're some of the strongest muscles in your entire body because you've basically evolved carry your entire body weight around all day and that's going through your legs. Now, the average person statistically can jump about 16 to 20 inches off the ground from a standing position. Elite athletes, and I mean really, really good athletes, might be able to reach 30 inches or more. When you jump up, what you're doing is you're accelerating your body upward against gravity, reaching a takeoff speed of about 8 to 11 feet per second. And I know the units are not ideal here, but still, these are small numbers in comparison to a falling elevator, especially if it's falling for more than a few seconds. Now, all this sounds impressive that we can do this until you realize the elevator is 67 miles per hour, and that translates to about 98 feet per second. You need to jump roughly 10 times harder, for lack of a better word, than your maximum capability to even be able to do that.

[00:10:05]And that's with only a free fall of a few seconds. Your leg muscles simply don't have enough ATP, enough energy, to actually be able to contract fast enough to generate that kind of force needed to do that, even for this simple problem of just falling for a few seconds. But wait, there's more bad news in this scenario. Even if your legs were somehow actually strong enough, let's say you were this superhuman person, you would face actually another problem, timing.

[00:10:33]You see, you need to jump at precisely the correct millisecond to make a difference. If you time your jump incorrectly, a little bit too early for instance, right? Then what you do is you would hit the ceiling of the elevator, and then a little too early, and then a crash down with the elevator anyway. If you jump too late, it's obvious, you've already hit the ground. What you need to have is reaction time of a fighter pilot or better, and the precision of an Olympic athlete, all while experiencing the terror of falling in an elevator, which would scare anybody. So, the question is, is there any scenario where jumping could actually work and save you, so to speak? What if the elevator only fell a really short distance, for a much smaller period of time? If an elevator dropped just 5 feet, you know, that's like, you know, the size of a human human height for instance, it would be falling at about 12 miles an hour when it hits the bottom. That's still faster than most people can actually jump to cancel the velocity exactly, but here's the interesting thing. At that speed, you might actually survive even if you didn't jump at all. The impact from that small height would be kind of like jumping off of a really tall table or a wall or something. Certainly jarring, maybe you'd sprain an ankle, you might even break a bone, but probably not fatal. I say probably because if you fall on your head, of course, even small falls can be really bad. So, don't do this, right? Your body can absorb that much force in most cases, especially if you bend at the knees to absorb a little bit of energy. So, let's go a little higher. How about 10 ft? A 10-ft fall.

[00:12:08]The elevator hits the ground at about 17 mph. Now, we're kind of in dangerous territory already. That's equivalent to jumping off of the roof of a one-story building. People have survived falls like this, but the injuries are super common, right? Broken bones happen all the time from that height. Concussions if you hit your head, internal damage to organs because remember when you hit the ground, your organs are moving and then they get bruised when they hit the inside of the other parts of your body.

[00:12:38]Your legs still can't jump hard enough to completely cancel the speed, but the fall itself might not permanently damage you if you're lucky. Now, here's where it gets cool to think about and really where I've been trying to skate to.

[00:12:51]There's a threshold somewhere around 15 to 20 ft where falls transition from probably survivable to probably fatal.

[00:13:00]I'm talking about not even with an elevator. Once an elevator falls from three stories or about 30 ft, uh it hits the ground at something like 30 mph.

[00:13:09]Now, at that speed, even without considering the jumping aspect of what we're talking about, the survival rate drops dramatically. Your organs in your body or basically, when you think about it, floating inside of your body suspended in fluid. I say not really floating, but they're suspended in fluid. And they continue moving downward when your body hits the ground. And so, even your skeleton stops abruptly, your bones can buckle, your internal organs can get bruised, causing catastrophic injuries from that height. By the time you reach a fall height of about 50 ft or about five stories, the elevator's already moving at 40 mph when it hits the ground. At 100 ft, that's about 10 stories, you're at that 67 mph that we talked about earlier when we started the whole discussion. At these speeds, the concept of jumping to save yourself becomes almost totally absurd.

[00:14:00]Basically, you need superhuman strength, literally 10 times beyond human capability, to jump. But, here's one more plot twist to this physics nightmare that actually, I think, makes it even harder to contemplate. You see, when you try to jump in a falling elevator, you're trying to push off a floor with your legs that's accelerating downward just as fast as you are. It's like trying to jump, like jump up in the air, while standing on a skateboard that's kind of rolling downhill, down a very, very steep hill. The platform you're pushing against, meaning the bottom of the elevator, is moving away from you and you're moving with it. So, it's really hard to make contact with the floor, and that makes it very hard to actually push up. Basically, the practical problem here is if you have an elevator and you're initially standing on the bottom, the cable snaps after the first few seconds, the butterflies hit your stomach, you're going to be moving downward at the same acceleration and velocity as the elevator, right? You're going to be moving down together. So, what's going to happen is you're rapidly going to start to feel weightless inside of this elevator, especially after a few seconds. So, you might be up here, sideways or something. Your feet may not even be touching the ground. So, it would be really hard to jump at the right moment to because it's hard to time it correctly, and you can't jump fast enough or hard enough anyway. But, on top of that, your feet are not even on the floor anymore. After the first few seconds, you're almost floating like an astronaut in a free-falling container. So, the reality check is the only real safety feature that could save you in the situation is already built into modern elevators. They have multiple redundant braking systems. That means backup systems for braking.

[00:15:36]Elevators have backup cables that are supporting the elevator, and if those cables fail, they have emergency brakes that automatically engage. Like, you don't have to do anything. They just clamp immediately, grinding metal on metal against the rails in the in the elevator shaft to stop it. These emergency brakes can stop a falling elevator, though you'd still probably experience a violent deceleration that can cause injuries, but hey, it's way better than hitting the ground at over 100, you know, miles an hour or something. So, the next time you see someone in a movie jump at the last second to survive a falling elevator, you'll know the truth. Physics doesn't care about Hollywood endings. So, the next time you get in an elevator, press the button, and you're going especially down a skyscraper, you know, maybe 30 floors, and you think about what would I do if the elevator snaps, uh always remember that you're safe because the elevator has built-in safety systems to protect against the situation. Ponder what we just talked about here, and always remember to stay curious. Learn anything at mathandscience.com.