• Question: Could a person survive in a falling lift if they jumped as it hits the ground?

    Asked by heverusgrape to Joel, Kristian, Tim, Venus, Zachary on 12 Nov 2013.
    • Photo: Kristian Harder

      Kristian Harder answered on 12 Nov 2013:

      Wow, that might be a good problem to solve with pencil, paper, and a few equations! 🙂 But I’ll just guess now.
      If you only jump a little bit, then it will probably not make a difference.
      If you jump very hard, then you’ll get hit by the ceiling of the accelerator coming down. So I guess overall the answer is no, at least in practice.
      Better to invest in science and technology to prevent accelerators from falling in the first place! 🙂

    • Photo: Joel Goldstein

      Joel Goldstein answered on 12 Nov 2013:

      In theory, if they jump at exactly the right time the person will reduce the force of the impact as their upward velocity relative to the lift will subtract from the downward velocity of the lift itself. If the height that the person could normally jump to is the same as the distance that the lift has fallen, there will be just a gentle touch down.
      Unfortunately, if the lift falls much further than a few metres it’s not going to help much.

    • Photo: Tim Hollowood

      Tim Hollowood answered on 12 Nov 2013:

      It does depend on all the exact conditions…but think of it this way. If you jump up in a stationary lift then the velocity upwards is the same as the velocity downwards when you return to the floor (well approximately). Now add the velocity of the lift which is falling. This means that when you come down you must add the velocity of the lift as well so there’s going to be a slightly bigger crash than without jumping.

    • Photo: Zachary Williamson

      Zachary Williamson answered on 15 Nov 2013:

      Nooooooo, please don’t try this!

      Let’s imagine you’re unfortunate enough to be in a falling elevator. Let’s say the elevator falls 20 metres before it hits the bottom of the elevator shaft. It will accelerate at 9.8 metres per second per second from the gravitational force. Using the basic equations of motion (have you done SUVAT yet?), we can calculate that the speed of the elevator, and by extension, the speed of you, will be 19.8 metres per second.

      Even a very in-shape person can only jump at, hmm, half a metre per second? That will decrease your landing speed from 19.8 metres per second to 19.3 metres per second. Not a great effect, you’ll almost certainly suffer the same fate as if you’d not jumped.

      Although the bigger problem probably isn’t your landing speed, it will the elevator cart crumpling on impact with you inside it! The floor of the elevator would rapidly squish and meet with the ceiling of the elevator. Not exactly a human-friendly place to be.

      p.s. elevators are extremely safe machines, with multiple fail-safes built in so that even when the power fails the elevator won’t plummet to the ground.

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