An elevator is falling, as in the real world, with some air resistance outside slowing the fall. There is a person inside the elevator. Would the person experience some force pulling them towards the floor? In other words, if the person was in the vertical center of the elevator at the start of the fall, assuming the fall is infinitely long, would they eventually land on the floor?
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6$\begingroup$ What do you think, and why? $\endgroup$– PeterCommented Jul 29 at 10:20
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$\begingroup$ @Peter, I think yes, the person must fall to the floor eventually, because the elevator would experience the same forces as the person inside, but also the air resistance slowing it down. So relative to the elevator, the person must be falling. However, I am not sure about one thing. Would the person also experience air resistance because there is air inside the elevator (forgot to explicitly mention in the question), or would they be falling together, and the air inside wouldn't slow down the person's fall? $\endgroup$– g00ddsCommented Jul 29 at 10:43
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4 Answers
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You said, "...air resistance outside slowing the fall..."
Well, how do you slow something that's moving? You push on it. The air slows the falling elevator by pushing up on it. But you're inside the elevator, shielded from the relative wind. What prevents you from falling faster than the elevator? That's easy! The floor of the elevator pushes up on you.
That upward push from the floor of the elevator feels exactly like the upward push that the spectators outside feel from the ground that they are standing on—the push that stops them from falling to the center of the Earth. We call that push, "gravity."
The upward push from the floor of the elevator—the push that stops you from falling faster than the elevator—is indistinguishable from gravity. If the elevator falls long enough to reach its terminal velocity (no longer accelerating downward) then the force you feel inside will be exactly equal to gravity.
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Because of the person's momentum they would initially lift up from the elevator floor then catch up with it staying as if weightless for an instant. The person in the elevator has air resistance and the elevator has air resistance but inside the elevator all the air is moving downward so the air resistance they experience would be nothing much whereas the elevator's acceleration downward would be slowed somewhat by its external air resistance so the person would "fall" to the floor of the elevator and stay there.
Lets hope the elevator has good emergency brakes and they come on before the elevator meets ground level.
PS
In country like the UK the chances of an elevator falling would be vanishingly small (even in extreme emergency situations) because they have many many safeguards built into their design construction and operation. An elevator also has to be certified maintained and overhauled at intervals. Modern equipment will also be logged and any signs of problems would be flagged. New generations of elevators in tall buildings operate in new and novel ways, its worth finding out about that and also the history of elevators if you have interest.
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1$\begingroup$ It's commonly understood that Elisha Otis invented the 'safety elevator' in the US in the 1800s. I have a hard time imagining that there are elevators in any part of the world that don't at least conform to the minimal safety requirements of 19th century US elevator technology, $\endgroup$ Commented Jul 29 at 20:51
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10$\begingroup$ "Because of the person's momentum they would initially lift up from the elevator floor" The elevator also has momentum, I don't see why the person would actually lift up unless they jump a bit or smth $\endgroup$ Commented Jul 29 at 23:15
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$\begingroup$ @aquirdturtle I at least imagine that would be the effect of inertia. Hard to put a definite reason to it, though. Could be an interesting follow up question, whether and how the person is lifted and how that's calculated. $\endgroup$ Commented Jul 30 at 9:34
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3$\begingroup$ Except for the air resistance, the inertia/gravity part of accelerating downwards should be the same for the person and the elevator - both start at rest, both are affected by the same gravity (remember the famous "feathers and bowling ball falling in vacuum") - so they would accelerate downwards at the same rate. But the elevator would be hindered by air resistance more... so actually, the person should stay on the ground right from the start, unless something hits the elevator from above (thus giving it additional acceleration that the person does not directly experience) $\endgroup$– SyndicCommented Jul 30 at 12:26
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2$\begingroup$ @aquirdturtle I agree that there is no force due to gravity that means the person leaves the ground but standing stores energy in our legs/muscles etc, when suddenly the elevator is dropping its likely that stored energy will recoil and the person will loose contact with the floor for a short time, also the sudden loss of the elevator floor will unbalance the person and they will loose contact for that reason. $\endgroup$– user417360Commented Jul 30 at 14:08
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Would the person experience some force pulling them towards the floor? - Yes as the downward force on the person due to the gravitational attraction of the Earth stays the same.
What changes is the the upward force on the person due to the floor.
If the elevator starts from rest and the air inside the elevator is not moving relative to the elevator/person then as the elevator increases in speed the upward force due to the elevator will increase from zero so that the acceleration of the person is the same as the acceleration of the elevator.
As time progresses and the speed of the elevator increases then so does the air resistance of the elevator which also means that the force on the person due to the floor of the elevator also increases.
This continues and the speed of the elevator and the person inside the elevators tends to a constant (terminal) speed when the net force on the elevator (and the person) is zero.
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@Farcher This is far from an easy problem for me. If the elevator and the person are stationary the elevator is supported by cables. The person is only stationary because they are imparting a force F = m x a onto the elevator floor where a is the acceleration due to Gravity or F = mg
When the elevator initially starts to fall its downward velocity will be small so no appreciable air resistance, whether the person will actually loose contact with the floor is debateable but for a short time both the person and the elevator will be accelerating downward at g and at the instant the elevator starts to drop the force imparted by the person onto the elevator floor will be zero. So its quite likely the person will spring somewhat away from the elevator floor for a very short time (you could say that the person's position within the elevator becomes indeterminate for a short time). As air resistance starts to become a significant force holding the elevator back the person will begin again to impart a force on the elevator floor.
When the elevator reaches terminal velocity the person will continue to impart some force onto the floor so will not move away from the floor.
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1$\begingroup$ Given that you have written what appears to be a correct and accepted answer, you should probably delete this one. Also, directing messages to other users in answers isn't really at thing, AFAIK. That's for comments. $\endgroup$ Commented Jul 29 at 20:45
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2$\begingroup$ There is no reason for the person not being in contact with the floor at any time during the motion if the elevator starting from rest. As soon as the elevator starts accelerating then so will the person in the lift at the same rate as the only force on the elevator is the downward attractive force due to the Earth and the only force on the person is the downward attractive force due to the Earth. $\endgroup$– FarcherCommented Jul 29 at 21:43
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1$\begingroup$ @JimmyJames Thank you I will remember your advice, earlier I was not allowed to post a comment but I can now. On balance for the time being I would rather leave the question in place, it might help people to come to their own logical conclusions as do the other answers posted. $\endgroup$– user417360Commented Jul 30 at 0:10
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$\begingroup$ @aquirdturtle I agree that there is no force due to gravity that means the person leaves the ground but standing stores energy in our legs/muscles etc, when suddenly the elevator is dropping its likely that stored energy will recoil and the person will loose contact with the floor for a short time, also the sudden loss of the elevator floor will unbalance the person and they will loose contact for that reason. $\endgroup$– user417360Commented Jul 30 at 14:08
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$\begingroup$ If we ignore air resistance for a moment, an object in freefall is weightless. So, while there's no reason for a person to lose contact with the floor, there would be no net force and the sensation would be as if you were floating above it, or close to it. Air resistance on the elevator car means it would not be in freefall, however. $\endgroup$ Commented Jul 30 at 14:34