# Why don't we "fly up" in an accelerating elevator?

• I
ago01
Earlier I was doing a sample problem for class that involved the work done by an elevator, and the problem gave us the normal force experienced by the person in the elevator (to calculate the acceleration of the elevator-person system).

I had done this wrong because I had wrongly assumed because the person isn't leaving the floor of the elevator that the net force from N and gravity must balance. After doing the calculations, it was clear N > mg, so there is an acceleration.

Mathematically I can work this out and if I had to regurgitate something on an exam I could do it just from the force diagrams. But I am wondering what the physical manifestation is.

What (I think) I do understand is the concept of the perceived weight of the person. If we stand them on a scale while the elevator is accelerating upwards, they feel heavier. If we do the same as the elevator is slowing down (or going down) they feel lighter. This is also consistent with my experiences. I suppose the problem I'm having is that if there is an imbalance between a surface and the normal force I had this idea that the object would simply fall through that surface (if N < mg) or "bounce" off the surface (if N > mg) and the only reason an object is ever held stationary on a surface is because the normal force exactly balances the gravitational force. This was reinforced by problems that, for example, drop a ball off a cliff. There's no normal force, so the downward acceleration is provided entirely by the gravitational force and the object falls. Or alternatively, a sliding block where it's not leaving the surface because N = mg.

In this elevator though the person isn't being "launched" up as the elevator accelerates. At least this hasn't been my personal experience and I've survived many elevator rides. Also, N > mg. So it seems to me that when moving vertically with a surface the normal force is the force providing the acceleration and no extra forces are required. Then, it would also seem that if I hit a ball with a paddle it's the normal force of the paddle's surface providing the acceleration to the ball at the time of impact (even though we would likely just simply treat this as another force). Is this the right idea?

• Lnewqban

Homework Helper
Gold Member
We could "fly up" if the elevator accelerates our bodies and then slow down or stop, just like the paddle does respect to the ball.
We could "sink through the floor" if the elevator allows us to fall and then slow down or stop, if that floor were not a solid surface.

ago01
We could "fly up" if the elevator accelerates our bodies and then slow down or stop, just like the paddle does respect to the ball.

So I suppose then as long as the surface is moving at the same acceleration relative to us we will move with that surface and the normal force provides the acceleration. Your explanation also makes sense, if the elevator suddenly stopped the person in the elevator would keep going due to the larger normal force that was imposed on it the instant before it stopped.

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2022 Award
if the elevator suddenly stopped the person in the elevator would keep going due to the larger normal force that was imposed on it the instant before it stopped.
If the elevator suddenly stopped, the person would keep moving by Newton's first law. They would be in projectile motion under gravity until they hit the ceiling of the elevator.

I don't understand your ideas about normal forces. A bat hitting a ball projects the ball because the bat accelerated to a significant non-zero velocity before impact. An elevator starts accelerating those inside it as soon as it starts moving, so there is no sudden impact, but a common acceleration.

Gold Member
if there is an imbalance between a surface and the normal force I had this idea that the object would simply fall through that surface (if N < mg) or "bounce" off the surface (if N > mg)
It is exactly the opposite:
• If ##N > mg##, and ##m## doesn't move, either the surface is breaking apart and ##m## is going through it (feeling like "falling" through it), or ##m## is deforming or breaking apart;
• IF ##N < mg##, and ##m## doesn't move, it feels the same as if the surface didn't move and ##m## was "bouncing" upward.

Homework Helper
It is exactly the opposite:
• If ##N > mg##, and ##m## doesn't move
Then Newton's second law is being violated.

Gold Member
Then Newton's second law is being violated.
Not if elasticity is involved, or something breaks.

Homework Helper
Not if elasticity is involved, or something breaks.
If net force is non-zero and acceleration is zero, that's a problem.

HomogenousCow
If the elevator's acceleration exceeds ##g## then indeed objects inside will fly up towards the ceiling, however below ##g## objects inside are still bound to the floor of the elevator by gravity.

Mentor
In the stationary ground frame of reference, both the elevator and the man have the same acceleration, and there is no relative acceleration between them. In the non-inertail frame of reference of the elevator, neither the man nor the elevator appears to be accelerating, but there is an additional fictitious gravitational acceleration (and force) on both of them, but again no relative acceleration. So, in the non-inertail frame of reference of the elevator, the total normal force on the man is N=mg', where g' = g + a.

Homework Helper
Another example would be the vomit comet: