# Elevators and Physics

This is a question some friends and I have been pondering for a while:
If I were in an elevator that was traveling downward at terminal velocity (a concept Cecil mentioned in this column) and holding a helium-filled balloon, and I let go of it, what would happen? I’m convinced it would go up, as usual, because the air in the elevator would travel with the elevator. My friend disagrees. He knows more about physics than I do. Who’s right?

Yes, the balloon would rise.

Oh, I should point out, that since you stated the elevator was falling at “terminal velocity” it is no longer in free-fall. If it IS in free fall, the balloon will not rise, it will just hang there. And so will you.

If the elevator has reached a constant speed (which it has if it’s at its terminal speed), then the physics inside it will be no different than if it were sitting on the ground, stationary.

It’s not accelerating in either case, which is the important thing.

Right. So when all is said and one, it will be like a normal helium balloon, lighter than air, and hence float up.

I’m not sure you guys are fully correct. Think about it this way. Surely the baloon would not suddenly begin to rise the moment terminal velocity is reached as the RATE of acceleration is decreaseing all the time due to friction. Without looking at the equations, I would guess that the balloon would rise slowly at first, then reach it’s normal rate of ascent once vt was reached.

Wow. The elevator must’ve been travelling faster then the speed of light since my post from this AM got dated March 3.

The acceleration of the lift does not enter the equation.

The question states that the elevator is AT its terminal velocity and is thus, by definition, not accelerating.

What the terminal velocity of a falling lift is, depends on the system and its inherent frictional properties and will be different for different lifts, unless you assume a frictionless system, in which case terminal velocity would not be reached anyway, since there would be no frictional retarding force to counteract the acceleration due to gravity

I’m sure the balloon would rise as normal.

To clarify the posts who say the balloon would rise–it would rise only w.r.t. the elevator, and would fall w.r.t. earth. I guess that’s obvious but you never know.

IANAP - but, at no point would its rate of ascent in the elevator be greater than its rate of descent towards the earth (I think). So - it would fall.

Of course, I forgot the last sentence -

But, it would fall more slowly than the rest of the elevator, so it would appear to go up.

Doesn’t seem to matter, since the question is asked from the POV of inside the elevator. And, if we assume the elevator has no windows, it is impossible to know that it is falling at all, since it’s falling at a constant velocity.

I disagree. Going out on a limb here but I’ll say that as the cable breaks and the car begins to free fall the ballon will drop if it’s resting on the cieling or at least the string will go slack if that’s what is restraining it. In normal 1G static state it’s more bouyant than air. At 0G everything is weightless so. If the elevator is falling with at least some resistance from air or shaft friction the balloon will just become slightly less bouyant. In no case will it rest on the floor unless the elevator is pushed downward faster than it would fall in a vacuum. When the elevator reaches terminal velocity it will rise again.

As the closest experiment put a helium balloon in a car. Accelerate, stop and make turns and watch which direction the balloon goes compared to everything heavier than air.

IIRC:

In all cases the balloon in air does the opposite of a rock in air.

The rock is stationary (later moving slowly) wrt the air around it, and falling at the same rate as the elevator.

So the only force acting on the rock is gravity, so it acceletates down. So it goes down wrt the elevator, since the elevator is falling at constant speed.