Why Does a Balloon Fall Up in an Elevator?

[hachikuda]

Imagine you are in an elevator accelerating downwards with acceleration g, holding a balloon (which would fly upwards if left outside). Now if the thread you are holding snaps, what will happen to the balloon?
Since the acceleration felt inside the elevator is 0, the balloon should not experience any buoyancy and continue to stay at the same position.

The difficulty I am having in understanding is, if this experiment is observed from outside (i.e. from an inertial frame of reference), the balloon seems to be in a free fall towards the ground, where as it should actually be rising up.

Where is the mistake?

 

[voko]

What about the air in the elevator? Should we suppose it moves together with the elevator?

If yes, then as soon as the thread snaps, the force of drag will be acting on the balloon, which makes the whole thing quite difficult.

If no, then the dynamics of the balloon will not be affected by the motion of the elevator after the thread snaps.

 

[A.T.]

The difficulty I am having in understanding is, if this experiment is observed from outside (i.e. from an inertial frame of reference), the balloon seems to be in a free fall towards the ground, where as it should actually be rising up.

Why should it be rising up in the inertial frame? The force of buoyancy is frame independent, and there is none, because there is no air pressure gradient in the elevator. Since gravity is the only force acting on the balloon in the inertial frame, it accelerates down.

 

[AlephZero]

The force of buoyancy is frame independent, and there is none, because there is no air pressure gradient in the elevator.

That is not true if the elevator is (approximately) a sealed box. In that case, the air inside the elevator is also accelerating, and the force causing the acceleration is a pressure gradient between the floor and the roof of the elevator.

Even when the acceleration is zero, the buoyancy force is just another name for the resultant force on the object caused by the pressure in the fluid. With no acceleration, there is still a pressure gradient, caused by the weight of the fluid. That statement is rather more "obvious" if you think about why pressure in water increase with depth, but the same is true of air.

 

[Dale]

There is no pressure gradient. The elevator is in free fall.

 

[A.T.]

the air inside the elevator is also accelerating, and the force causing the acceleration is a pressure gradient between the floor and the roof of the elevator.

No, the force causing the acceleration is gravity.