Sealed accelerating elevator

[Jazzyrohan]

If a sealed elevator moving with a constant velocity in upward direction suddenly starts accelerating upwards with an acceleration "a" ,will all the air molecules inside the elevator also accelerate with the same acceleration?

 

[phinds]

If a sealed elevator is accelerating upwards with an acceleration "a" ,will all the air molecules inside the elevator also accelerate with the same acceleration?

What do you think and why?

 

[Jazzyrohan]

What do you think and why?

A body in an accelerating frame has the same acceleration as that of the frame if it is in direct contact with the frame,right?
So I think the air molecules will not be moving with the same acceleration and someone in the elevator will feel the air accelerating in the opposite direction.
Am I right?

 

[Ibix]

Am I right?

Remember the equivalence principle - this is similar to being in (for example) a decompression chamber at rest on the Earth's surface. If you are correct, in a decompression chamber there would be a downwards wind until the air pooled on the floor.

 

[PeroK]

A body in an accelerating frame has the same acceleration as that of the frame if it is in direct contact with the frame,right?
So I think the air molecules will not be moving with the same acceleration and someone in the elevator will feel the air accelerating in the opposite direction.
Am I right?

Where is your elevator initially? In gravity-free space? Where is the someone in the elevator initially? What happens to someone in the elevator as it accelerates? If there were only one air molecule (or a million) in the elevator, what would happen to that? If there is enough air in the elevator for someone to breathe, how does that change things?

 

[Jazzyrohan]

Where is your elevator initially? In gravity-free space? Where is the someone in the elevator initially? What happens to someone in the elevator as it accelerates? If there were only one air molecule (or a million) in the elevator, what would happen to that? If there is enough air in the elevator for someone to breathe, how does that change things?

The elevator is subject to gravitational force on earth.That someone is standing on the floor in the elevator.

 

[PeroK]

The elevator is subject to gravitational force on earth.That someone is standing on the floor in the elevator.

Have you ever been in an elevator? Did it feel like the air was moving down?

 

[phinds]

A body in an accelerating frame has the same acceleration as that of the frame if it is in direct contact with the frame,right?
So I think the air molecules will not be moving with the same acceleration and someone in the elevator will feel the air accelerating in the opposite direction.
Am I right?

I think there is a subtly that has been missed in the responses so far. Those responses are looking at the macro level and correctly pointing out that your idea (apparently) that the air would pool at the bottom of the elevator is a non-starter. BUT ... they are overlooking the fact that you are right at one level in that the air in a non-accelerating elevator car in space would distribute itself evenly whereas the air in an elevator car on the ground on Earth or accelerating at 1G in space, WOULD in fact have a differential of air pressure due to the acceleration. I don't know if human measurement devices exist that can tell the difference in air pressure over, say, 10 feet at 1G, but if they could it would be there.

 

[PeroK]

I think there is a subtly that has been missed in the responses so far.

Perhaps you missed this:

If there were only one air molecule (or a million) in the elevator, what would happen to that? If there is enough air in the elevator for someone to breathe, how does that change things?

 

[phinds]

Perhaps you missed this:

Didn't miss it but missed the point (so effective missed it, yeah)

 

[anorlunda]

This video demonstrates the action graphically. In the video, the acceleration is horizontal, thus eliminating the complication of Earth's gravity.

 

[Ibix]

This video demonstrates the action graphically. In the video, the acceleration is horizontal, thus eliminating the complication of Earth's gravity.

I must admit, that "balloon goes the wrong way" thing is one where, even knowing how and why it works, something low down in my brain just goes "Nuh uh! Must be fake!" Even when I'm watching it in reality.

 

[jrmichler]

I don't know if human measurement devices exist that can tell the difference in air pressure over, say, 10 feet at 1G

There is, and it does:

The image is of an aircraft altimeter showing 920 feet altitude above mean sea level at a barometric pressure reading of 29.92 inches mercury. The skinny hand is 10,000 feet per numbered division, the short hand is 1000 feet per division (10,000 feet per revolution), and the large hand is 100 feet per division (1000 feet per revolution). The little tick marks are 20 feet apart.

You could also use an ordinary barometer. One thousand feet of altitude change is one inch of mercury pressure change, so 10 feet is 0.01 inch mercury. A good barometer should show that if you tap it lightly.

Or you can calculate the rate of change of pressure with altitude. It's the same rho*g*h calculation used for liquids. Rho for air is about 0.0765 lbs/cubic foot at standard temperature and pressure.