# Air compression via acceleration?

When we are sitting in our cars, and the car begins accelerating we are "pushed back" due to acceleration. Or if you have a ball in an empty vehicle, when it starts accelerating, the ball will roll to the back of the car.

I was wondering, is this also true in air? If there is an air-tight vehicle that undergoes massive acceleration will the air be compressed to the back of the vehicle? How much acceleration is needed to compress the air?

Yes, acceleration will compress the air.

Take for example a cubic box 1 meter per side.
Per wikipedia...
At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 1.2754 kg/m3.

100 kpa = 10197 kg/m2 according to this pressure unit calculator.

So, if you wanted to accelerate the box at such a rate that the pressure at the rear of the chamber were 2 atmospheres instead of 1 you would have to accelerate it at (10197/1.2754) g. Doing the arrithmatic that would be about 78,352 m/s2.

Gold Member
You can actually see this effect quite easily. If you have a helium balloon floating in your car, if you slam on the brakes, the balloon will actually move backward toward the rear of the car. That is because the acceleration causes the air to compress toward the front, creating a density gradient and the balloon "floats" to the area of lower density due to what is effectively buoyancy. Kind of cool.

So does this simply cause lower air pressure at the front of the vehicle or could it potentially create a vacuum at the front of the vehicle?

The vacuum will only be able in if we run this in an antimatter environment. this will allow the acceleration to be forced using the nuclear explosions of anti matter with the particles surrounding this enclosed space. next the vacuum will only happen if you reach an accelleration of 1.354E8 Km/(sxs) due to the Borne Oppenheimer approximation. So in conclusion the vacuum is possible but highly unlikely.

mfb
Mentor
For realistic accelerations (<= 1g), the air pressure difference is similar to the regular vertical difference at the same length: If you climb on a ladder, the air pressure up there is lower, too, but just by a tiny amount (~1/2000 for 4 meters).
You won't get a perfect vacuum, but you get a good approximation if the scale height is small compared to the length of the car. This would require accelerations of more than 10000 g. Possible in ultracentrifuges, but not with a size of 4m.

@physicswinner: Can you show us how you get that number, and where do you use the Born–Oppenheimer approximation? In addition, how is that related to antimatter?
If you just want to post random buzzwords, this might be the wrong place.

russ_watters
Mentor
You can actually see this effect quite easily. If you have a helium balloon floating in your car, if you slam on the brakes, the balloon will actually move backward toward the rear of the car. That is because the acceleration causes the air to compress toward the front, creating a density gradient and the balloon "floats" to the area of lower density due to what is effectively buoyancy. Kind of cool.
I don't think the pressure /density gradient plays a significant role: buoyancy does not require or even take it into account.

mfb
Mentor
You need a pressure gradient (usually provided by gravity) to get buoyancy. Otherwise, in which direction should the force point?

russ_watters
Mentor
Check the equation for buoyant force: where is the density variation? Buoyant force just requires a continuous fluid, a volume and a direction and magnitude for gravity.

Asked another way: for a solid object, does the buoyancy significantly change as it sinks?

AlephZero
Homework Helper
I don't think the pressure /density gradient plays a significant role: buoyancy does not require or even take it into account.

Buoyant force just requires a continuous fluid, a volume and a direction and magnitude for gravity.

I agree the density gradient is insignificant, but gravity causes a vertical pressure gradient even in a solid object. You can think about buoyancy either way, and get to the correct equation.

Note there may be other causes of pressure gradients, for example in a rotating system. Think about the well known experiment with objects more and less dense than water in a centrifuge, for example.

russ_watters
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