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How would one calculate the acceleration of an object released into a vacuum? Imagining you have a Person in an airlock and that airlock suddenly opens depressurizing instantly from 1atm to 0 how could one calculate the acceleration? I tried doing $\frac{1}{2}A\cdot \frac{p}{m}$ because I assumed that when depressurizing into a vacuum the air pressure inside the capsule would push on the back of the person outward providing acceleration according to the pressure. When I plug in my numbers the result is an acceleration of over a 100G! Something must be wrong right? Could a human survive such an acceleration because of the short period and if they were in a space suit? Your help is much appreciated.

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  • $\begingroup$ Atmospheric pressure over even a square meter is a lot of force. If all that force was focused on the person you would get great acceleration. But, in an airlock situation, most of the gas would escape around the person in the airlock, and the actual acceleration would but much lower - but much harder to compute, depending on the details of the geometry and the equations of compressible fluid flow. $\endgroup$ Commented Apr 3, 2020 at 1:02
  • $\begingroup$ Bear in mind that there is also air between the person and the airlock, and this air has inertia, so the force it exerts on the person will not immediately jump to zero. As the pressure differential between back and chest rises, air is also flowing around from behind. These effects all propagate at the speed of sound, which depends primarily on temperature - which reduces as the air decompresses. Compared to that, how "instantly" does the airlock really operate? Subsonic door? dematerialization within the Placnck time? Hypothetical limit conditions do often produce silly answers. $\endgroup$ Commented Apr 3, 2020 at 10:54

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For an idealised system like whole air in the room is at the back of the person who stands at the door is apparently too high and this link 1. Link has already shows the necessary calculations so I didn't put them here and for more broad calculations you may refer this link 2. Link.

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