# Spring behaviour under high atmospheric pressure

We have a spring inside a chamber. We compress the spring and then let it decompress freely. Will its decompression (its speed and displacement) be the same if the air pressure of the chamber is $1\;\mathrm{atm}$ or $3000\;\mathrm{atm}$? If not, how will it be affected?

• What do you reckon? – lemon Jul 22 '16 at 8:50
• Won't be affected. – Deep Jul 22 '16 at 11:35
• I reckon it WILL be affected. It will depend on the thickness of the spring, the more thickness, the more drag will be. And in extreme pressure, this drag is substantial. – ergon Jul 22 '16 at 11:45

In 3000atm it's speed of decompression will be slower because it is facing greater air density and the expanding spring has to move it. There will also be less "resonance" as the denser air damps the spring movement.

# Damping

The density of atmospheric air is approximately 1.225 kg/m$^3$. At 3000 atm, the density would be 3675 kg/m$^3$ compared to the density of water of 1000 kg/m$^3$. I don't know the viscosity of high density air, but as @DirkBruere answered, it could be a significant factor in the damping of the spring decompression.

The relative difference in decompression speed would depend on the spring stiffness. For example the motion of a slinky would be affected in a major way, but the motion of a car suspension spring might be similar in either environment.

# Stiffness Change

Another factor to consider is the deformation of the spring due to the high pressures at its surface. 3000 atm is approximately 44,000 psi. That is likely enough to deform the steel cross section, making a difference in the spring stiffness.

• how many kilograms per square centimeter is 3000 atm? – ergon Jul 22 '16 at 15:03
• @ergon: Pressure is force/area. You are asking for mass/area, which doesn't make sense. If it helps, 1 atm is 101,325 Pascals. – James Jul 22 '16 at 15:13
• I don't think the air density is correctly calculated for 3000 atm. That is high above the critical pressure of air (38 atm) where the ideal gas formula is no longer valid. – mpv Sep 28 '17 at 15:33