Little physics problem

[Thomas Okken]

(07-26-2018 06:38 PM)Joe Horn Wrote:  Doesn't the answer depend on whether the object is airtight (like a glass sphere or submarine) or open to the air (like normal boats)?

It can get even more complicated than that: scuba divers maintain their depth using a Buoyancy Control Device, BCD for short, which is an inflatable life-jacket like device worn on the torso. They can increase their buoyancy by letting air into the BCD from their air tank, and reduce their buoyancy by letting air out, releasing it into the water.

So, the BCD is like the swim bladder that fish use to control their buoyancy.

The tricky bit is that the BCD provides an unstable equilibrium: if you go up, whether by swimming or by being pushed up by a current, the BCD will expand, because the air inside it is more compressible than the water, and so you become more buoyant, making you tend to rise even further. And when you go down, the air in the BCD gets compressed more than the water, making you less buoyant, and thus tending to sink even lower.

This is similar to how weather balloons can reach such high altitudes: they are barely buoyant when they are launched, but the higher they go, the more they expand, because of the lower pressure.

Both systems would reach a stable equilibrium altitude or depth, if they were rigid. Being airtight is not a sufficient condition for reaching a stable equilibrium.