problem

Discussion in 'Physics' started by braddy, Jan 20, 2006.

Dec 29, 2004
83
0
Hi,
I am lost with this problem.

A bottle containig air is closed with a watertight yet smoothly moving piston. The bottle with its air has a total mass of 0.30kg. At the surface of a body of water whose temperature is a uniform 285 K throughout, the volume of air contained in the bottle is 1.5L.
Recall that the pressure of water increases with depth below the surface, D, as p=po+ρ *g*D, where po is the surface pressure and ρ=1.0 kg/L.
The bottle is submerged.

a- What is the volume of the air in the bottle as a function of depth?
b- Calculate the buoyant force on the bottle as a function of depth?

There are other questions but I need to understand thoses first.

B

2. CoulombMagician Active Member

Jan 10, 2006
37
0
a) Boyle's law P*V/T = constant. T is constant here so at a depth D the pressure is p and the piston compresses the gas inside until the internal pressure is also p. At this point the new volume V is

V = V0*p0/p = (p0/p)*1.5L

B) The bouyant force is the weight of the displaced water less the weight of the bottle

F = 1.0kg/L * 1.5L * (p0/p) -0.3kg

When Archimedes discovered this principle while he was bathing he was reportedly so excited that he ran naked thorough the city streets.

Dec 29, 2004
83
0
Thank you,
I understand your reasonning but how can we find the p0??

4. CoulombMagician Active Member

Jan 10, 2006
37
0
It is one atmosphere, ~15 psi if my memory is working.

Dec 29, 2004
83
0
OK thanks CoulombMagician!