problem

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

  1. braddy

    Thread Starter Well-Known Member

    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.
     
  3. braddy

    Thread Starter Well-Known Member

    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.
     
  5. braddy

    Thread Starter Well-Known Member

    Dec 29, 2004
    83
    0
    OK thanks CoulombMagician!
     
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