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The Hydrostatic problem

  1. Feb 22, 2008 #1
    1. The problem statement, all variables and given/known data

    A uniform ball of radius r = 0,3m swim in the water so the half of the ball is in the water. What is the work W required to pull out the ball from the water. (You can assume that the density of the water is ρ = 1000 kg/m³, the acceleration of gravity g = 9,81 m/s², ignore air and fluid resistance).

    2. Relevant equations
    - According to hydrostatic law and equilibrium's law the weight force G = mg is equal to lift force F = Vρg, V is volume of the ball inside the water, V =2/3r³π.

    G =2/3r³πρg .

    - Work W is W = ʃ[mg - ρg(πh²R - 1/3πh³)]dh, (h =0 to h = r)
    Expression πh²R - 1/3πh³ represent the volume of ball immersed in water during the process of pulling out the ball.

    3. The attempt at a solution

    - W =7/12r³πρgr.
    W = 145,54J.
    Last edited: Feb 22, 2008
  2. jcsd
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