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Homework Help: Buoyancy without density of fluid

  1. Nov 3, 2008 #1
    1. The problem statement, all variables and given/known data
    A ball of mass m_b and volume V is lowered on a string into a fluid of density rho_f. Assume that the object would sink to the bottom if it were not supported by the string.
    What is the tension T in the string when the ball is fully submerged but not touching the bottom?
    It claims that rho_f is not needed in the part representing buoyancy
    2. Relevant equations

    I think it should be:
    T=Fg - B
    where T is the force of tension and B is the buoyancy force.
    Fg=rho(object)*V*g
    B=rho_f*V*g
    therefore, T=mg - rho_f*V*g

    how can you not use rho_f in calculating the buoyancy force?

    3. The attempt at a solution
     
  2. jcsd
  3. Nov 3, 2008 #2

    mgb_phys

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    Science Advisor
    Homework Helper

    You need the density, unles you are going to quote the answer in terms of density.
    Imagine the fluid is air and a metal ball, if you change the fluid to water - then the tension in the string is going to change.
     
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