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Homework Help: Submerged Sphere in a Beaker

  1. Nov 15, 2008 #1
    A cylindrical beaker of height 0.100 {m} and negligible weight is filled to the brim with a fluid of density rho = 890 {kg/m}^3. When the beaker is placed on a scale, its weight is measured to be 1.00 {N}. (Intro 1 figure)

    A ball of density rho_b = 5000 {kg/m}^3 and volume V = 60.0 {cm}^3 is then submerged in the fluid, so that some of the fluid spills over the side of the beaker. The ball is held in place by a stiff rod of negligible volume and weight. Throughout the problem, assume the acceleration due to gravity is g = 9.81 {m/s}^2.

    Intro 1:

    Intro 2:

    Part A
    What is the weight W_b of the ball?
    Express your answer numerically in newtons.
    I got 2.94N

    Part B
    What is the reading W_2 of the scale when the ball is held in this submerged position? Assume that none of the water that spills over stays on the scale.
    Calculate your answer from the quantities given in the problem and express it numerically in newtons.
    I got 1 N

    Part C
    What is the force F_r applied to the ball by the rod? Take upward forces to be positive (e.g., if the force on the ball is downward, your answer should be negative).
    Express your answer numerically in newtons.

    I am lost for this one, is it just m_bg(1- rho_w/rho_c)?

    Part D
    The rod is now shortened and attached to the bottom of the beaker. The beaker is again filled with fluid, the ball is submerged and attached to the rod, and the beaker with fluid and submerged ball is placed on the scale. (Intro 2 figure)

    What weight W_3 does the scale now show?
    Express your answer numerically in newtons.

    Please help, this is due really soon.
  2. jcsd
  3. Nov 15, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor


    I'm not sure what rho_w & rho_c refer to. In any case, consider the forces acting on the ball, one of which is F_r. What's the net force on the ball?

    What was added to the beaker? What was removed?
  4. Nov 21, 2008 #3
    Thanks man.
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