1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Archimedes' principle

  1. Jan 4, 2005 #1
    A ball of mass m_b and volume V is lowered on a string into a fluid of density p_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? Express your answer (T) in terms of the given quantities and g , the acceleration due to gravity.


    Although the fact may be obscured by the presence of a liquid, the basic condition for equilibrium still holds: The net force on the ball must be zero.

    Here are the steps that I went through:
    Compute the mass m_f of the fluid displaced by the object when it is entirely submerged.
    Express your answer in terms of p_f, v, m_b, and g.

    m_f = p_f*V

    f_buoyant = p_f* V * g

    How do I get from here to finding the tension?

    Thanks.
     
  2. jcsd
  3. Jan 4, 2005 #2

    Doc Al

    User Avatar

    Staff: Mentor

    As the problem states: The net force on the ball must be zero. So what are the forces acting on the ball? (Hint: Three forces act on the ball.)
     
  4. Jan 4, 2005 #3
    Tension of string, m_b*g, and F_buoyancy?
     
  5. Jan 4, 2005 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Right. Now write the equation that relates them and solve for Tension.
     
  6. Jan 4, 2005 #5
    So these 3 forces must add up to 0?
    I don't think this is right (both the signs and equation I'm unsure of), but would it be

    F_T + m_b*g + p_f* V * g (F_buo) = 0, where p_f = m_f/V

    Then isolate F_T to solve for the answer?
     
  7. Jan 4, 2005 #6

    Doc Al

    User Avatar

    Staff: Mentor

    Yes, the forces add to 0. But don't forget that forces are vectors: Direction matters! (Which way do the forces act?) Be sure to use a consistent sign convention: For example, let forces acting upward be positive; downward, negative. Then rewrite your equation.
     
  8. Jan 4, 2005 #7
    The answer for F_T does not depend on m_f. What am I supposed to do now?

    What I did

    F_t - (m_b*g) + f_buo = 0

    F_T = (m_b*g) - F_buo , F_buo = g*m_f

    F_T = g(m_b - m_f)

    but this is wrong
     
    Last edited: Jan 4, 2005
  9. Jan 4, 2005 #8
    Never mind; got it! Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Archimedes' principle
  1. Archimede's Principle (Replies: 3)

  2. Archimedes Principle (Replies: 2)

  3. Archimedes' Principle (Replies: 3)

  4. Archimedes principle (Replies: 2)

Loading...