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!

Need Help finding radius of ball using bouyancy

  1. Nov 11, 2007 #1
    1. The problem statement, all variables and given/known data
    An iron ball is suspended by a thread of negligible mass from an upright cylinder that floats partially submerged in water. The cylinder has a height of 6.00cm, a face area A=12.0 cm^2 on the top and bottom, and a density [tex]\rho_c=.300\frac{g}{cm^3}[/tex], and 2.00 cm of its height is above the water. What is the radius of the ball?

    2. Relevant equations [tex]\sum F=0[/tex] [tex]F_b=\rho*V*g[/tex]
    Using Newton's Second and Archimedes' Principle I have used the following method. My concern comes at the point that I get the expression (V'-V)<-- this will yeild a NEGATIVE quantity and r cannot = negative. My problem is that the V'=volume of water displaced and V= volume of the cylinder. I think I need to assume that the CYLINDER IS HOLLOW in order to get a positive quantity. But whay is the volume of a hollow cylinder if I am not given an inner and outer radius??

    3. The attempt at a solution

    Subscript c is cylinder, b is the ball, and V' is the portion of the cylinder under water.

    [tex]\sum F=0[/tex]

    [tex]\Rightarrow W_c+W_b-F_{bouyant}=0[/tex]

    [tex]\Rightarrow m_cg+m_bg-\rho_cV_c'g=0[/tex]

    [tex]\Rightarrow \rho_cV_c+\rho_bV_b=\rho_cV_c'[/tex]

    [tex]\Rightarrow V_b=\frac{\rho_c(V_c'-V_c)}{\rho_b}[/tex]

    I don't find it necessary to move any further than this last step as finding the r is easy enough from there. However it is in this last step that you can see that if I use
    V=height*cross-sectional area...I will get a negative number for V'-V.

    What should I be using for V? Shoud it be zero? I think that is a bold assumption, or is it?

    Thank you,

    Edit: After looking at my diagram, I have encountered another problem: Do I need to consider the bouyant force on the ball, too?

    I do not not see why I wouldn't.

    Okay. I also noticed that for F_bouyant I should have used rho_water NOT of the cylinder.

    Guess I need to re-work this. :( So I guess in re-working this my question is still: do I need to consider the bouyant force on the ball, too?
    Last edited: Nov 11, 2007
  2. jcsd
  3. Nov 11, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I think the problem is that you're multiplying V'c by the density of the cylinder and not the density of water which is what you need to do for the buoyant force.
  4. Nov 11, 2007 #3
    Yeah Kurdt, I just caught that. But tell me, should I be taking into account the Bouyant Force of the ball?

    See "Edits" in post #1.
  5. Nov 11, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Thats a good thought, and yes I would do that. Its not that much harder.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?