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!

A floating metal tube

  1. Mar 4, 2005 #1
    A hollow steel tube (diameter = 3.84 cm) is sealed at one end and loaded with lead shot to give a total mass of 0.161 kg. When the tube is floated in pure water, what is the depth, z, of its bottom end? :rofl:
     
  2. jcsd
  3. Mar 4, 2005 #2

    xanthym

    User Avatar
    Science Advisor

    The hollow tube will experience a Buoyant Force due to displaced liquid given by Archimedes' Principle:
    {Buoyant Force} = ρgV
    where ρ is the liquid density, g the gravitational acceleration, and V the displaced liquid volume.

    The tube will sink into the water until its sealed end reaches an equilibrium position where the buoyant force described above exactly equals the tube's weight "mg" on land. If the tube's sealed end sinks to a depth "z", the displaced liquid volume will be:
    V = πr2z
    so the equilibrium condition is satisfied by:
    mg = {Buoyant Force} = ρgV = ρgπr2z
    ⇒ z = m/(πr2ρ)
    For this problem, {m = 0.161 kg}, {r = (3.84 cm)/2 = 0.0192 m}, and {ρ = 1.0 g/cm^3 = 1000 kg/m^3}, so that:
    z = (0.161)/{π(0.0192)2(1000)}
    z = (0.139 m)



    ~~
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A floating metal tube
  1. Will it float? (Replies: 4)

  2. Buoyancy and floating (Replies: 5)

  3. Floating iceberg (Replies: 7)

Loading...