1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Finding an increase in depth, pressure and thrust

  1. Sep 14, 2013 #1
    1. The problem statement, all variables and given/known data
    A cylindrical tank of radius 4cm is partly filled with water.A solid metal sphere of radius 3cm is lowered into the water by means of a thin wire until it is totally immersed. Find the increase in
    (i) the depth
    (ii) the pressure at a point on the base
    (iii) the thrust on the base(in terms of π )

    2. Relevant equations
    Pressure = (depth)(g)(density)

    3. The attempt at a solution
    h = depth of water before sphere added

    Volume of water before sphere added = 16(π )(h)

    volume after sphere added = 16(π)(h) + (4/3)(π)(64)

    pressure = (1)gh (since the density of water is 1/cm^3)

    I'm not sure what to do next I'd presume I have to get the depth(h) somehow?
  2. jcsd
  3. Sep 14, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Check that second term on the right ...
  4. Sep 14, 2013 #3
    Oh sorry V = 16πh + (4/3)π(27) = 16πh + 36π

    I'm still not sure how to get the height
  5. Sep 14, 2013 #4
    Would this be correct?
    V = volume after sphere is added

    V = 16πh +36π

    but V also = 16π(x+h) ........... where x is the additional depth the water has risen)

    16π(x+h) = 16πh + 36π

    16πx + 16πh = 16πh +36π ............ 16πh cancels

    16πx = 36π

    x = 36/16 =2.25 cm

    (ii) convert to kg/m^3 and meters so our answer will be in pascals

    1000g(0.0225+h) - 1000gh = 1000g(0.0225) +1000gh - 1000gh = 22.5g Pa

    (iii) F = 22.5g(16π) = 360πg N

    (these are the answers my book gives)
    Last edited: Sep 14, 2013
  6. Sep 14, 2013 #5

    rude man

    User Avatar
    Homework Helper
    Gold Member

    OK but you should include g = 9.8 in your answer.

    I also advise using Rt and Rs for radius of the tank and sphere instead of the number, until the very end. That way you can check units term-by-term as you go along.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted