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!

Bouyant Force problem

  1. Jan 3, 2010 #1
    AP physics B problem- Buoyant Forces?


    A slab of ice floats on a freshwater lake. What is the minimum volume of the slab such that a 70 kg man can stand on it without getting his feet wet? The density of ice is 0.922 kg/m^3 and the density of freshwater is 1,000 kg/m^3

    I have gotten to mass(ice) + mass(person) = Density of water x volume submerged

    From there I have two unknown variables I am at a loss
     
  2. jcsd
  3. Jan 3, 2010 #2

    diazona

    User Avatar
    Homework Helper

    Your unknown variables are the mass of the ice and the volume of the ice, right? What other equation relates them to each other?
     
  4. Jan 3, 2010 #3

    Doc Al

    User Avatar

    Staff: Mentor

    Hint: How does the volume submerged relate to the volume of ice?
     
  5. Jan 3, 2010 #4
    density = mass/volume , but I only know the density. Also the volume submerged would equal the total volume, but I don't know where to go with that....
     
  6. Jan 3, 2010 #5

    Doc Al

    User Avatar

    Staff: Mentor

    Good. Express the mass of the ice in terms of its volume.
     
  7. Jan 3, 2010 #6
    so density= m/v so m=density x volunme submerged, but how would that help you if you don't know the volume submerged.
     
  8. Jan 3, 2010 #7

    Doc Al

    User Avatar

    Staff: Mentor

    The volume is what you are trying to find.
     
  9. Jan 3, 2010 #8
    so volume submerged = m/density (sorry if I'm a little slow at this I'm not really great at physics) how would you solve that if you only know the density... You still have two unknown variables
     
  10. Jan 3, 2010 #9

    Doc Al

    User Avatar

    Staff: Mentor

    Use the definition of density to rewrite the equation you gave in post #1 completely in terms of volume, not mass. You'll only have one variable.
     
  11. Jan 3, 2010 #10
    so you would end up with mass of ice + mass of person = density of water x (mass of ice/ density of ice)

    so you would just simplify it from there, but how would you do that

    [ m(i) + m(p) ] / density of water= m/ density of ice

    how would you get both onto one side?
     
    Last edited: Jan 3, 2010
  12. Jan 3, 2010 #11
    thank you by the way :-) You're a huge help
     
  13. Jan 3, 2010 #12

    Doc Al

    User Avatar

    Staff: Mentor

    Start with your original equation:
    Replace each mass with its equivalent in terms of density and volume.
     
  14. Jan 3, 2010 #13
    densityof ice(volume ice) + 70 = Density of water x volume submerged

    I cant seperate the mass into volume and density of the person because I don't know either of those
     
  15. Jan 3, 2010 #14

    Doc Al

    User Avatar

    Staff: Mentor

    Perfect. Now you can solve for the volume. (Remember your answer to my question in post #3.)

    Skip that one--my mistake. :uhh: You already know the person's mass.
     
  16. Jan 3, 2010 #15
    so [ density of ice(volume ice) + 70 ] / density of water= volume of ice
    how would you divide it with the seventy still there
     
  17. Jan 3, 2010 #16

    Doc Al

    User Avatar

    Staff: Mentor

    No. Go back to the previous equation and collect all terms with volume to one side. Then you can isolate the volume and solve for it.
     
  18. Jan 3, 2010 #17
    70 = Density of water (volume ice) + density of ice(volume ice)

    70= volume of ice(density of water +density of ice)

    would that be right?
     
  19. Jan 3, 2010 #18

    Doc Al

    User Avatar

    Staff: Mentor

    Almost. But you messed up a sign when you moved a term from left to right.
     
  20. Jan 3, 2010 #19
    70= volume of ice(density of water - density of ice)

    so from there you would just simplify

    ohhhhh I get it.

    Thanks you so much you were a huge help
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Bouyant Force problem
  1. Bouyant Force (Replies: 5)

  2. Bouyant force (Replies: 3)

  3. Bouyant Problems (Replies: 10)

  4. Bouyant Force Problem (Replies: 3)

Loading...