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Homework Help: Fluid Questions

  1. Mar 27, 2010 #1
    1. The problem statement, all variables and given/known data
    A metal object is suspended from a spring scale. The scale reads 920 N when the object is suspended in air, and 750 N when the object is completely submerged in water.

    a. Find the volume of the object.
    b. Find the density of the metal.

    2. Relevant equations
    d=m/v or v=md or m=dv
    D of Water=1.00x103kg/m3

    3. The attempt at a solution

    Part A: v=md


    Honestly, I'm fairly sure that ^ is completely wrong... :uhh:

    Part B: d=m/v

    I am completely lost..
  2. jcsd
  3. Mar 27, 2010 #2
    BUMP. Help please.
  4. Mar 27, 2010 #3
    Do you know about the buoyant force?
  5. Mar 27, 2010 #4
    I have an equation sheet which mentions it.

    Buoyant Force: Fbuoyant=DVg

    I know:
    Dh2o=1.00x10^3 kg/m^3
    g=9.80 m/s^2
  6. Mar 27, 2010 #5
    Okay, and you know that the buoyant force on a submerged body is directed in the opposite direction to gravity. It's always helpful to make a draw of what's really going on here.

    So now you should think about what does the Archimedes principle states:

    Real weight (920N) = apparent weight (measured as 750N) + weight of displaced fluid (buoyant force).

    If you work out the maths here, you will get the volume. Don't hesitate to ask if you're not sure though.
  7. Mar 27, 2010 #6
    Would I set it up like this?


    and solve for v?
    Last edited: Mar 27, 2010
  8. Mar 27, 2010 #7
    No, that's not the answer sorry.

    I just gave you the equation that you have to use to work out the volume. It's not that tedious to plug numbers in.

    950 = 720 + DVg

    Letting D be the density of the fluid...
  9. Mar 27, 2010 #8
    Oh haha, okay you got it yeah.
    And once you have the volume you can use the density equation (D = m/v) to get the density of the body.

    Hope it's clear ;)
  10. Mar 27, 2010 #9
    I got .0872 for v.
  11. Mar 27, 2010 #10
    What would I plug in for the mass?



    What would I plug in?
  12. Mar 27, 2010 #11
    Oh, when calculating the density, you should think that it is not important in which surroundings are you doing it, because rigid bodies will always have the same density. So for the density you should basically search what's the real mass of the body i.e.:

    real weight (920) = M(Kg) ยท g(9.81m/s^2)
  13. Mar 27, 2010 #12

    920/.0872 will give me Density? :confused:
  14. Mar 27, 2010 #13
    Nope, 920N is the weight. Weight and mass are two different things, the mass can be calculated as:

    M = weight/gravity

    Hence, M = 93.78Kg. Now you can plug this M in the density formula.
  15. Mar 27, 2010 #14
    So the answer Part B is:


    which equals 1075.458716 or 1.1x10^3?
  16. Mar 27, 2010 #15
    Is v= .0872 correct, by the way?
  17. Mar 27, 2010 #16
    As long as your volume was .0872, that should be right. But check that out concerning the volume:

    920-750 = 9.81 x 10^3 x V, are you sure that V is .0872?
  18. Mar 27, 2010 #17
    No, v definitely is not .0872.

    To find v do I set it up like this?

  19. Mar 27, 2010 #18
    V=.0173 is what I have now...
  20. Mar 27, 2010 #19
    Yeah, that's what I was wondering, I think you did some kind of algebra error or calculator typo, because I keep getting .0173 for the Volume.

    Check now for the density as:

    D = 93.78Kg / .0173m^3
  21. Mar 27, 2010 #20
  22. Mar 27, 2010 #21

    Part A: V=.0171 m^3
    Part B: D= 5.4x10^3

    Is this correct? Also, what unit would density be in?
  23. Mar 27, 2010 #22
    Yeah, that is numerically correct. Now for the units of the density, if we have:

    D = m/V, we should know that mass is in (Kg) and V in (m^3], so density is just (Kg/m^3).
  24. Mar 27, 2010 #23
    Thank you so much. :smile:
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