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Buoyancy problem, please check my work

  1. Apr 13, 2004 #1
    Buoyancy problem, please check my work :)

    Can you check my work here?

    A crown is weighed in air and submerged in water. The scale reads 7.84 N in air and 6.86 N in water.
    find (a) the buoyant force (b) the volume of the crown (c) the density of the crown (d) is the crown made of gold?

    (a) 7.84-6.86=.98 N
    (b) Bouyant force=Volume(submerged object)*density(liquid) *gravity
    so .98=v*1000*9.8 V=.0001 m^3 (=.1 cm^3)
    (c) Density Object= (Weight object/Bouyant Force)*Density Liquid
    p=(7.84/.98)1000 ;p=8000 kg/m^3
    (d) I'm not sure the density of gold, I think its more than double this density though. So No, the crown is not made of Gold.

    Thanks for any help!!!
     
  2. jcsd
  3. Apr 13, 2004 #2
    Looks good to me! :smile:

    Quick search shows that "A cubic centimetre of gold will weighs 19.3 grams" so that makes the gold density 19,300 kg/m3.

    By the way, you don't have to use this equation to find the object density:

    [tex]\rho _o = \frac{W_o}{B}\rho _l[/tex]

    It's correct but the dependency on the density of the liquid is not needed, since:

    [tex]B\rho _o = W_o\rho _l[/tex]

    [tex]\rho _lv_og\rho _o = m_og\rho _l[/tex]

    So the liquid density cancels and you get:

    [tex]v_o\rho _o = m_o[/tex]

    Which is (amazingly :tongue:) exactly the defintion of mass density. :smile: You have the object's mass, since you know its weight in air.
     
    Last edited: Apr 13, 2004
  4. Apr 13, 2004 #3

    Doc Al

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    Staff: Mentor

    Looks good to me.
    Right.
    Right. (But 1 m^3 = 1,000,000 cm^3)
    Right. Though I'm used to the simpler "Density = Mass/Volume", what you've done is equivalent.
    Right. The density of gold is about 19,300 Kg/m^3

    Note: Chen, you beat me again! :mad:
     
  5. Apr 13, 2004 #4
    Tsk tsk. :wink:
     
  6. Apr 13, 2004 #5

    Doc Al

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    Staff: Mentor

    I'm getting old and slow, I guess. :biggrin:
     
  7. Apr 13, 2004 #6
    We both even said "Looks good to me". :tongue:

    mmmkay, enough monkey business now, gotta get back to studying Bible again. :frown:
     
  8. Apr 13, 2004 #7
    Awesome. Thanks a lot Chen and Doc Al. It's a great thing when people compete over helping you first. Haha. :biggrin: Thanks again.
     
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