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: 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

    User Avatar

    Staff: Mentor

    Looks good to me.
    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

    User Avatar

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook