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Archimedes Principle

  1. Jan 17, 2016 #1
    . The problem statement, all variables and given/known data
    A block oak weighs 90 N in air. A piece of lead weighs 130 N in water. The two weigh together 100N in water. Calculate the relative density of the wood.


    2. Relevant equations
    F=mxg
    F(archimedes)= density x Volume x g

    3. The attempt at a solution
    F (g)oak = 90 N
    F= mxg
    m= 90N/9.81 m/s2
    m= 9.17 gram
    Oak in water = 130-100 N =30 N
    Farchimedes oak = 90N-30N =60N
    60N =1000kg/m3 x V x 9.81 m/s2
    V=60N/9810
    V=0.00611
    Now that I have calculated V I can find density
    rho = 9.17kg/ 0.00611 m3
    density = 1499
    Relative density is 1499 /1000 kg/m3 = 1.499
    But the correct answer is 0.75
     
    Last edited by a moderator: Jan 17, 2016
  2. jcsd
  3. Jan 17, 2016 #2

    haruspex

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    Check your signs. In water, oak+lead=100N, while lead =130N.
     
  4. Jan 17, 2016 #3
    How to do find N Force of oak in water ??
     
  5. Jan 17, 2016 #4

    haruspex

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    Your method was ok but you made a mistake with the signs. Manipulate the two equations I wrote above.
     
  6. Jan 17, 2016 #5
    100+130?
     
  7. Jan 17, 2016 #6

    haruspex

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    Please, don't make wild guesses.
    If Ow+Lw=100 and Lw=130, what is Ow?
     
  8. Jan 17, 2016 #7
    Sorry /D its -30 so 90-(-30) = 120
     
  9. Jan 17, 2016 #8

    haruspex

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    Right. Does this get you to the right answer?
    (How do you interpret the weight of -30N?)
     
  10. Jan 17, 2016 #9
    Yes I just calculated it. Negative force means opposite direction . But i don't know in this context
     
  11. Jan 17, 2016 #10

    haruspex

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    If the wood were immersed in the water without being bound to the lead, what would happen?
     
  12. Jan 17, 2016 #11
    It floats ofcourse
     
  13. Jan 17, 2016 #12

    haruspex

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    Right, hence the negative net force.
     
  14. Jan 17, 2016 #13
    Oh I see . thank you very much :)
     
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