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Archimedes Principle question

  1. Nov 28, 2011 #1
    I have found a question that has got to my nerves :

    A block of wood of length 40 cm and area of cross-section 15 cm2 floats in water with 3/8 of it's length above water. What is the density of wood ? (Density of water - 1g/cm3).

    My attempt to get the solution :

    Length of wood above water = 3/8 * 40 = 15cm
    Length of wood below water = (40-15)cm = 25cm

    Now, Upthrust = 375cm3*1*10 = 3750 N

    Rest, I don't know !

    Please help. It's urgent because I am going to face some deadly questions the day after tomorrow. Thank You.
  2. jcsd
  3. Nov 28, 2011 #2
    When an object floats and is motionless, its weight exactly equals the upward thrust. The upward thrust is the weight of water displaced.

    If you know the weight and volume, you can determine the density.

    You have an error with your units. The upward thrust is not 3750 Newtons.
  4. Nov 28, 2011 #3
    Then what is it ?
  5. Nov 28, 2011 #4
    You are multiplying cm^3 by grams/cm^3. You do not get newtons. You get grams. A gram is not a unit of force. Newtons, however, are.

    I don't know the purpose of the 10.
    Last edited: Nov 28, 2011
  6. Nov 28, 2011 #5
    kg/m^3 times m^3 times gravitational acceleration(m/sec^2) = newtons

    g=9.8 m/sec^2
  7. Nov 28, 2011 #6
    alright , first u need to realize that the upthrust force = the wieght of the body....

    ie a floating object displaces it's own wieght of the fluid in which it is floating.

    so, F1 = upthrust = 0.0375 * 1000 * 10 = 375
    and F2 = weight of block = P*V*g =p*0.06*10

    so solving this ... my answer comes out to be 0.625g/cm^-3
  8. Nov 28, 2011 #7
    The upward force is equal to the weight of the water displaced by the body, not the displaced body.
  9. Nov 28, 2011 #8
    yes sir, u are right , but in this case aas the object is floating thus there has to be no net force (or otherwise it wud produce an acceleration)

    so, keeping newton's 2 nd law in mind, we can come to the conclusion that :

    upthrust = weight of the water displaced by the block of wood
    and as there is no acceleration hence
    upthrust = actuall weight of the block

    Please correct me if i am wrong :)
  10. Nov 28, 2011 #9
    I was correcting your language, not the physics. Yes there is an upward force, but it is not a net force. I never said the upward force was the net force.
  11. Nov 28, 2011 #10
    .625 gm/cm^3 is the correct result. It's density is 5/8 that of water because 3/8 of its volume remains above the surface of the water.
    Last edited: Nov 28, 2011
  12. Nov 28, 2011 #11
    I had a typo in my previous message. Originally I had typed .675 but meant to type .625 gm/cm^3. It has been corrected.
  13. Nov 28, 2011 #12
    Oh my god !! I have found the answer. Thanks everybody, thanks.
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