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Help with Archimedes' Principle

  1. Mar 1, 2009 #1
    1. The problem statement, all variables and given/known data

    A solid aluminum sphere has a radius of 1.84 m and a temperature of 77.5 °C. The sphere is then completely immersed in a pool of water whose temperature is 26.7 °C. The sphere cools, while the water temperature remains nearly at 26.7 °C, because the pool is very large. The sphere is weighed in the water immediately after being submerged (before it begins to cool) and then again after cooling to 26.7 °C. Use Archimedes' principle to find the magnitude of the difference between the weights.



    2. Relevant equations

    Volume of the sphere: (4/3) pi (R)^3
    V=26.094

    and change in volume: coefficient of volume expansion for aluminum (69 x 10^-6) * (Initial Volume: 26.094) * (Change in Temp: -50.8)
    = - .0915

    This is the other equation I have:
    difference in weight = -(density)(gravity)(volume)
    But the answer I get isn't right...


    3. The attempt at a solution

    I think everything I am doing is right up until the part about finding the difference in weights. I don't know what equation to use, or how to use it I guess. Any help would be appreciated.
     
  2. jcsd
  3. Mar 1, 2009 #2

    mgb_phys

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    Remember the difference in volume leads to a different upthrust because of the different amount of water displaced - the mass of the Al sphere doesn't change.
     
  4. Mar 1, 2009 #3
    So, are you saying that the difference between the weights would be zero? I thought that would make sense, but I tried that also (although I thought it seemed too easy) and the homework tool said it wasn't right... all I know is the units are newtons ...
     
  5. Mar 2, 2009 #4

    mgb_phys

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    No the weight would be different because the shrunk ball would displace less water and so receive less upthrust and so weigh more.
    But the difference in volume corresponds to a different amount of water - not a different amount of Al so it is the density of water not Al that you need.
     
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