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Aluminium covered with gold submerged into water

  1. Jan 15, 2015 #1
    1. The problem statement, all variables and given/known data

    A piece of aluminum is completely covered with a gold shell to form an
    object of weight W. When you suspend the object from a spring balance
    and submerge it in water, the balance reads T. The density of water,
    aluminum and gold is ρw, ρa, and ρg, respectively. The gravitational
    acceleration is g.

    What is the weight of the gold covering the object? Express
    your answer in the given constants.

    2. Relevant equations

    m/V = Ro

    3. The attempt at a solution
    I don't know where to start
     
    Last edited: Jan 15, 2015
  2. jcsd
  3. Jan 15, 2015 #2

    Borg

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    Artj0m, Welcome to PF! What formulas do you know that relate density to weight?
     
  4. Jan 15, 2015 #3
    m/v = ρ
     
  5. Jan 15, 2015 #4

    Borg

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    OK. Let's ignore the gold for now to make the problem simplier. If you put the aluminum in the water, what happens to the volumn of the water? Do you see a possible relation that you can work with?
     
  6. Jan 15, 2015 #5
    Yes, the buoyancy. I understand the concept, but the problem is that I eventually have to separate the two metals.
     
  7. Jan 15, 2015 #6

    Borg

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    In order to solve the final equation, yes. Let's ignore W (and the gold) for now though.
    When the aluminum is put into the water, the water level will rise. What do you think the relationship is for the increased water level w.r.t. the aluminum?
     
    Last edited: Jan 15, 2015
  8. Jan 15, 2015 #7
    The amount of volume the water rises is equal to the volume of the object.
    That I understand.
    I'm just having troubles with writing a good equation.
     
  9. Jan 15, 2015 #8

    NascentOxygen

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    So, what is the upward bouyancy force you can attribute to this volume, V, of displaced water? What is the formula?
     
  10. Jan 15, 2015 #9

    Borg

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    What is the relationship between the Vw increase and Va? Can you apply your formula from post 3 to gain more info?
     
  11. Jan 15, 2015 #10
    If I apply the formula, I know that Vw = mw / ρw = malu / ρw

    Because of the Buoyancy, B = Walu = mw * g = malu * g
    So mw = malu
     
  12. Jan 15, 2015 #11

    Borg

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    Are you sure about this part? Typo?
     
  13. Jan 15, 2015 #12
    The piece of aluminum covered with a gold shell is in equilibrium so:

    T=W-(ρw*V*g)
     
  14. Jan 15, 2015 #13

    Borg

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  15. Jan 15, 2015 #14

    Borg

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    @Daan Janssen - The goal of the homework section isn't to give people the answers. It's to guide them to the answer so that they understand how to solve it for themselves.
     
  16. Jan 15, 2015 #15
    Yes, sorry, I do understand that. I myself, just as Artj0m, don't know how to get to the answer. It is just there to insure we get the right answer out of it.

    I've really been trying and I know I am very close to the right answer. I'm hoping you could guide us to it
     
  17. Jan 15, 2015 #16

    Borg

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    OK. However, I think that your answer is wrong.
     
  18. Jan 15, 2015 #17
    The answer was taken out of a correction sheet from Eindhoven University. The Question was part of a final exam. I doubt that it would be wrong. It could still be ofcourse :p
     
  19. Jan 15, 2015 #18

    Borg

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    It wouldn't be the first time that I was wrong. I'm having someone check my work before I guide you both down the wrong path.
     
  20. Jan 15, 2015 #19
    Daan, although that is correct, that is not what the question is asking for. Artjom, I think you may have summed your forces incorrectly. Do you draw force diagrams? I find that drawing a diagram really helps me get the forces right.
     
  21. Jan 16, 2015 #20

    NascentOxygen

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    Without the water, the spring balance will record the full weight of the metal. Dipping the metal into water reduces the balance reading. You should be able to come up with an equation involving expressions for these components.
     
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