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Homework Help: Question on Archimedes principle.

  1. Dec 16, 2011 #1
    1. The problem statement, all variables and given/known data

    A solid sphere of mass m=2 kilogram and specific gravity s=0.5 is held stationary to a tank as shown in figure. The tank is accelerating upward with a=2ms-2. calculate the tension in the string? If suddenly string break then the acceleration of the ball in frame of tank.
    2. Relevant equations

    Archimedes principle

    3. The attempt at a solution
    see in attachment.
    for second question. My answer is
    net force =B-mg=20 so acceleration in frame of ground is 10. In frame it should 10-2=8.

    Attached Files:

    Last edited: Dec 16, 2011
  2. jcsd
  3. Dec 16, 2011 #2


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    Hi Vkash,
    What is your question?

  4. Dec 16, 2011 #3
    I have tried to answer these questions. Where am i wrong.
  5. Dec 16, 2011 #4


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    The problem is easiest to solve if you use the accelerating frame of reference, fixed to the tank. Have you learnt about accelerating frames of reference? You feel heavier in a lift which accelerates upward as if the gravitational acceleration g would be bigger. And you feel lighter in a frame of reference accelerating downward. In a falling lift you are weightless.

    Buoyant force arises because of the weight of the liquid. In a falling tank, there would be no buoyant force. You could immerse any object into the liquid, it would stay at the same place.
    This tank accelerates upward with a=2 m/s^2. Everything feels heavier, as if the gravitational constant would be g'=g+2 instead of 10 m/s^2. Even the buoyant force will be larger than in the tank in rest.

    Can you proceed?

  6. Dec 16, 2011 #5
    yes i have read this in starting mechanics.(working with non inertial frame of reference)
    In your way.
    Is it correct?

    if string is snapped.
    answer of second question.
  7. Dec 16, 2011 #6


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    I hope It will be OK if you calculate the buoyant force correctly.

  8. Dec 16, 2011 #7
    volume of ball is 2/500=4*10-3
    here i did it wrong.
    It should B=(4*10-3)*(10+2)*(1000)
    thanks ehild. I got the mistake.
  9. Dec 16, 2011 #8


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    Well done!

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