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Math Help - I can't seem to get this one...

  1. #1
    Junior Member
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    Jan 2008
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    I can't seem to get this one...

    A circular swimming pool has a diameter of 16 m, the sides are 4 m high, and the depth of the water is 2.5 m. How much work (in Joules) is required to pump all of the water over the side? (The acceleration due to gravity is 9.8 m/s^2 and the density of water is 1000 kg/m^3.)

    I keep getting 86000ish for an answer yet its not right, anyone have any method of solving this? Thanks
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  2. #2
    Oli
    Oli is offline
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    Apr 2008
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    The amount of potential energy you need to give to a mass to raise it h metres is mgh. i.e It is is linear in h.
    Therefore the amount of energy you need to give the water for the pool to raise it up to the lip of height 4 metres (remembering, the water at the top of the pool is easier to get out than the water at the bottom) is the same as if you were to lift all that same amount of water a height of 2.75 metres (the average height you need to raise the water). You can only do this calculation because potential energy is linear in h.
    Therefore the answer is
    2.75mg, where m is the total mass of the water, which is: 2.5*Pi*8^2*1000.

    So the answer should be:
    2.75*2.5*Pi*8^2*1000*9.8
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