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Homework Help: How to lift water out of a pool

  1. Jun 5, 2007 #1
    1. The problem statement, all variables and given/known data
    given, diameter and height of pool, depth of water, density of water and gravitational acceleration.
    g = 9.8
    height is 4m
    2r = 20m
    depth of water = 3.5m
    density =1000kg/m^3
    So, I'm supposed to find how much work is needed in joules to lift the water out of the pool.

    2. Relevant equations
    could I use density times gravity times volume to get my force?
    is my distance for my water to travel 4.5m?

    3. The attempt at a solution
    Anyways, I've tried to use my volume for the pool and the volume I have of water * density *gravity to come up with my force and then used 4.5m as my distance to come up with my work needed to lift water out of a pool. I ended up with 1.08E7 joules but that's incorrect so any help would be appreciated.

    BTW, this is a cal 2 problem/integration problem
  2. jcsd
  3. Jun 5, 2007 #2
    if it is a cal2/integration problem why aren't you doing any integration? do you know the formula for work?
  4. Jun 5, 2007 #3


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    Staff Emeritus
    Science Advisor

    Use the volume of the water and the density to get mass. It would appear that the pool is a right circular cyliner.

    Rasining a mass m some distance h in a gravity field producing a local acceleration g increases the potential energy by mgh.

    Well that depends, if one is lifting the CM of the pool water 4 m or (4 m + 1.75 m) or 5.75 m, which is 4 m from the top of the pool.
  5. Jun 5, 2007 #4
    I've tried integrating it and I've tried astronuc's advice with no success, any ideas?
    Last edited: Jun 5, 2007
  6. Jun 5, 2007 #5
    I'm retarded, integration works. Alright, so with a mixture of the advice, correct answer is 2474002 joules. Thanks again fellas.
  7. Jun 5, 2007 #6
    weight density = 9800 N/m^3

    work = integral {0 to 3.5} (9800)(pi*10^2)(4 - y)dy

    work = 2.4 * 10^7 Joules
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