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Homework Help: Determine acceleration when lifting a bucket.

  1. Apr 26, 2012 #1
    1. The problem statement, all variables and given/known data
    A bucket of water is raised up out of
    a well with a device of the rope, and
    pulleys as shown in figure. The bucket is hanging from the
    the lower hook and the upper hook is
    attached to a fixed cross bar of the well. If
    the mass of the bucket and the water together
    is m, and the man pulls the rope with
    a force F, how large is the span's acceleration
    up? The mass of ropes and pulleys
    can be neglected, as well as frictional forces.

    http://bayimg.com/daOdPAAde [Broken]

    Answer: (3F/m)-g

    2. Relevant equations

    F=mg and maybe F=ma

    3. The attempt at a solution

    Due to gravity there is a force downward. Since the mass of the bucket and the water together is m, the downward force is mg. From figure I see that the device is constructed so that the cable runs three times between the bucket and the hook before I pull it. Therefore the force required for the bucket to move upwards is F=mg/3≥.

    From here I am stuck. I know that F=ma and therefore a=F/m. However, if I insert F=mg/3 and m=mg, I get the wrong answer.
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Apr 26, 2012 #2
    You are forgetting about the weight. Acceleration is determined by the net force in F=ma.
  4. Apr 26, 2012 #3
    The weight as in F=mg. Please explain, I can´t really see what I am doing wrong.
  5. Apr 26, 2012 #4
    The force up is 3F. What is the force down? You are considering it as if the bucket full of water were sitting on a frictionless horizontal surface and you are pulling it horizontally.
    Last edited: Apr 26, 2012
  6. Apr 26, 2012 #5
    I understand that the force upwards is 3F. And the force down is F=mg, caused by gravity. Is that right? How is now acceleration related. Well, F=ma, so 3F=3ma. From "you are forgetting about the weight", I understand it as 3ma-mg. So far so right? Sorry about my incompetence of the subject.
  7. Apr 26, 2012 #6
    The force up is 3F. The force down is mg. The net force is 3F-mg. The net force is what Newton's Second Law equates to the product of mass and acceleration. The mass is m not 3m.
  8. Apr 26, 2012 #7
    Thank you LawrenceC. It makes sense now.
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