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Force Exerted Non-Uniform Circular Motion

  1. Dec 9, 2014 #1
    1. The problem statement, all variables and given/known data
    A bucket of water (10kg) is swung vertically. Radius is 1 m. It takes 1 second to spin the bucket in a full circle.
    a. How much force has to be exerted at the top of its motion?
    b. How much force must be exerted at the bottom?

    2. Relevant equations
    vtop=sqrt(gr)
    top: Ftension= mv2/r - mg
    bottom: Ftension= mv2/r + mg
    ac=v2/r

    3. The attempt at a solution
    This is a fairly straightforward question, but I'm getting different answers. I'm not sure if this exerted force means the same thing as force of tension. If so, then I have force at the top = 0 N, force at the bottom is 588 N.
    If v=sqrt (9.8) as the minimum velocity at the top, then conservation of energy gives 1/2mv2top+mg2r=1/2mv2bottom.
    Thus, velocity at the bottom of the bucket's motion is 7 m/s. Using the equation F=mv2/r+mg, I get the 588 N answer.
    However, when I initially completed this in class, I was told that 490 N was the correct answer for part b. Does this somehow have to do with the 1 second time provided in the original problem, such as assuming constant velocity? I've been thinking over this for quite a while and I just keep getting more confused.
    Thanks for any help in advance!
     
  2. jcsd
  3. Dec 9, 2014 #2

    haruspex

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    Yes.

    You are not told it is the minimum speed to maintain circular motion, so you've no basis for saying the tension is 0 there.

    Yes.
    No, it won't be constant velocity.
    Start again, but taking the tension at the top to be some unknown value. Derive everything else in terms of that, including the time to complete a swing (that's the hard bit). Then set that time equal to 1.
     
  4. Dec 9, 2014 #3
    Okay, so if I use 1/2mv2top+mg2r=1/2mv^2bottom, and top: Ftension= mv2/r - mg bottom: Ftension= mv2/r + mg I get Tension at bottom = mv^2(top)/r+4mg/r+mg, which simplifies to Tbottom=Ttop + 6mg.

    As for the time, I'm not really sure what to do with that. T=2*pi*r/v, but that is constant velocity.

    I used a vertical circular motion simulator to help me visualize the situation, but it returns tension at the top as -296.78 N. Is this even possible?
     
    Last edited: Dec 9, 2014
  5. Dec 9, 2014 #4

    haruspex

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    Correct.
    Hint: SHM.
    Depends what sign convention was used. If up is positive and you asked for the force on the bucket exerted by the tension then it will be negative.
     
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