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Vertical Circular Motion Problem

  1. Dec 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Circular Motion.PNG
    2. Relevant equations
    Centripetal Acceleration = v2/r
    Fnet = ΣF
    3. The attempt at a solution
    The block exerts a force W equal to its weight on the box at the top most position.
    This upward W minus W downwards and an unknown F downwards equals a net Fc downwards. So F equals Fc

    At the bottom position there is a W downwards and the total force on the box is this W plus something else
    The net force is Fc upwards since the speed is constant

    Now I get completely confused.
     
  2. jcsd
  3. Dec 5, 2014 #2

    ehild

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    What is the direction of the force the stone applies at the box? What is the force the box exerts on the stone? So what is your unknown force???
    That "something else " is the normal force from the block, the block exerts on the stone.
     
  4. Dec 5, 2014 #3
    What if I think in terms of pseudo force? The pseudo force at the top position is the centripetal force upwards, so the force exerted by the stone on the box is
    Fc - mg = mg
    => Fc = 2mg

    At the bottom position, pseudo force is downwards, along with mg. So the force by the stone on the box is 3mg. But the answer is 7mg :(
     
  5. Dec 5, 2014 #4

    ehild

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    You make yourself confused with the pseudo force. It is not the centripetal force. Use inertial frame of reference. The stone moves together with the box along a circle. It needs the appropriate centripetal force. The centripetal force is the resultant of two forces, what are they at the top of the circle?
     
  6. Dec 5, 2014 #5
    I think at the top its (mg - N). But isn't there also an mg downwards? And isn't the normal force self adjusting?

    Um, can you tell me how the normal force varies as the box goes around the circle?
     
  7. Dec 5, 2014 #6

    haruspex

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    Yes, it adjusts as necessary to keep the stone moving in the circle - as long as that does not involve its going negative.
    You think the resultant is that?
    I think you may be getting confused by the happenstance that the normal force equals mg here. Set that aside for the moment and just label it N. Which way does N act at the top? Which way does the weight mg act at the top?
     
  8. Dec 5, 2014 #7

    ehild

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    The picture shows the box touching the stone on the upper side. The box can only push the stone, in what direction? Up or down?
     
  9. Dec 5, 2014 #8
    You're not told that there are external forces acting on the circle. In addition to what has been already said, it can be helpful to think about it in terms of a conserved quantity.

    I don't see a reason to assume that the velocity is constant as the problem says.
     
  10. Dec 5, 2014 #9

    ehild

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    The normal force would be 3mg in case of constant speed. If case of conservation of energy, the normal force would be 7mg.
     
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