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Conceptual centripetal problem of a spinning ball attached to a string

  1. Jun 26, 2013 #1
    1. The problem statement, all variables and given/known data
    If you swing a ball in a vertical circle using a thin string, at the bottom of the circle the tension in the string must be greater than the ball's weight. True or false?


    2. Relevant equations
    F = mvv/r
    F = mg


    3. The attempt at a solution
    The correct answer, it says, it's true. But why isn't it false? Why can't the tension and the ball's weight have an equal magnitude of force?
    Is it because the "thin" string is also pushing down on the ball so the net weight is ball's weight + thin string weight?
     
  2. jcsd
  3. Jun 26, 2013 #2
    What is the speed of ball at the bottom?
     
  4. Jun 26, 2013 #3
    The exact value is not given but you can assume that the ball is in continuous rotation.
     
  5. Jun 26, 2013 #4

    WannabeNewton

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    What are the forces acting on the ball at the bottom? What sign should the acceleration of the ball be in order for it its trajectory to remain uniformly circular? Remember that something needs to accelerate the ball radially at each instant in an appropriate direction in order for its direction at each instant to change so as to maintain a circular trajectory.
     
  6. Jun 26, 2013 #5
    Forces acting on the ball: Tension and Gravitational force, in opposite direction.
    Sign: If we call the gravitational force negative, then the acceleration is positive. If the gravitational force is positive, then the acceleration is negative.
    So why does the magnitude of tension be greater than the weight? Why can't it be the same amount of force?
     
  7. Jun 26, 2013 #6

    haruspex

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    If they were the same, what would the vertical acceleration be? Is the vertical velocity changing at this point?
     
  8. Jun 26, 2013 #7
    Did you draw thw FBD of the ball. Once you draw the FBD, you will get the answer.
     
  9. Jun 27, 2013 #8
    I think this is right...

    True. At the bottom of the circle the net force must point upwards or otherwise center of circle. In order for this to happen, the gravitational force must be therefore less than the tension force exerted upwards.
     
  10. Jun 28, 2013 #9

    haruspex

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    Yes.
     
  11. Jun 28, 2013 #10
    Oh I see. Thx
     
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