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Min. speed

  1. Oct 21, 2004 #1
    I'm not sure what formula to use on this?

    A ball of mass 15.9 g is attached to a cord of
    length 0.478 m and rotates in a vertical circle.
    The acceleration of gravity is 9.8 m/s^2

    What is the minimum speed the ball must
    have at the top of the circle so the cord does
    not become slack? Answer in units of m/s.
     
  2. jcsd
  3. Oct 21, 2004 #2
    For all your questions, please show us what you have tried first. Begin with a free-body diagram of the ball at the top of the circle.
     
  4. Oct 23, 2004 #3
    V min = Square root [(Ms)(g)(R)]

    =Square root (15.9)(0.478)(9.8)

    =Square root (74.48196)

    =8.63 m/s ?
     
  5. Oct 23, 2004 #4
    Now, remember...this is minumum speed...

    ....so the tension of the string is mimumum, or zero when the ball is at the top of its path (thus, only the force of gravity would equal the centripetal force.)

    With this knowledge, draw a free body diagram of the ball when it is on the top of the path....
     
    Last edited: Oct 23, 2004
  6. Oct 23, 2004 #5

    So would it be the square root of the radius times gravity?

    = square root (0.478)(9.8)

    = 2.16 m/s^2 ??
     
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