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Sliding Off A Semi-Circle

  1. Dec 5, 2006 #1
    1. The problem statement, all variables and given/known data
    A boy sits on top of an igloo shaped like a semi-circle of Radius R. He begins to slide down the semi-circle. At what height above the ground does the boy slide off the semi-circle? Assume g=9.8 m/s2, and no friction.
    http://img207.imageshack.us/img207/4010/probmd1.jpg [Broken]

    2. Relevant equations
    Conservation of energy? Or centrifugal force?

    3. The attempt at a solution
    Couldn't think of any starting points; tried conservation of energy, but failed. Answer is obviously in terms of R. Can anyone shed the light on this problem?
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Dec 5, 2006 #2


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    At each point you will need to consider how quickly the boy is moving around the exterior of the circle, and how much force on the boy directed towards the inside of the circle will be needed to keep him moving in a circle at that speed.
  4. Dec 5, 2006 #3
    I do not quite understand how I should break gravity into different vectors, or is it even the right approach finding the velocity? The force you are talking about is the centrifugal force right?
    But, my teachers seems to be hinting that conservation of energy is needed. Care to explain further?
  5. Dec 5, 2006 #4


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    Conservation of energy will tell you the speed of the boy at any height. The speed is related to the centripetal force required to stay in circular motion. Consider all of the forces acting on the boy and resolve them into components in the direction of motion (tangent to the circle until he separates from it) and perpendicular to the motion (the radial direction).
  6. Dec 6, 2006 #5


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    To give you a BIG hint:
    WHICH force acting on the boy will be zero when he slides off the semi-circle?
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