Rolling ball

  1. Sep 2, 2008 #1
    Q: A ball is at rest on an inclined plane. It begins to roll down with an acceleration of 2 m/s^2. How long does it take the ball to roll 50 m?

    This is my work:

    find time using, s = ut + 1/2 a t^2

    t = sqrt(2s/a)

    Plug in the s = 50 and a = 2

    Am I right?

    Thanks a lot.
     
  2. jcsd
  3. Sep 2, 2008 #2

    HallsofIvy

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    Where have you used the fact that this is a rolling ball and not a falling mass point? In particular, you have not taken into account the rotational kinetic energy.
     
  4. Sep 2, 2008 #3
    Thanks for your reply.

    A falling object accelerates with acceleration of gravity, g. Here the given acceleration, as I understand, is the acceleration of the center of mass (linear acceleration). Even though the ball is rolling, C.M is moving in a straight line along the incline so that we can use the equation of kinematics.

    Conservation of energy gives me an expression for the final velocity as a function of initial height of the ball above the ground, and will not allow me to find the time of travel.
     
  5. Sep 2, 2008 #4

    LowlyPion

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    That is correct. Your approach looks correct for this problem.
    X = 1/2 a t2 in this case because you are given its constant acceleration.
     
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