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Homework Help: Rolling ball hits sphere

  1. Apr 15, 2009 #1
    A uniform solid sphere of radius R and massM rolls without slipping on
    a horizontal plane. The centre of mass of the sphere moves initially with
    velocity ~v directed perpendicularly to a fixed block of height h < R.
    The sphere hits the block and the collision is such that the point P on
    the sphere which touches the block does not slip and remains in contact
    with the block until the sphere starts rolling on top of the block. See
    figure below

    a) Compute the initial kinetic energy of the sphere and its angular
    momentum with respect to the point P.
    [Notice: The angular momentum is a vector, so it is characterised
    by its length and direction.]
    b) Determine the minimum value, vmin, of the initial speed of the
    centre of mass of the sphere, which allows it to climb over the block
    (express the result in terms of the parameters of the problem and
    the gravitational acceleration g).
    c) Assuming that the initial velocity of the centre of mass is greater
    than the vmin found in (b), compute the amount of mechanical
    energy dissipated in the process.
    Why is energy not conserved?

    Hi guys.

    So I got the first bit. I think K is just equal to sum of translational and rotational energies- that is K=1/2Mv^2+2/5MR^2. and then using the P-A theorem find the angular momentum to be 7/5MVR.

    I'm not so sure how to go about the second part though. I got v=gsqrth^2-2hr but don't think this is right.

    any help appreciated!
  2. jcsd
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