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Math Help - Wedge problem

  1. #1
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    Wedge problem

    Hi,

    Can anyone help with this question please:

    A block of mass m = 3kg and a wedge of mass M = 2kg lay on a frictionless plane. The wedge has width l = √ 3 m and height h = 1m. At t = 0 the block is at distance d = 3m from the wedge and it is hit sharply and set in motion with velocity v = 2 m/s towards the wedge.

    (pic attached)

    Assuming that there is no friction between the block and the wedge:

    a) Compute the maximum height reached by the block on the wedge and the velocity of the wedge at the time when height is reached.
    b) Determine the final state of the system. How long does it take to reach this state?

    I'm lost with this one. Would appreciate any help.

    Thanks
    Attached Thumbnails Attached Thumbnails Wedge problem-wedge.bmp  
    Last edited by jackiemoon; February 10th 2009 at 01:31 PM. Reason: Forgot attachment
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  2. #2
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    Quote Originally Posted by jackiemoon View Post
    Hi,

    Can anyone help with this question please:

    A block of mass m = 3kg and a wedge of mass M = 2kg lay on a frictionless plane. The wedge has width l = √ 3 m and height h = 1m. At t = 0 the block is at distance d = 3m from the wedge and it is hit sharply and set in motion with velocity v = 2 m/s towards the wedge.

    Assuming that there is no friction between the block and the wedge:

    a) Compute the maximum height reached by the block on the wedge and the velocity of the wedge at the time when height is reached.
    b) Determine the final state of the system. How long does it take to reach this state?
    so m > M ... ?

    no matter.

    (a) when the block reaches its height position on the wedge, the block and wedge will be moving at the same velocity. momentum and energy are conserved ...

    mv_o = (m+M)v_f

    solve for v_f


    \frac{1}{2}mv_o^2 = \frac{1}{2}(m+M)v_f^2 + mgh_{max}

    solve for h_{max}


    (b) after the block reaches its highest point, it will slide back down the incline and the end result is like that of an elastic collision.

    momentum is conserved ...

    mv_{1o} = mv_{1f} + Mv_{2f}

    since the collision is elastic, the initial and final velocities have the relationship ...

    v_{1o} = v_{2f} - v_{1f}

    use both equations to solve for v_{2f} and v_{1f}
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