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Classical Mechanics - Block Friction Problem

  1. Jun 20, 2009 #1
    1. The problem statement, all variables and given/known data

    A block of mass [tex]M[/tex] is placed on a horizontal plane with kinetic friction coefficient equal to [tex]\mu[/tex]. A particle with mass [tex]m[/tex] and velocity [tex]\vec{v_0}[/tex] hits the block in a completely inelastic collision (i.e. the two bodies get stuck together). Knowing that the angle between [tex]\vec{v_0}[/tex] and the horizontal plane is [tex]\theta[/tex], calculate the final velocity of the block and the impulse between block and particle in the collision. (See attached picture).

    2. Relevant equations

    Impulse-momentum theorem

    3. The attempt at a solution

    I really do not know where to start from, but if I had to guess I would use conservation of momentum on the horizontal and vertical axis to begin:

    on the [tex]x[/tex] axis: [tex]m v_0 \cos \theta = (M+m)v_f + J_F[/tex]

    on the [tex]y[/tex] axis: [tex]m v_0 \sin \theta = J_N[/tex]

    where [tex]J_F \mbox{ and } J_N [/tex] are the impulses of the friction force and normal reaction respectively. Then I would need a third equation, maybe with energy conservation. Someone has a different approach or would like to make any suggestion?? Thanks in advance for your help.
     

    Attached Files:

  2. jcsd
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