# Homework Help: Classical Mechanics - Block Friction Problem

1. Jun 20, 2009

### TomAlso

1. The problem statement, all variables and given/known data

A block of mass $$M$$ is placed on a horizontal plane with kinetic friction coefficient equal to $$\mu$$. A particle with mass $$m$$ and velocity $$\vec{v_0}$$ hits the block in a completely inelastic collision (i.e. the two bodies get stuck together). Knowing that the angle between $$\vec{v_0}$$ and the horizontal plane is $$\theta$$, 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 $$x$$ axis: $$m v_0 \cos \theta = (M+m)v_f + J_F$$

on the $$y$$ axis: $$m v_0 \sin \theta = J_N$$

where $$J_F \mbox{ and } J_N$$ 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.

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