# Mechanics is fun! (3)

A particle falls and strikes a wedge of equal mass with velocity $$v$$. After colliding with the wedge, it bounces horizontally with the speed $$\frac12 v$$. There is friction between the wedge and the particle, with coefficient of friction $$\mu_1$$, as well as between the wedge and the horizontal surface, with coefficient of friction $$\mu_2$$. For this to occur, $$\mu_1$$ and $$\mu_2$$ cannot be smaller than the minimal values $$\mu_1^\textrm{min}$$ and $$\mu_2^\textrm{min}$$.

Find $$\mu_1^\textrm{min} + \mu_2^\textrm{min}$$.

Assumptions and Details

• Neglecting any toppling effects of the wedge and the angle of incline is x such that $$\sin x = 3/5$$.
• The coefficient of restitution for the collision is 9/16.
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