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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