An incline of angle θ rises towards the right and accelerates horizontally towards the right with acceleration a. A block remains stationary relative to it. If g sinθ > a cosθ, the minimum coefficient of friction required is:
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Question

An incline of angle θ rises towards the right and accelerates horizontally towards the right with acceleration a. A block remains stationary relative to it. If g sinθ > a cosθ, the minimum coefficient of friction required is:

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G1 Physics · Accepted Answer

In the wedge frame, pseudo force ma acts horizontally left. Along the incline, the net tendency down the plane is m(g sinθ - a cosθ). The normal reaction is N = m(g cosθ + a sinθ). For limiting equilibrium, μₘᵢₙN = m(g sinθ - a cosθ). Hence μₘᵢₙ = (g sinθ - a cosθ)/(g cosθ + a sinθ).