A rough wedge of angle θ rises towards the right and accelerates horizontally leftward with magnitude a. A block remains at rest relative to it. Assume tanθ > μ and cosθ > μ sinθ. The complete range of a for which sticking is possible is:
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Question

A rough wedge of angle θ rises towards the right and accelerates horizontally leftward with magnitude a. A block remains at rest relative to it. Assume tanθ > μ and cosθ > μ sinθ. The complete range of a for which sticking is possible is:

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G1 Physics · Accepted Answer

In the wedge frame, pseudo force ma acts rightward. Along the plane, the signed friction requirement is f = m(g sinθ-a cosθ), while N = m(g cosθ+a sinθ). Sticking requires |g sinθ-a cosθ| ≤ μ(g cosθ+a sinθ). Solving the two inequalities gives the stated lower and upper bounds.