A rough incline of angle 37° rises towards the right and accelerates horizontally towards the right. A block remains stationary relative to it. Take g = 10 m/s², sin37° = 3/5 and cos37° = 4/5. At what acceleration of the incline is no friction required?
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Question

A rough incline of angle 37° rises towards the right and accelerates horizontally towards the right. A block remains stationary relative to it. Take g = 10 m/s², sin37° = 3/5 and cos37° = 4/5. At what acceleration of the incline is no friction required?

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G1 Physics · Accepted Answer

No friction is required when the components of gravity and pseudo force along the incline cancel: mg sinθ = ma cosθ. Thus a = g tanθ = 10×(3/4) = 7.5 m/s².