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Acceleration of Block on Smooth Inclined Plane

When an inclined plane is given a horizontal acceleration b Since the body lies in an accelerating frame, an inertial force (mb) acts on it in the opposite direction (Fig. 4).
 
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Fig. 4
 
Normal reaction R = mg cosθ + mb sinθ
 
and ma = mg sin θ – mb cos θ
 
∴ a = g sinθ – b cosθ

 

Note: The condition for the body to be at rest relative to the inclined plane:
 
a = g sinθ – b cosθ = 0
 
∴ b = g tanθ




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