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Question: A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated hori...

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that block does not slip on the wedge. The force exerted by the wedge on the block has a magnitude.

A

mg

B

mg cosθ

C

mg/cosθ

D

mg tan

Answer

mg/cosθ

Explanation

Solution

mg sin θ = ma cos θ or a = g tan θ

N = ma sin θ + mg cos θ = mg tan θ sin θ + mg cos θ = mgcos⁡θ\frac { \mathrm { mg } } { \cos \theta } (sin2θ + cos2θ) = mgcos⁡θ\frac { \mathrm { mg } } { \cos \theta }