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Titan97
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Homework Statement
A block of mass m is kept on a smooth wedge of angle α and mass M which is in turn kept on a smooth floor.
When the system is released from rest, calculate the force exerted by block on the wedge.
Homework Equations
None.
The Attempt at a Solution
Let the block a have a velocity vx and vy along x and y-axis with respect to earth. Differentiating w.r.t time, it has an acceleration ay along y-axis. For the block to be in contact with the wedge, ##a_y=asin\alpha##
Let ##N## be the normal reaction Force between wedge and block..
From F.B.D of wedge, ##Nsin\alpha=Ma## , so ##N=Macosec\alpha##
From F.B.D of block, ##mgcos\alpha-N=ma_y## and ##mgsin\alpha=ma_x##
hence, ##mgcos\alpha-N=masin\alpha## and ##a=\frac{mgcos\alpha}{msin\alpha+Mcosec\alpha}##
Therefore, $$N=\frac{mgcos\alpha}{\frac{m}{M}sin^2\alpha+1}$$
Is this correct?