Q

# What is minimum value of Force P for Motion along the horizontal surface ???

Also, tell its direction with respect to the horizontal axis ???
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For the below figure

For the minimum value of P, its angle from the horizontal should be equal to the angle of friction.

I.e   $\alpha=tan^{-1}(\mu)$= angle of friction.

And the minimum value of P is given by

$P_{min}=\frac{\mu mg}{\sqrt{1+\mu^{2}}}$

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