# Find the value of pushing force P just to move the block. If the coeffecient of friction between block and the floor is given as .

Minimum Force to avoid sliding of body down on an inclined plane -

$P=W \left[\frac{sin(\lambda-\theta)}{cos(\theta+\lambda)} \right ]$

P = Pulling force

$\lambda=$ Angle of Inclination

$\theta=$ Angle of friction

- wherein

For equilibrium

$R+P sin\alpha=W cos\lambda$

$P cos \alpha+F=W sin \lambda$

Use $F=\mu R$

3 + mg sin $\theta$ = P + $\mu$ mg cos $\theta$

$3 + \frac{100}{\sqrt{2}} = P + 0.6 \times \frac{100}{\sqrt{2}}$

P = 32 N

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