A block kept on a rough inclined plane , as shown in the figure , remains at rest upto a maximum force 2 N down the inclined plane. The maximum external external force up the inclined plane that does not move the block is 10 N . The coefficient of static friction between the block and the plane is : 

[Take g = 10 m/s2

                                                                                                                   

Answers (1)

Minimum Force to move a body downward along the surface of Inclined Plane -

  

Use condition of equilibrium.

R+P sin \alpha=W cos \lambda

F= P cos \alpha + W sin \lambda

Use  F=\mu R

P=\frac{W sin(\theta-\lambda)}{cos(\alpha-\theta)}

- wherein

P = Pulling force 

\alpha= Angle of P with horizontal 

\lambda= Inclined angle

R = Reaction

W = Weight

 

            

For 2N force

2+mg \sin \theta = \mu mg\cos 30 ........(1)

For 10N force

10= mg\sin 30+\mu mg\cos 30 ........(2)

From (1) and (2)

12 = 2\mu mg \cos \left ( 30 \right )

8=mg\sin 30

\Rightarrow \frac{12}{8} = \mu \cot 30 = 2\mu \times \sqrt{3}

\mu =\frac{\sqrt{3}}{2}

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