A block of mass 2kg is pushed against a rough vertical wall with a force of 40N, coefficient of static friction being 0.5. Another horizontal force of 15N, is applied on the block in a direction parallel to the wall. Will the block move? If yes, in which direction? If no, find the frictional force exerted by the wall on the block.
AnswerNet force the block $=\sqrt{20^2+15^2}-(0.5)\times 40$$=25-20=5\text{N}$
$\therefore\tan\theta=\frac{20}{15}=\frac{4}{3}$
$\Rightarrow\mu=\tan^{-1}\Big(\frac{4}{3}\Big)=53^{\circ}$
So, the block will move at an angle 53° with an 15N force.