A block of mass 2 kg is pushed against a rough vertical wall with a force of 40N. Coefficient of static friction being 0.5. Another horizontal force of 15 N, 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.

Explanation

The force which may cause the tendency of motion or motion in the body is its own weight and the applied horizontal force of `15 N`

The resultant of the force `F = sqrt(20^(2) + 15^(2)) = 25 N`
Hence , net driving force `F_("driving") = 25 N` in a direction
`tan ^(-1) ((15)/(20)) = 37^(@)` with the verticle
The friction opposing the tendency of relative mosion act in a direction opposite to the resultant force
maximum resisting force = limiting friction `f_("lim") = mu N = 0.5 xx 40 = 20N`
As driving force is greater then maximum resisting force bence the block will move and friction will be kinetic nuture and `f = 20N`,
The direction of friction force will be opposite to the direction of net force
Acceleration of block ` a = (F_("net") - f_(r))/(m) = (25 - 20)/(2) = 2.5ms^(2)`