A block of mass 2 kg is pushed against a rough vertical wall with a force os 40 N. Coefficient of static friction being 0.5. Another horizontal force is 15 N, is applied on the block in a direction paralle 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 15N. The resultant of the forces.
`F=sqrt(20^(2)+15^(2))=25` N in a direction `tan^(-1)((15)/(20))=37^(@)` with the vertical.

The friction will by its very virtue of opposing the tendency of relative motion, act in a direction opposite to the resultant force. Now, for the acceleration to be minimum, the minimum force required `=F-muN` (as, `muN` is the maximum frictional force)
`=25-0.5xx40=5N`
Minimum acceleration is `(5)/(2)=2.5 m//s^(2)`