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

Normal reation on the block from the wall will be `(F_("net") =0`, perpendicular to the wall)

`R =F =20N`
Therefore, limiting friction `f_(1) =muR =((1)/(4)) (20) =5N`
Weight of the block is `w = mg =(1)(10) = 10N`
A horizontal force of `10N` is applied to the block. Both weight and this force along the wall the wall. The resultant of these two force will be `10sqrt2N` in the direction shown in figure. Since ,this resultant is greater than the limiting friction. The block willmove in the direction of `F_("net")`with acceleration.
`a =(F_("net")-f_(L)/(m) =(10 sqrt2-5)/(1) =9.14 m//s^(2))`