Question

A block of mass 2 kg is pushed normally against a rough vertical wall with a force of 40N, co-efficient of static friction being 0.5 Another horizontal force of 15N is applied on the wall Will the block move? If yes, in which direction and acceleration? If no, find the frictional force exerted by the wall on the block?

Answer 1

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 = $\sqrt{{20}^2+{15}^2}=25N$
Hence, net driving force $F_{driving}=25N$ is a direction $ta{n}^{-1}\left(\frac{15}{20}\right)={37}^0$ with the vertical.
The friction opposing the tendency of relative act in a direction opposite to the resultant force.
Maximum resisting force = limiting friction
$f_{lim}=\mu N=0.5\times 40=20N$
As driving force is greater than maximum resisting force, hence the block will move and friction will be kinetic nature and $f_r$ = 20 N
The direction of friction force will be opposite to the direction of net force.
Acceleration of block, $a=\frac{F_{net}-f_r}{m}=\frac{25-20}{2}=2.5m{s}^2$