Question

A block of mass $1kg$ is pushed against a rough vertical wall with a force of $20N$, coefficient of static friction being $\frac{1}{4}.$ Another horizontal force of $10N$ is applied on the block in a direction? If no, find the frictional force exerted by the wall on the block. (g= $10m/s^2$).

Answer 1

Normal reaction on the block from the wall will be $N=F=20N$
Therefore, limiting friction $f_L=\mu N=\left(\frac{1}{4}\right)\left(20\right)=5N$
Weight of the block is
$W=mg=\left(1\right)\left(10\right)=10N$
A horizontal force of 10 N is applied to the block. The resultant of these two forces will be $10\sqrt{2}$ N in the direction shown in figure. Since, this resultant is greater than the limiting friction. The block will move in the direction of $\overrightarrow{F_{net}}$ with acceleration $a=\frac{F_{net}-f_L}{m}=\frac{10\sqrt{2}-5}{1}=9.14m/s^2$