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 parallel to the wall. Will the block move? If yes, with what acceleration? If no, find the frictional force exerted by the wall on the block. $(g=10m/s^2)$.

Answer 1

Case I; $F_2$ in upward direction;

frictional force,

$f_{max}=\mu N=\mu F_1=\frac{1}{4}\times 20=5N$

Weight of mass $=mg=1\times 10=10N$

If $F_2$ in upward direction then

$F_2-mg=10-10=0$

No frictional force acts and there is no acceleration.

Case II; $F_2$ in downward direction;

$F_2+mg-f_{max}=ma$

$10+10-5=1.a$

$a=15m/s^2$