Question

In Fig. an object of mass M is kept on a rough table as seen from above. Forces are applied on it as shown. Find the direction of static friction if the object does not move.

Answer 1

Here limiting value of friction force
$f_{lim}={\mu }_{s}N=0.4\times 10\times 10=40N$
The resuttant of exrernal force acting on the block
$F_{net}=\sqrt{(15{)}^2+(20{)}^2}=25N$
If the block is at rest,$f=F_{net}=25N$
As $f<f_{lim}$.
Here actual friction force acting on the block is less than $f_{lim}$. The friction in this case is of static nature.
For the direction of friction force, we draw the free body diagram of find the resultant force.
The direction of static friction is opposite to the direction of the resultant force FR. Its magnitude is equal to 25 N at angle, $tan\theta =\frac{15}{20}=\frac{3}{4}$ or $\theta ={37}^0$ as shown in Fig 7.19.