Question

An object of mass $M$ is kept on a rough table as seen from above. Forces are applied as shown. Find the direction (from the vertical) of static friction if the object does not move.

• A. ${30}^{\circ }$
• B. ${37}^{\circ }$
• C. ${45}^{\circ }$
• D. ${53}^{\circ }$

Answer 1

The correct option is D ${53}^{\circ }$

The net force acting on the block will be
Resultant force $=\sqrt{{15}^2+{20}^2}=25N$
Angle with horizontal ${\tan }^{-1}\left(\frac{15}{20}\right)={37}^0$

The direction of static friction is opposite to the direction of the resultant force its magnitude is equal to $25N$ and it making an angle of ${37}^0$ with horizontal and ${90}^0-{37}^0={53}^0$ with vertical