Question

What will be the net resultant of two forces of 20N and 30N acting on an object:
a- If the two forces are acting along the same direction.

Answer 1

We know the magnitude of the resultant of two vectors $\overrightarrow{\sf{P}}$ and $\overrightarrow{\sf{Q}}$ is given by,

$\displaystyle\longrightarrow\sf{\left|\overrightarrow{\sf{P}}+\overrightarrow{\sf{Q}}\right|=\sqrt{P^2+Q^2+2PQ\cos\theta}}$

where $\theta$ is the angle between them.

But if $\overrightarrow{\sf{P}}$ and $\overrightarrow{\sf{Q}}$are acting along the same direction then $\sf{\theta=0.}$ Hence the resultant will be,

$\displaystyle\longrightarrow\sf{\left|\overrightarrow{\sf{P}}+\overrightarrow{\sf{Q}}\right|=\sqrt{P^2+Q^2+2PQ\cos0}}$

$\displaystyle\longrightarrow\sf{\left|\overrightarrow{\sf{P}}+\overrightarrow{\sf{Q}}\right|=\sqrt{P^2+Q^2+2PQ}\quad[\,\cos0=1\,]}$

$\displaystyle\longrightarrow\sf{\left|\overrightarrow{\sf{P}}+\overrightarrow{\sf{Q}}\right|=\sqrt{(P+Q)^2}}$

$\longrightarrow\sf{\left|\overrightarrow{\sf{P}}+\overrightarrow{\sf{Q}}\right|=\left|\overrightarrow{\sf{P}}\right|+\left|\overrightarrow{\sf{Q}}\right|}$

Let $\overrightarrow{\sf{R}}$ be the resultant force of the two forces 20 N and 30 N acting on the object in the same direction. Hence,

$\displaystyle\longrightarrow\sf{\left|\overrightarrow{\sf{R}}\right|=20+30}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\left|\overrightarrow{\sf{R}}\right|=50\ N}}}$

And the direction of this resultant is also along the two ones.