Question

Two forces, 80N and 100N acting at an angle of 60 degrees with each other, pull on an object. What single force would replace the two forces?

Answer 1

We use the law of Cosines, resultant force

$F =\sqrt{(F_{1})^2 + (F_{2})^2 + 2 F_{1} F_{2} cos \theta }$

Here, $(F_{1})$ and $(F_{2})$ are forces acting at angle $\theta$ with each other.

Given $F_{1} = 80 N$, $F_{2} = 100 N$ and $\theta = 60^0$.

Substituting these given values in above formula we get

$F =\sqrt{(80)^2 + (100)^2 + 2 \times 80 \times 100 \ cos 60^0 } = 156. 20 \ N$.

Thus, the resultant force is 156 N.