Question

1. two forces of magnitudes 5 n and 8 n act on a body at an angle of 60°. use the parallelogram law of vectors to find the resultant force.

Explanation:

Step1: Recall parallelogram law formula

The formula for the magnitude of the resultant force $R$ of two forces $F_1$ and $F_2$ acting at an angle $\theta$ is $R = \sqrt{F_1^{2}+F_2^{2}+2F_1F_2\cos\theta}$.

Step2: Substitute given values

Here, $F_1 = 5$ N, $F_2=8$ N and $\theta = 60^{\circ}$, and $\cos60^{\circ}=\frac{1}{2}$.
$R=\sqrt{5^{2}+8^{2}+2\times5\times8\times\frac{1}{2}}$
$=\sqrt{25 + 64+40}$
$=\sqrt{129}$
$\approx 11.36$ N

Answer:

$11.36$ N