Question

Two forces each numerically equal to $ 10 dynes$ are acting as shown in the following figure, then their resultant is

10 dynes 10 dynes 

Answer 1

We have to find the resultant force.

Step 1: Given data and formula.

The resultant force is given by a formula: $R=\sqrt{{F_1}^2+{F_2}^2+2\times F_1\times F_2\times \cos \theta }$

$F_{1}and{F}_2$= Two forces are acting from the figure

$F_1=F_2$= $10dynes$

$\theta$=$180-60=120°$

$\theta$= Angle between the two forces.

Step 2: Calculations.

replacing the values in the formula we get,

$$\begin{gathered} R=\sqrt{{F_1}^2+{F_2}^2+2\times F_1\times F_2\times \cos \theta } \\ R=\sqrt{{10}^2+{10}^2+2\times 10\times 10\times \cos 120°} \\ R=\sqrt{{10}^2+{10}^2+2\times 10\times 10\times \frac{-1}{2}} \\ R=\sqrt{{10}^2+{10}^2-{10}^2} \\ R=\sqrt{{10}^2} \\ R=10 \end{gathered}$$

Therefore then their resultant force is $10dynes$.