Answer to Question #96966 in Mechanics | Relativity for Bg

Question

The forces of 10N and 20N are in plain at an angle 60⁰ to each other. Find the resultant and the direction using
1. Analytical method
2. Scle drawing method

Answer 1

1)

$$F_x=F_{1x}+F_{2x}=10+20\cos 60^{\circ}=20N$$

$$F_y=F_{1y}+F_{2y}=0+20\sin 60^{\circ}=10\sqrt{3}N$$

The absolute value of the resultant force

$$F=\sqrt{F_x^2+F_y^2}=\sqrt{20^2+(10\sqrt{3})^2}=26.46N$$

Direction

$$\theta =\tan^{-1}\frac{F_y}{F_x}=\tan^{-1}\frac{10\sqrt{3}}{20}=41^{\circ}$$

2)