Answer to Question #141664 in Physics for Drew

Question

What is the resultant and the angle of the coplanar forces which is 100 N at 30°, 141.4 N at 45 ° and 100 N at 240 °? Show your solution and draw position of the resultant in the x-y plane. Final answer must be in 3 significant figures.

Answer 1

Find the components:

$$F_{1x}=F_1\text{cos}30°=86.6\text{ N},\\ F_{1y}=F_1\text{sin}30°=50\text{ N}.\\ F_{2x}=F_2\text{cos}45°=99.98\text{ N},\\ F_{2y}=F_2\text{sin}45°=99.98\text{ N}.\\ F_{3x}=F_3\text{cos}240°=-50\text{ N},\\ F_{3y}=F_3\text{sin}240°=-86.6\text{ N}.\\$$

The resultant is

$$F_x=F_{1x}+F_{2x}+F_{3x}=137\text{ N},\\ F_y=F_{1y}+F_{2y}+F_{3y}=63.4\text{ N},\\ F=\sqrt{F_x^2+F_y^2}=151\text{ N},\\\space\\ \theta=\text{arctan}\frac{F_y}{F_x}=24.9°$$

above x-axis.