Question

Find the magnitude and direction of the resultant ( R ) by adding the following forces using the component method: 12.0 lb. At 30 degrees above the x axis, 15.0 lb. at 140 degrees and 8.0 lb. at 79 degrees S of W. Represent the given vectors.

Answer 1

x-components:

$$A_x=12\text{ cos}30º=10.4\text{ lb},\\ B_x=15\text{ cos}140º=-11.5\text{ lb},\\ C_x=8\text{ cos}(180º+79º)=1.53\text{ lb}.$$

y-components:

$$A_y=12\text{ sin}30º=6\text{ lb},\\ B_y=15\text{ sin}140º=9.64\text{ lb},\\ C_y=8\text{ sin}(180º+79º)=-7.85\text{ lb}.$$

Resultant:

$$R_x=A_x+B_x+C_x=0.43\text{ lb}, \\ R_y=A_y+B_y+C_y=7.79\text{ lb},\\ R=\sqrt{R_x^2+R_y^2}=7.80\text{ lb}.$$