Question

Four sled dogs are pulling a 1000kg load, Sled dog A is pulling the load at 20 N, 10° north of east. Sled dog B is pulling the load at 55 N, 70° north of east. Sled dog C is pulling the load at 45 N, 33° north of west, while sled dog D exerts 30 N at a direction of 80° south of west. What is the resultant force acting on the load?

Answer 1

Find the x- and y-component of the resultant:

$$R_x=R_E=20\cos10°+55\cos70°-\\-45\cos33°-30\cos80°=-4.44\text{ N}.\\\space\\ R_y=R_N=20\sin10°+55\sin70°+\\+45\sin33°-30\sin80°=50.1\text{ N}.\\\space\\ R=\sqrt{R_N^2+R_E^2}=50.3\text{ N}.\\\space\\ \theta=\arctan\frac{R_N}{|R_E|}=84.9°\text{ N of W}.$$