A crate on a frictionless floor is pulled by three forces and remains at rest

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A crate on a frictionless floor is pulled by three forces and remains at rest. Two of the forces are

\vec{F}_1=120\,\text{N}

due east and

\vec{F}_2=80\,\text{N}

due north. Determine the magnitude and direction of the third force

\vec{F}_3

that keeps the crate in equilibrium. Express the direction as an angle south of west.