Three coplanar forces

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

\vec{F_1}

\vec{F_2}

and

\vec{F_3}

act simultaneously at a point. The forces

\vec{F_1}

and

\vec{F_2}

are given by

\vec{F_1}=6\mathbf{i}-8\mathbf{j}\;\text{N}

and

\vec{F_2}=-4\mathbf{i}+10\mathbf{j}\;\text{N}

. (i) If the system is in equilibrium, determine the force

\vec{F_3}

in component form. (ii) Calculate the magnitude of

\vec{F_3}

and the angle it makes with the positive

x

-axis. (iii) Explain, with reference to a vector diagram, how the three forces satisfy the triangle (polygon) law of forces in equilibrium.