Two forces act simultaneously on a particle: making an angle of with the positive -axis

PHYSICS · Subjective · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two forces act simultaneously on a particle:

\mathbf{F}_1 = 100\,\text{N}

making an angle of

60^{\circ}

with the positive

x

-axis, and

\mathbf{F}_2 = 150\,\text{N}

acting at

210^{\circ}

measured anticlockwise from the positive

x

-axis. (i) Resolve each force into its rectangular components. (ii) Obtain the rectangular components of the resultant force

\mathbf{R}=\mathbf{F}_1+\mathbf{F}_2

. (iii) Determine the magnitude of

\mathbf{R}

. (iv) Find the angle that

\mathbf{R}

makes with the positive

x

-axis, stating clearly the quadrant in which it lies.