Three coplanar forces act at a point P in the horizontal plane

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

Problem

Three coplanar forces act at a point P in the horizontal plane. •

\vec F_1 = 30\,\text{N}

along the positive

x

-axis. •

\vec F_2 = 40\,\text{N}

along the positive

y

-axis. •

\vec F_3

has a fixed magnitude of

50\,\text{N}

but an unknown direction. (a) By resolving

\vec F_1

and

\vec F_2

into components, write the vector

\vec R = \vec F_1 + \vec F_2

\hat i,\;\hat j

form. (b) The point P is required to remain in equilibrium. Determine the angle that

\vec F_3

must make with the positive

x

-axis (give all possible values between

0^{\circ}

and

360^{\circ}

). (c) Sketch, to scale, the vector diagram showing the three forces and label clearly the angle(s) found.