Two forces act on a small metal ring lying on a smooth horizontal table

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

Problem

Two forces act on a small metal ring lying on a smooth horizontal table. Force

\vec F_1

has magnitude

50\,\text{N}

and is directed due east. Force

\vec F_2

has magnitude

80\,\text{N}

and is directed

30^{\circ}

north of west. (a) Resolve

\vec F_1

and

\vec F_2

into components along the

x

-axis (east) and the

y

-axis (north). (b) The ring remains at rest when a third force

\vec F_3

is applied. Calculate the magnitude of

\vec F_3

. (c) Determine the direction of

\vec F_3

measured counter-clockwise from the east direction. (d) Express

\vec F_3

completely in

\hat i,\;\hat j

notation and verify that the component sums along each axis are zero.