Two forces act simultaneously on a particle

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

Two forces act simultaneously on a particle. Force

\mathbf{F}_1

has magnitude

8\,\text{N}

and acts at

30^{\circ}

above the positive

x

-axis. A second force

\mathbf{F}_2

has unknown magnitude and direction. The resultant

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

is directed wholly along the positive

y

-axis (that is, its

x

-component is zero) and has magnitude

12\,\text{N}

. Solve the following: (i) Set up the component equations for

\mathbf{F}_R

in terms of the unknown magnitude

F_2

and its direction angle

\theta

measured from the positive

x

-axis. (ii) Determine the numerical values of

F_2

and

\theta

. (iii) State fully the vector

\mathbf{F}_2

in unit-vector form.