Three forces act on a particle in a plane: • has magnitude and is directed above the…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Three forces act on a particle in a plane: •

\mathbf{A}

has magnitude

6\,\text{N}

and is directed

30^{\circ}

above the positive

x

–axis. •

\mathbf{B}

has magnitude

5\,\text{N}

and is directed

40^{\circ}

below the positive

x

–axis (fourth quadrant). •

\mathbf{C}

has magnitude

4\,\text{N}

and is directed along the negative

y

–axis. Using the scale

1\,\text{cm}=1\,\text{N}

: (i) Draw the three vectors from a common origin. (ii) By suitable constructions obtain the resultant

\mathbf{R}=\mathbf{A}-\mathbf{B}+\mathbf{C}

. (iii) Measure the magnitude and direction of

\mathbf{R}

with respect to the positive

x

–axis. (iv) Resolve

\mathbf{A}

\mathbf{B}

and

\mathbf{C}

into rectangular components, calculate

\mathbf{R}

algebraically and compare your numerical result with the graphical one.