Refer to figure (2-E1). Find (a) the magnitude, (b) x and y components and (c) the angle with the X - axis of the resultant of $\to O A, \to B C$ and $\to D E$ .

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Solution

X and Y components of all the forces given
x component of $\to O A$ = 2 cos $30^{0} = \sqrt{3}$

x component of $\to B C$ = 1.5 cos $120^{0}$ = $\frac{(1.5)}{2} = - 7.5$

x component of $\to D E$ = 1 cos $270^{0}$ = $1 \times 0 = 0$

y component of $\to O A = 2$ sin $30^{0} = 1$

y component of $\to B C$ = 1.5 sin $30^{0} = 120^{0}$ = $\frac{(\sqrt{3} \times 1.5)}{2} = 1.3$

y component of $\to D E$ = 1 sin $270^{0} = - 1$

x component of resultant,

$R_{x} = \sqrt{3}$ - 0.75+0

= 0.98 m

Resultant y component,

$R_{y}$ = 1+1.3-1 = 1.3 m

$∴$ Resultant, R = $\sqrt{(0.98)^{2} + (1.3)^{2}}$

= $\sqrt{0.96 + 1.69}$

= $\sqrt{2.65}$

= 1.6 m
The magnitude of the resultant of the given displacement is 1.6 m
Angle made with X-axis

If it makes an angle $α$ with +ve x axis, then

tan $α$ = $\frac{y component}{x component}$

= $\frac{1.3}{0.98} = 1.332$

$\Rightarrow α = t a n^{- 1} (1.32)$

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Refer to figure (2-E1). Find (a) the magnitude, (b) x and y components and (c) the angle with the X - axis of the resultant of →OA,→BC and →DE.

Refer to figure (2-E1). Find (a) the magnitude, (b) x and y components and (c) the angle with the X - axis of the resultant of $\to O A, \to B C$ and $\to D E$ .