008 Components of a force at different pairs of axes

Part (a)
y-component of P with respect to x and y axis
 

 

$P_y = 800 \sin 30^\circ$

$P_y = 400 \, \text{ N}$           answer
 

Part (b)
y'-component of P with respect to x' and y' axis
 

 

$P_{y'} = 800 \sin 60^\circ$

$P_{y'} = 692.82 \, \text{ N}$            
 

Part (c)
y-component of P with respect to x' and y axis
 

 

The figure formed is in the shape of equilateral triangle. Thus,

$P_y = 800 \, \text{ N}$           answer
 

Part (d)
y'-component of P with respect to x and y' axis

By Sine Law
$\dfrac{P_{y'}}{\sin 30^\circ} = \dfrac{P}{\sin 120^\circ}$

$P_{y'} = \dfrac{P \, \sin 30^\circ}{\sin 120^\circ}$

$P_{y'} = \dfrac{800 \, \sin 30^\circ}{\sin 120^\circ}$

$P_{y'} = 461.88 \, \text{ N}$           answer