# 008 Components of a force at different pairs of axes

**Problem 008**

A force P = 800 N is shown in Fig. P-008.

- Find the y-component of P with respect to x and y axis.
- Find the y'-component of P with respect to x' and y' axis.
- Find the y-component of P with respect to x' and y axis.
- Find the y'-component of P with respect to x and y' axis.

**Solution 008**

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**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*

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