FIGURE 8.1 below shows a system of forces with four coplanar forces acting on the same point - NSC Mechanical Technology Fitting and Machining - Question 8 - 2018 - Paper 1

The vertical components are calculated as follows:

1. For the 800 N at 30°: $800 \sin(30°) = 800 \times 0.5 = 400 \, N$

2. For the 650 N at 20°: $650 \sin(20°) = 650 \times 0.342 = 222.31 \, N$

3. For the 1150 N at 150°: $1150 \sin(150°) = 1150 \times 0.5 = 575 \, N$

4. For the 550 N at 270°: $550 \sin(270°) = -550 \, N$

The total vertical component is:

$E_V = 400 - 222.31 - 550 = -372.31 \, N$

The magnitude of the equilibrant is given by:

$E = \sqrt{E_H^2 + E_V^2}$

This leads to:

$E = \sqrt{(-153.62)^2 + (-372.31)^2} = \sqrt{23609.58 + 138228.61} = \sqrt{161838.19} \approx 402.76 \, N$

The direction of the equilibrant can be determined using the arctangent function:

$\theta = \tan^{-1}\left(\frac{E_V}{E_H}\right)$

Substituting the values gives:

$\theta = \tan^{-1}\left(\frac{-372.31}{-153.62}\right) \approx 67.58° \text{ North from East}$