Coplanar forces of magnitudes $$\(8 \mathrm{~N}, 12 \mathrm{~N}, 10 \mathrm{~N}\)$$ and $$\(P \mathrm{~N}\)$$ act at a point in the directions shown in the diagram. The system is in equilibrium. Find $$\(P\)$$ and $$\(\theta\)$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................
Exam No：9709_w20_qp_41 Year：2020 Question No：3
Answer:
Resolve forces either horizontally or vertically
$P \cos \theta=12+8 \cos 30-10 \cos 45[=11.857]$
$P \sin \theta=10 \sin 45-8 \sin 30[=3.071]$
$\begin{array}{l}P=\sqrt{\left(11.857^{2}+3.071^{2}\right)} \\ \theta=\tan ^{-1}\left(\frac{3.071}{11.857}\right)\end{array}$
$P=12.2$ and $\theta=14.5$
$P \cos \theta=12+8 \cos 30-10 \cos 45[=11.857]$
$P \sin \theta=10 \sin 45-8 \sin 30[=3.071]$
$\begin{array}{l}P=\sqrt{\left(11.857^{2}+3.071^{2}\right)} \\ \theta=\tan ^{-1}\left(\frac{3.071}{11.857}\right)\end{array}$
$P=12.2$ and $\theta=14.5$
Knowledge points:
4.1.2 understand the vector nature of force, and find and use components and resultants； Calculations are always required, not approximate solutions by scale drawing.
4.1.3 use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero （Solutions by resolving are usually expected, but equivalent methods (e.g. triangle of forces, Lami’s Theorem, where suitable) are also acceptable; these other methods are not required knowledge, and will not be referred to in questions.）
Solution:
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