Moderate -0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions to find two unknowns. While it involves multiple forces and some trigonometry, it's a routine textbook exercise with a well-established method (resolve horizontally and vertically, solve simultaneous equations). The 6 marks reflect the calculation steps rather than conceptual difficulty, making it slightly easier than average.
\includegraphics{figure_3}
Coplanar forces of magnitudes 8 N, 12 N, 10 N and \(P\) N act at a point in the directions shown in the diagram. The system is in equilibrium.
Find \(P\) and \(\theta\). [6]
Question 3:
3 | Resolve forces either horizontally or vertically | M1 | Correct number of relevant terms
P cos θ = 12 + 8 cos 30 – 10 cos 45 [= 11.857] | A1
P sin θ = 10 sin 45 – 8 sin 30 [= 3.071] | A1
( )
P= 11.8572 +3.0712 | M1 | OE. Use of correct method for finding P
θ=tan −1 3.071
11.857 | M1 | OE. Use of correct method for finding θ
P = 12.2 and θ = 14.5 | A1 | Both correct
6
Question | Answer | Marks | Guidance
\includegraphics{figure_3}
Coplanar forces of magnitudes 8 N, 12 N, 10 N and $P$ N act at a point in the directions shown in the diagram. The system is in equilibrium.
Find $P$ and $\theta$. [6]
\hfill \mbox{\textit{CAIE M1 2020 Q3 [6]}}