Standard +0.3 This is a straightforward equilibrium problem requiring students to resolve forces in two perpendicular directions and use basic trigonometry. The 6-8-10 Pythagorean triple provides a hint that simplifies the solution. While it requires setting up equations and solving them, the method is standard and the arithmetic is clean, making it slightly easier than average.
\includegraphics{figure_2}
The diagram shows three coplanar forces acting at the point \(O\). The magnitudes of the forces are \(6 \text{ N}\), \(8 \text{ N}\) and \(10 \text{ N}\). The angle between the \(6 \text{ N}\) force and the \(8 \text{ N}\) force is \(90°\). The forces are in equilibrium. Find the other angles between the forces. [4]
Question 2:
2 | [10 cos α = 8 or 10 cos β = 6] | M1 | Introduce α or β, an angle between the
10N force and the vertical or horizontal
and attempt to resolve forces
α = 36.9 or β = 53.1 | A1
Angle between 6N and 10N is 126.9 | B1
Angle between 8N and 10N is 143.1 | B1
4
Alternative scheme for Question 2
10 6 8
= =
sin90 sinγ sinδ | M1 | Attempt to use Lami’s theorem
γ (8 and 10), δ (6 and 10)
All correct | A1
Angle between 8N and 10N is γ =143.1 | B1
Angle between 6N and 10N is δ =126.9 | B1
Question | Answer | Marks | Guidance
\includegraphics{figure_2}
The diagram shows three coplanar forces acting at the point $O$. The magnitudes of the forces are $6 \text{ N}$, $8 \text{ N}$ and $10 \text{ N}$. The angle between the $6 \text{ N}$ force and the $8 \text{ N}$ force is $90°$. The forces are in equilibrium. Find the other angles between the forces. [4]
\hfill \mbox{\textit{CAIE M1 2018 Q2 [4]}}