Moderate -0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions and finding the resultant. While it involves multiple forces at different angles, the method is routine for M1 level: resolve horizontally and vertically, then use Pythagoras and trigonometry. The 6 marks reflect computational work rather than conceptual difficulty, making it slightly easier than average.
\includegraphics{figure_3}
Coplanar forces of magnitudes 8 N, 12 N and 18 N act at a point in the directions shown in the diagram. Find the magnitude and direction of the single additional force acting at the same point which will produce equilibrium. [6]
Use of Pythagoras or appropriate trig to find magnitude or angle
Magnitude is 27.6 (N)
A1
Not for resultant
Direction is 27.9° below ‘negative x-axis’
A1
Not for 27.9° only; direction must be clearly specified
Total:
6
Question
Answer
Marks
Question 3:
3 | M1 | For resolving forces in any one direction
E.g. X =18+12sin60°−8sin30° 14 + 6√3 | A1 | One correct equation or expression
E.g. Y =8cos30°+12cos60° 6 + 4√3 | A1 | Second correct equation or expression (X and Y may denote
components of resultant of given 3 forces or may be components
of the fourth force that would produce equilibrium)
[(14 + 6√3)2 + (6 + 4√3)2] or [tan–1 (6 + 4√3)/( 14 + 6√3)] | M1 | Use of Pythagoras or appropriate trig to find magnitude or angle
Magnitude is 27.6 (N) | A1 | Not for resultant
Direction is 27.9° below ‘negative x-axis’ | A1 | Not for 27.9° only; direction must be clearly specified
Total: | 6
Question | Answer | Marks | Guidance
\includegraphics{figure_3}
Coplanar forces of magnitudes 8 N, 12 N and 18 N act at a point in the directions shown in the diagram. Find the magnitude and direction of the single additional force acting at the same point which will produce equilibrium. [6]
\hfill \mbox{\textit{CAIE M1 2018 Q3 [6]}}