CAIE M1 2022 November — Question 1 5 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2022
SessionNovember
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeEquilibrium of particle under coplanar forces
DifficultyModerate -0.5 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions to form two simultaneous equations. While it involves trigonometry and solving simultaneous equations, it's a routine textbook exercise with a clear method that any competent M1 student should handle comfortably, making it slightly easier than average.
Spec3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces

\includegraphics{figure_1} Coplanar forces of magnitudes \(P\) N, \(Q\) N, 16 N and 22 N act at a point in the directions shown in the diagram. The forces are in equilibrium. Find the values of \(P\) and \(Q\). [5]

Question 1:
AnswerMarks Guidance
1Attempt at resolving horizontally or vertically M1
3 terms.
AnswerMarks Guidance
Pcos25=22+16cos55A1
Q+16sin55=Psin25A1 Allow their P.
Attempt to solve for P or QM1 No missing/extra terms.
P=34.4 Q=1.43A1 P=34.40025941, Q=1.431745128 .
5
AnswerMarks Guidance
QuestionAnswer Marks
Question 1:
1 | Attempt at resolving horizontally or vertically | M1 | Allow sign errors, allow sin/cos mix.
3 terms.
Pcos25=22+16cos55 | A1
Q+16sin55=Psin25 | A1 | Allow their P.
Attempt to solve for P or Q | M1 | No missing/extra terms.
P=34.4 Q=1.43 | A1 | P=34.40025941, Q=1.431745128 .
5
Question | Answer | Marks | Guidance
\includegraphics{figure_1}

Coplanar forces of magnitudes $P$ N, $Q$ N, 16 N and 22 N act at a point in the directions shown in the diagram. The forces are in equilibrium.

Find the values of $P$ and $Q$. [5]

\hfill \mbox{\textit{CAIE M1 2022 Q1 [5]}}