CAIE M1 2020 June — Question 2 6 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2020
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeEquilibrium of particle under coplanar forces
DifficultyStandard +0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions to form two simultaneous equations. While it involves some algebraic manipulation and trigonometry, it follows a routine method taught in M1 with no novel insight required. The presence of the parameter P and unknown angle θ makes it slightly above average difficulty for basic equilibrium questions, but it remains a textbook-style problem.
Spec3.03b Newton's first law: equilibrium3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0

\includegraphics{figure_2} Coplanar forces of magnitudes 20 N, \(P\) N, \(3P\) N and \(4P\) N act at a point in the directions shown in the diagram. The system is in equilibrium. Find \(P\) and \(\theta\). [6]

Question 2:
AnswerMarks Guidance
2Resolving forces in either direction M1
20cosθ=4Pcos30A1
4P+2Psin30=20sinθA1
3
cosθ= P
10
P
sinθ=
4
3 1
P2 + P2 =1
AnswerMarks
100 16M1
P=3.29A1
θ=55.3A1
6
AnswerMarks Guidance
QuestionAnswer Marks
Question 2:
2 | Resolving forces in either direction | M1
20cosθ=4Pcos30 | A1
4P+2Psin30=20sinθ | A1
3
cosθ= P
10
P
sinθ=
4
3 1
P2 + P2 =1
100 16 | M1
P=3.29 | A1
θ=55.3 | A1
6
Question | Answer | Marks
\includegraphics{figure_2}

Coplanar forces of magnitudes 20 N, $P$ N, $3P$ N and $4P$ 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 Q2 [6]}}