CAIE M1 2019 March — Question 3 6 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2019
SessionMarch
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicForces, equilibrium and resultants
TypeEquilibrium of particle under coplanar forces
DifficultyModerate -0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions and solving simultaneous equations. While it involves trigonometry and multiple forces, it's a routine textbook exercise with a clear method (resolve horizontally and vertically, set sums to zero). The 6 marks reflect straightforward algebraic manipulation rather than conceptual difficulty, making it slightly easier than average.
Spec3.03e Resolve forces: two dimensions3.03m Equilibrium: sum of resolved forces = 0

\includegraphics{figure_3} Four coplanar forces of magnitudes \(F\) N, \(5\) N, \(25\) N and \(15\) N are acting at a point \(P\) in the directions shown in the diagram. Given that the forces are in equilibrium, find the values of \(F\) and \(α\). [6]

Question 3:
AnswerMarks Guidance
3M1 Attempt to resolve forces horizontally or vertically
F cos α = 15 cos 20 – 5 (= 9.095...)A1
F sin α = 15 sin 20 + 25 (= 30.13....)A1
F = ( 15cos20−5 )2 +( 15sin20+25 )2M1 Use Pythagoras or trigonometry to find F
 ( 15sin20+25 ) 
∝ =tan−1  ( 15cos20−5 )
AnswerMarks Guidance
 M1 Use trigonometry to find α
α = 73.2 and F = 31.5A1
6
AnswerMarks Guidance
QuestionAnswer Marks
Question 3:
3 | M1 | Attempt to resolve forces horizontally or vertically
F cos α = 15 cos 20 – 5 (= 9.095...) | A1
F sin α = 15 sin 20 + 25 (= 30.13....) | A1
F = ( 15cos20−5 )2 +( 15sin20+25 )2 | M1 | Use Pythagoras or trigonometry to find F
 ( 15sin20+25 ) 
∝ =tan−1  ( 15cos20−5 )
  | M1 | Use trigonometry to find α
α = 73.2 and F = 31.5 | A1
6
Question | Answer | Marks | Guidance
\includegraphics{figure_3}

Four coplanar forces of magnitudes $F$ N, $5$ N, $25$ N and $15$ N are acting at a point $P$ in the directions shown in the diagram. Given that the forces are in equilibrium, find the values of $F$ and $α$. [6]

\hfill \mbox{\textit{CAIE M1 2019 Q3 [6]}}