CAIE M1 2016 November — Question 4 6 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2016
SessionNovember
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicMoments
TypeCoplanar forces in equilibrium
DifficultyModerate -0.3 This is a standard three-force equilibrium problem requiring resolution in two perpendicular directions to find two unknowns. While it involves some trigonometry and simultaneous equations, it's a routine mechanics exercise with a clear method that students practice extensively. Slightly easier than average due to the straightforward setup and standard technique.
Spec3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces
4 \includegraphics[max width=\textwidth, alt={}, center]{a92f97e2-343f-4cac-ae38-f18a4ad49055-2_334_832_1617_660} Three coplanar forces of magnitudes \(F \mathrm {~N} , 2 F \mathrm {~N}\) and 15 N act at a point \(P\), as shown in the diagram. Given that the forces are in equilibrium, find the values of \(F\) and \(\alpha\).
Question 4:
AnswerMarks Guidance
Answer/WorkingMark Guidance
(Resolve horizontally)M1 For resolving forces horizontally
\(2F + F\cos60 = 15\cos\alpha\)A1
(Resolve vertically)M1 For resolving forces vertically
\(F\sin60 = 15\sin\alpha\)A1
(Pythagoras or \(\tan\alpha\))M1 For using Pythagoras or using \(\tan\alpha\) to find \(F\) and \(\alpha\)
\(F = 5.67\) and \(\alpha = 19.1\)A1 [6] Allow \(F = 15\sqrt{7}/7\) 
## Question 4:

| Answer/Working | Mark | Guidance |
|---|---|---|
| (Resolve horizontally) | M1 | For resolving forces horizontally |
| $2F + F\cos60 = 15\cos\alpha$ | A1 | |
| (Resolve vertically) | M1 | For resolving forces vertically |
| $F\sin60 = 15\sin\alpha$ | A1 | |
| (Pythagoras or $\tan\alpha$) | M1 | For using Pythagoras or using $\tan\alpha$ to find $F$ and $\alpha$ |
| $F = 5.67$ and $\alpha = 19.1$ | A1 | [6] Allow $F = 15\sqrt{7}/7$ |

---
4\\
\includegraphics[max width=\textwidth, alt={}, center]{a92f97e2-343f-4cac-ae38-f18a4ad49055-2_334_832_1617_660}

Three coplanar forces of magnitudes $F \mathrm {~N} , 2 F \mathrm {~N}$ and 15 N act at a point $P$, as shown in the diagram. Given that the forces are in equilibrium, find the values of $F$ and $\alpha$.

\hfill \mbox{\textit{CAIE M1 2016 Q4 [6]}}
This paper (7 questions)
View full paper
Q1 4 Q2 5 Q3 6 Q4 6 Q5 8 Q6 10 Q7 11