CAIE M1 2020 June — Question 3 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
DifficultyModerate -0.3 This is a standard equilibrium problem requiring resolution of forces in two perpendicular directions to find two unknowns. While it involves some trigonometry and simultaneous equations, it's a routine M1 exercise with a clear method and no conceptual challenges—slightly easier than average due to its straightforward approach.
Spec3.03m Equilibrium: sum of resolved forces = 0
3 \includegraphics[max width=\textwidth, alt={}, center]{55090630-1413-45cd-8201-4d58662db6bd-04_586_1003_260_571} Four coplanar forces of magnitudes \(40 \mathrm {~N} , 20 \mathrm {~N} , 50 \mathrm {~N}\) and \(F \mathrm {~N}\) act at a point in the directions shown in the diagram. The four forces are in equilibrium. Find \(F\) and \(\alpha\).
Question 3:
AnswerMarks Guidance
AnswerMark Guidance
Attempt to resolve, either direction with correct number of termsM1
\(F\cos\alpha = 40\sin30 + 20\sin60 - 50\sin45 (= 1.965...)\)A1
\(F\sin\alpha = 50\cos45 + 20\cos60 - 40\cos30 (= 10.714...)\)A1
Method for either \(F\) or \(\alpha\)M1
\(F = \sqrt{(1.965...)^2 + (10.714...)^2} = 10.9\ (10.893)\)A1
\(\alpha = \tan^{-1}(10.714.../1.965...) = 79.6\ (79.606...)\)A1 
## Question 3:

| Answer | Mark | Guidance |
|--------|------|----------|
| Attempt to resolve, either direction with correct number of terms | M1 | |
| $F\cos\alpha = 40\sin30 + 20\sin60 - 50\sin45 (= 1.965...)$ | A1 | |
| $F\sin\alpha = 50\cos45 + 20\cos60 - 40\cos30 (= 10.714...)$ | A1 | |
| Method for either $F$ or $\alpha$ | M1 | |
| $F = \sqrt{(1.965...)^2 + (10.714...)^2} = 10.9\ (10.893)$ | A1 | |
| $\alpha = \tan^{-1}(10.714.../1.965...) = 79.6\ (79.606...)$ | A1 | |

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3\\
\includegraphics[max width=\textwidth, alt={}, center]{55090630-1413-45cd-8201-4d58662db6bd-04_586_1003_260_571}

Four coplanar forces of magnitudes $40 \mathrm {~N} , 20 \mathrm {~N} , 50 \mathrm {~N}$ and $F \mathrm {~N}$ act at a point in the directions shown in the diagram. The four forces are in equilibrium.

Find $F$ and $\alpha$.\\

\hfill \mbox{\textit{CAIE M1 2020 Q3 [6]}}
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