CAIE M1 2012 November — Question 4 7 marks

Exam BoardCAIE
ModuleM1 (Mechanics 1)
Year2012
SessionNovember
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeResultant of three coplanar forces
DifficultyStandard +0.3 This is a standard mechanics question requiring resolution of forces in two perpendicular directions and use of Pythagoras/trigonometry to find magnitude and direction of resultant. It involves routine application of component methods with straightforward angles (30°, 60°, 90°), making it slightly easier than average but still requiring systematic working through multiple steps.
Spec3.03e Resolve forces: two dimensions3.03p Resultant forces: using vectors
4 \includegraphics[max width=\textwidth, alt={}, center]{2bb3c9bb-60f0-440d-a148-b4db3478ca31-2_387_1091_2019_525} Three coplanar forces of magnitudes \(8 \mathrm {~N} , 12 \mathrm {~N}\) and 2 N act at a point. The resultant of the forces has magnitude \(R \mathrm {~N}\). The directions of the three forces and the resultant are shown in the diagram. Find \(R\) and \(\theta\).
AnswerMarks Guidance
\(M1\) For resolving forces in the 'x' and 'y' directions
\(X = 12\cos25° - 8\cos10°\) (= 2.9972....)A1
\(Y = 12\sin25° + 8\sin10° - 2\) (= 4.4606....)A1
\(M1\) For using \(R^2 = X^2 + Y^2\)
\(R = 5.37\)A1
\(M1\) For using \(\tan\theta = X/Y\)
\(\theta = 33.9\)A1 7 
$M1$ | | For resolving forces in the 'x' and 'y' directions
$X = 12\cos25° - 8\cos10°$ (= 2.9972....) | A1 |
$Y = 12\sin25° + 8\sin10° - 2$ (= 4.4606....) | A1 |
$M1$ | | For using $R^2 = X^2 + Y^2$
$R = 5.37$ | A1 |
$M1$ | | For using $\tan\theta = X/Y$
$\theta = 33.9$ | A1 | 7
4\\
\includegraphics[max width=\textwidth, alt={}, center]{2bb3c9bb-60f0-440d-a148-b4db3478ca31-2_387_1091_2019_525}

Three coplanar forces of magnitudes $8 \mathrm {~N} , 12 \mathrm {~N}$ and 2 N act at a point. The resultant of the forces has magnitude $R \mathrm {~N}$. The directions of the three forces and the resultant are shown in the diagram. Find $R$ and $\theta$.

\hfill \mbox{\textit{CAIE M1 2012 Q4 [7]}}
This paper (7 questions)
View full paper
Q1 4 Q2 5 Q3 7 Q4 7 Q5 8 Q6 9 Q7 10