| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Resultant of coplanar forces |
| Difficulty | Moderate -0.8 This is a straightforward mechanics question requiring resolution of forces into components and vector addition. Part (i) involves standard trigonometric resolution and Pythagoras (5 marks for routine calculation), while part (ii) is a simple observation about symmetry requiring no calculation. The techniques are basic and well-practiced, making this easier than average for A-level. |
| Spec | 3.03e Resolve forces: two dimensions3.03p Resultant forces: using vectors |
| Answer | Marks |
|---|---|
| 5 (i) | x-component = 4+8cos30°+12cos60° |
| Answer | Marks |
|---|---|
| θ = 60.9° with the 4N force or R = 34.8 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| B1 | 5 | 16.928 |
| Answer | Marks | Guidance |
|---|---|---|
| (ii) | R = 34.8 | |
| θ = 29.1° with the 16N force | B1 | |
| B1 | 2 | ft R from (i) |
| Answer | Marks | Guidance |
|---|---|---|
| Page 7 | Mark Scheme | Syllabus |
| Cambridge International AS/A Level – May/June 2015 | 9709 | 43 |
Question 5:
--- 5 (i) ---
5 (i) | x-component = 4+8cos30°+12cos60°
[= 10 + 4√3]
y-component = 8sin30°+12sin60°+16
[= 20 + 6√3]
R = 34.8 or θ = 60.9° with the 4N force
θ = 60.9° with the 4N force or R = 34.8 | B1
B1
M1
A1
B1 | 5 | 16.928
30.392
2 2 2
For using R = X + Y or tan θ = Y ÷ X
(ii) | R = 34.8
θ = 29.1° with the 16N force | B1
B1 | 2 | ft R from (i)
ft 90 – θ from (i)
Page 7 | Mark Scheme | Syllabus | Paper
Cambridge International AS/A Level – May/June 2015 | 9709 | 43\includegraphics{figure_1}
Four coplanar forces of magnitudes 4 N, 8 N, 12 N and 16 N act at a point. The directions in which the forces act are shown in Fig. 1.
\begin{enumerate}[label=(\roman*)]
\item Find the magnitude and direction of the resultant of the four forces. [5]
\end{enumerate}
\includegraphics{figure_2}
The forces of magnitudes 4 N and 16 N exchange their directions and the forces of magnitudes 8 N and 12 N also exchange their directions (see Fig. 2).
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item State the magnitude and direction of the resultant of the four forces in Fig. 2. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2015 Q5 [7]}}