| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on smooth peg or cylinder |
| Difficulty | Standard +0.8 This is a non-trivial statics problem requiring knowledge that the center of mass of a semicircular lamina is at distance 4r/(3π) from the diameter, setting up moment equilibrium about point A with careful geometry (30° angle, forces at different points), and resolving forces in two directions. The multi-step nature, geometric complexity, and need to recall/apply a non-standard center of mass formula place it above average difficulty. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| 5(i) | OG = 2 × 0.7sin(π / 2) / (3π / 2) (= 0.297) | B1 |
| 0.9R = 14(0.7cos30 – 0.297sin30) | M1A1 | Attempts to take moments about A |
| R = 7.12 N | A1 | |
| Total: | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| 5(ii) | H = 7.12sin30 and V = 14 − Rcos30 | M1 |
| tanθ = (14 – 7.12cos30) / (7.12sin30) | M1 | Uses tanθ = V / H, where θ is the required angle |
| θ = 65.6 | A1 | |
| Total: | 3 | |
| Question | Answer | Marks |
Question 5:
--- 5(i) ---
5(i) | OG = 2 × 0.7sin(π / 2) / (3π / 2) (= 0.297) | B1
0.9R = 14(0.7cos30 – 0.297sin30) | M1A1 | Attempts to take moments about A
R = 7.12 N | A1
Total: | 4
--- 5(ii) ---
5(ii) | H = 7.12sin30 and V = 14 − Rcos30 | M1 | Resolves horizontally and vertically
tanθ = (14 – 7.12cos30) / (7.12sin30) | M1 | Uses tanθ = V / H, where θ is the required angle
θ = 65.6 | A1
Total: | 3
Question | Answer | Marks | Guidance\includegraphics{figure_3}
A uniform semicircular lamina of radius $0.7$ m and weight $14$ N has diameter $AB$. The lamina is in a vertical plane with $A$ freely pivoted at a fixed point. The straight edge $AB$ rests against a small smooth peg $P$ above the level of $A$. The angle between $AB$ and the horizontal is $30°$ and $AP = 0.9$ m (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Show that the magnitude of the force exerted by the peg on the lamina is $7.12$ N, correct to 3 significant figures. [4]
\item Find the angle with the horizontal of the force exerted by the pivot on the lamina at $A$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2017 Q5 [7]}}