| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | March |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Conical or hemispherical shell composite |
| Difficulty | Standard +0.3 This is a standard two-part centre of mass question requiring routine application of formulas. Part (i) involves calculating the centre of mass of a composite body (cylinder curved surface + base) using standard techniques with given dimensions. Part (ii) applies equilibrium conditions (limiting friction and toppling) which is a textbook scenario. The calculations are straightforward with no novel insight required, making it slightly easier than average. |
| Spec | 6.04d Integration: for centre of mass of laminas/solids6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| 2(i) | M = 2π x 0.2 x 0.9 + π x 0.22 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| = 2π x 0.2 x 0.9 x 0.9/2 | M1 | Takes moments about the base |
| Answer | Marks |
|---|---|
| x = 0.405 m AG | A1 |
| Total: | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| 2(ii) | tanθ = 0.2/0.405 | M1 |
| µ = tanθ | B1 | |
| µ = 0.494 | A1 | |
| Total: | 3 | |
| Question | Answer | Marks |
Question 2:
--- 2(i) ---
2(i) | M = 2π x 0.2 x 0.9 + π x 0.22 | B1 | M = total mass of the container
(cid:76)
(2π x 0.2 x 0.9 + π x 0.22)x
= 2π x 0.2 x 0.9 x 0.9/2 | M1 | Takes moments about the base
(cid:76)
x = 0.405 m AG | A1
Total: | 3
--- 2(ii) ---
2(ii) | tanθ = 0.2/0.405 | M1 | θ is the angle of slope of the plane
µ = tanθ | B1
µ = 0.494 | A1
Total: | 3
Question | Answer | Marks | GuidanceA cylindrical container is open at the top. The curved surface and the circular base of the container are both made from the same thin uniform material. The container has radius $0.2 \text{ m}$ and height $0.9 \text{ m}$.
\begin{enumerate}[label=(\roman*)]
\item Show that the centre of mass of the container is $0.405 \text{ m}$ from the base. [3]
\end{enumerate}
The container is placed with its base on a rough inclined plane. The container is in equilibrium on the point of slipping down the plane and also on the point of toppling.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the coefficient of friction between the container and the plane. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2017 Q2 [6]}}