| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Coplanar forces in equilibrium |
| Difficulty | Standard +0.8 This is a 3D moments problem requiring knowledge that the center of mass of a uniform cone is at 3h/4 from the vertex, calculation of the perpendicular distance from P to the line of action of weight, and taking moments about P. While it involves multiple steps and spatial reasoning about a tilted cone, the techniques are standard for M2 level and the question provides significant guidance by asking students to show a specific moment value first. |
| Spec | 3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks |
|---|---|
| (ii) | 3 |
| Answer | Marks |
|---|---|
| F = 13(.0) | M1 |
| Answer | Marks |
|---|---|
| [2] | P to centre of mass (= 0.3 m) |
Question 2:
--- 2 (i)
(ii) ---
2 (i)
(ii) | 3
Horizontal distance = 0.8 × × sin30
4
0.8
OR 0.8tan30cos30 – sin30
4
Mom. = (0.6sin30 × 20 =) 6 Nm AG
OR
0.8
Mom = 20cos30 × 0.8tan30 – 20sin30 ×
4
Mom = 6 Nm AG
6 = F × 0.8tan30
F = 13(.0) | M1
A1
[2]
M1
A1
M1
A1
[2] | P to centre of mass (= 0.3 m)
Resolves Wt // and perp axis and finds
moments of both components
Takes moments about P\includegraphics{figure_2}
A uniform solid cone with height $0.8$ m and semi-vertical angle $30°$ has weight $20$ N. The cone rests in equilibrium with a single point $P$ of its base in contact with a rough horizontal surface, and its vertex $V$ vertically above $P$. Equilibrium is maintained by a force of magnitude $F$ N acting along the axis of symmetry of the cone and applied to $V$ (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Show that the moment of the weight of the cone about $P$ is $6$ N m. [2]
\item Hence find $F$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2014 Q2 [4]}}