| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on inclined plane |
| Difficulty | Challenging +1.2 This is a standard mechanics problem requiring center of mass calculation for composite bodies (using the known formula for cone's COM at h/4 from base), resolution of forces on an incline, and friction/toppling conditions. While it involves multiple steps and careful geometric reasoning about the limiting equilibrium position, the techniques are all standard M2 material with no novel insights required. The multi-part structure and need to handle both friction and toppling conditions elevates it slightly above average difficulty. |
| Spec | 3.03u Static equilibrium: on rough surfaces6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks |
|---|---|
| (ii) | µ = Wsin20/(Wcos20) |
| Answer | Marks |
|---|---|
| x = 0.732 | M1 |
| Answer | Marks |
|---|---|
| A1 | 2 |
| 4 | µ = tan20 |
Question 4:
--- 4 (i)
(ii) ---
4 (i)
(ii) | µ = Wsin20/(Wcos20)
µ = 0.364
Wx/2 + W(x+4.4/4) = 2WOG
OG = 0.4tan70 ( = 0.4/tan20)
x = 0.732 | M1
A1
M1
A1
B1
A1 | 2
4 | µ = tan20
Attempts to take moments
OG = distance to C from M\includegraphics{figure_4}
A uniform solid cone has base radius $0.4$ m and height $4.4$ m. A uniform solid cylinder has radius $0.4$ m and weight equal to the weight of the cone. An object is formed by attaching the cylinder to the cone so that the base of the cone and a circular face of the cylinder are in contact and their circumferences coincide. The object rests in equilibrium with its circular base on a plane inclined at an angle of $20°$ to the horizontal (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Calculate the least possible value of the coefficient of friction between the plane and the object. [2]
\item Calculate the greatest possible height of the cylinder. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2016 Q4 [6]}}