| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with string support |
| Difficulty | Standard +0.3 This is a standard mechanics problem requiring knowledge that the center of mass of a semicircular arc is at distance 2r/π from the diameter, followed by straightforward geometry and moment equilibrium. The geometry calculation is given as 'show that' (reducing difficulty), and the moment equation involves only one unknown. Slightly above average due to the 3D spatial reasoning and semicircular arc property, but otherwise routine for M2 level. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks |
|---|---|
| (ii) | OG = 0.4sin(π/2)/(π/2) |
| Answer | Marks |
|---|---|
| W = 21.2 N | B1 |
| Answer | Marks |
|---|---|
| A1 | 3 |
| 2 | = 0.25464... |
Question 2:
--- 2 (i)
(ii) ---
2 (i)
(ii) | OG = 0.4sin(π/2)/(π/2)
d = OG cos70 + 0.4sin70
d = 0.463 AG
0.463W = 15 × 0.8cos35
W = 21.2 N | B1
M1
A1
M1
A1 | 3
2 | = 0.25464...\includegraphics{figure_2}
A uniform wire has the shape of a semicircular arc, with diameter $AB$ of length $0.8$ m. The wire is attached to a vertical wall by a smooth hinge at $A$. The wire is held in equilibrium with $AB$ inclined at $70°$ to the upward vertical by a light string attached to $B$. The other end of the string is attached to the point $C$ on the wall $0.8$ m vertically above $A$. The tension in the string is $15$ N (see diagram).
\begin{enumerate}[label=(\roman*)]
\item Show that the horizontal distance of the centre of mass of the wire from the wall is $0.463$ m, correct to 3 significant figures. [3]
\item Calculate the weight of the wire. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2016 Q2 [5]}}