| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2004 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod hinged to wall with string support |
| Difficulty | Standard +0.3 This is a straightforward statics problem requiring moments about point A, resolving forces horizontally and vertically, and basic trigonometry to find the string angle. It's slightly easier than average because the setup is standard, the rod is perpendicular to the wall (simplifying geometry), and it's a routine three-part question with clear steps—no novel insight required, just systematic application of equilibrium conditions. |
| Spec | 6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| (i) For taking moments about A (N.B. A moment = a force is M0) | M1 | |
| \(30 \times 0.6 = T \times 1.2 \times \frac{0.5}{1.3}\) or \(30 \times 0.6 = T \times 1.2 \sin 22.62°\) | A1 | |
| Tension is 39 N | A1 | 3 marks |
| (ii) Horizontal component is 36 N | B1 ft | |
| For taking moments about B (\(1.2Y = 30 \times 0.6\)) or for resolving forces vertically (\(30 - T \sin 22.62°\)) | M1 | |
| Vertical component is 15 N | A1 ft | 3 marks |
**(i)** For taking moments about A (N.B. A moment = a force is M0) | M1 |
$30 \times 0.6 = T \times 1.2 \times \frac{0.5}{1.3}$ or $30 \times 0.6 = T \times 1.2 \sin 22.62°$ | A1 |
Tension is 39 N | A1 | 3 marks
**(ii)** Horizontal component is 36 N | B1 ft |
For taking moments about B ($1.2Y = 30 \times 0.6$) or for resolving forces vertically ($30 - T \sin 22.62°$) | M1 |
Vertical component is 15 N | A1 ft | 3 marks
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\includegraphics[max width=\textwidth, alt={}, center]{81411376-b926-4857-bc9b-ac85d7957f3d-2_333_737_762_705}
A uniform rod $A B$ of length 1.2 m and weight 30 N is in equilibrium with the end $A$ in contact with a vertical wall. $A B$ is held at right angles to the wall by a light inextensible string. The string has one end attached to the rod at $B$ and the other end attached to a point $C$ of the wall. The point $C$ is 0.5 m vertically above $A$ (see diagram). Find\\
(i) the tension in the string,\\
(ii) the horizontal and vertical components of the force exerted on the rod by the wall at $A$.
\hfill \mbox{\textit{CAIE M2 2004 Q2 [6]}}