| Exam Board | OCR |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2010 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Two jointed rods in equilibrium |
| Difficulty | Challenging +1.2 This is a standard M3 statics problem requiring moments about two points and resolution of forces. Part (i) is straightforward moment calculation about B with given geometry. Part (ii) requires taking moments about C for the whole system and using the result from (i), involving some trigonometry but following a well-established method. More challenging than basic C1/M1 questions due to the two-rod system and trigonometric manipulation, but still a textbook exercise without requiring novel insight. |
| Spec | 3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
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\includegraphics[max width=\textwidth, alt={}, center]{08760a55-da6c-41f2-a88a-289ecc227f69-3_812_773_260_685}
Two uniform rods $A B$ and $B C$, each of length $2 a$, have weights $2 W$ and $W$ respectively. The rods are freely jointed to each other at $B$, and $B C$ is freely jointed to a fixed point at $C$. The rods are held in equilibrium in a vertical plane by a light string attached to $A$ and perpendicular to $A B$. The rods $A B$ and $B C$ make angles $45 ^ { \circ }$ and $\alpha$, respectively, with the horizontal. The tension in the string is $T$ (see diagram).\\
(i) By taking moments about $B$ for $A B$, show that $W = \sqrt { 2 } T$.\\
(ii) Find the value of $\tan \alpha$.
\hfill \mbox{\textit{OCR M3 2010 Q3 [9]}}