| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Non-uniform rod hinged or with applied force |
| Difficulty | Standard +0.3 This is a standard M2 equilibrium problem requiring resolution of forces in two directions and taking moments about a point. While it involves multiple forces at angles and a non-uniform rod, the solution follows a routine three-equation approach (resolve horizontally, resolve vertically, take moments) with straightforward trigonometry and algebra. The problem is slightly above average difficulty due to the multiple angles and three unknowns, but requires no novel insight beyond standard mechanics techniques. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| \(F\cos 45 = 10\cos 60\) | M1 | Resolving horizontally |
| \(F = 7.07\) | A1 | \(7.071 = 5\sqrt{2}\) |
| \(F\sin 45 + 10\sin 60 = W\) | M1 | Resolving vertically |
| \(W = 13.7\) | A1 | \(13.660 = 5(\sqrt{2}+\sqrt{3})\) |
| [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Mark | Guidance |
| M1 | Moments about \(A\) | |
| \(Wd\cos 30 = (F\sin 75)0.5\) | A1 | |
| \(d = 0.289\) m | A1 | |
| [3] |
## Question 3:
### Part (i):
| Working/Answer | Mark | Guidance |
|---|---|---|
| $F\cos 45 = 10\cos 60$ | M1 | Resolving horizontally |
| $F = 7.07$ | A1 | $7.071 = 5\sqrt{2}$ |
| $F\sin 45 + 10\sin 60 = W$ | M1 | Resolving vertically |
| $W = 13.7$ | A1 | $13.660 = 5(\sqrt{2}+\sqrt{3})$ |
| | [4] | |
### Part (ii):
| Working/Answer | Mark | Guidance |
|---|---|---|
| | M1 | Moments about $A$ |
| $Wd\cos 30 = (F\sin 75)0.5$ | A1 | |
| $d = 0.289$ m | A1 | |
| | [3] | |
---3\\
\includegraphics[max width=\textwidth, alt={}, center]{d9970ad1-a7f4-429a-bad1-43e8d114b968-2_442_789_941_676}
A non-uniform $\operatorname { rod } A B$ of length 0.5 m is freely hinged to a fixed point at $A$. The rod is in equilibrium at an angle of $30 ^ { \circ }$ with the horizontal with $B$ below the level of $A$. Equilibrium is maintained by a force of magnitude $F$ N applied at $B$ acting at $45 ^ { \circ }$ above the horizontal in the vertical plane containing $A B$. The force exerted by the hinge on the rod has magnitude 10 N and acts at an angle of $60 ^ { \circ }$ above the horizontal (see diagram).\\
(i) By resolving horizontally and vertically, calculate $F$ and the weight of the rod.\\
(ii) Find the distance of the centre of mass of the rod from $A$.
\hfill \mbox{\textit{CAIE M2 2016 Q3 [7]}}