| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Rod on smooth peg or cylinder |
| Difficulty | Standard +0.3 This is a standard M2 statics problem requiring resolution of forces and taking moments about a point. The setup is straightforward with given values, requiring routine application of equilibrium conditions (ΣF=0, Σmoments=0) and friction inequality μR≥F. While it involves multiple steps and careful geometry, it follows a well-practiced template with no novel insight required, making it slightly easier than average. |
| Spec | 3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| M1 | Moments about \(A\) | |
| \(P \times 1.6 = 10g\cos60 \times 1.2\) | A1 | |
| \(P = 36.75\) N | A1 | Allow 36.8 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(R + 36.75\sin30 = 10g\) | M1 | Attempt at resolving vertically or taking moments |
| A1 FT | May be implied. \(R = 79.6(25)\) | |
| \(F = 36.75\cos30\) | B1 FT | Expect 31.8. Or second correct equation involving \(F\) or \(R\) or both |
| \(\mu = 31.8/79.6\) | M1 | For use of \((\text{their})F = \mu(\text{their})R\); \(R\) not \(= 10g\) or their \(P\) from (i) |
| \(\mu = 0.4(00)\) | A1 | AWRT; www. Allow inequality |
## Question 3(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| | M1 | Moments about $A$ |
| $P \times 1.6 = 10g\cos60 \times 1.2$ | A1 | |
| $P = 36.75$ N | A1 | Allow 36.8 |
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## Question 3(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $R + 36.75\sin30 = 10g$ | M1 | Attempt at resolving vertically or taking moments |
| | A1 FT | May be implied. $R = 79.6(25)$ |
| $F = 36.75\cos30$ | B1 FT | Expect 31.8. Or second correct equation involving $F$ or $R$ or both |
| $\mu = 31.8/79.6$ | M1 | For use of $(\text{their})F = \mu(\text{their})R$; $R$ not $= 10g$ or their $P$ from (i) |
| $\mu = 0.4(00)$ | A1 | AWRT; www. Allow inequality |
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\includegraphics[max width=\textwidth, alt={}, center]{5addd79d-d502-455c-936f-27005483164e-3_483_787_260_641}
A uniform rod $A B$ of mass 10 kg and length 2.4 m rests with $A$ on rough horizontal ground. The rod makes an angle of $60 ^ { \circ }$ with the horizontal and is supported by a fixed smooth peg $P$. The distance $A P$ is 1.6 m (see diagram).\\
(i) Calculate the magnitude of the force exerted by the peg on the rod.\\
(ii) Find the least value of the coefficient of friction between the rod and the ground needed to maintain equilibrium.
\hfill \mbox{\textit{OCR M2 2012 Q3 [8]}}