| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Maximum or minimum mass |
| Difficulty | Standard +0.3 This is a standard M2 moments problem requiring taking moments about the pivot point to find limiting equilibrium conditions. The two-part calculation (parts a and b) involves straightforward application of the moments principle with clearly defined geometry, though students must correctly identify the pivot and set up moment equations. Slightly above average difficulty due to the two-part nature and need to consider limiting cases, but follows a well-practiced textbook template. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Part (a): Centre of mass of rod is 3 m from river bank. Taking moments about \(A\), edge of bank: \(3 \times 15 = 50x\); \(x = 0.9\) | B1, M1, A1 | Use of centre of mass is centre of rod; Or resolve \(R = 65g\) Moments about any point (correct) 0.9 |
| Part (b): Taking moments about \(A\): \(50 \times 2 = 15 \times 3 + m \times 8\); \(55 = 8m\); \(m = 6\frac{7}{8}\); Mass is \(6\frac{7}{8}\) kg | M1A1, A1, A1 | M1 3 terms, 2 correct; Accept 6.88 and 6.87 |
| Part (c): Centre of mass of rod is 3 m from river bank | E1 | Centre of mass is at centre of rod |
| Part (d): eg Woman is a particle; The mass is a particle; The plank is a rigid rod | E1 | |
| Total: 9 |
| Answer/Working | Marks | Guidance |
|---|---|---|
| **Part (a):** Centre of mass of rod is 3 m from river bank. Taking moments about $A$, edge of bank: $3 \times 15 = 50x$; $x = 0.9$ | B1, M1, A1 | Use of centre of mass is centre of rod; Or resolve $R = 65g$ Moments about any point (correct) 0.9 |
| **Part (b):** Taking moments about $A$: $50 \times 2 = 15 \times 3 + m \times 8$; $55 = 8m$; $m = 6\frac{7}{8}$; Mass is $6\frac{7}{8}$ kg | M1A1, A1, A1 | M1 3 terms, 2 correct; Accept 6.88 and 6.87 |
| **Part (c):** Centre of mass of rod is 3 m from river bank | E1 | Centre of mass is at centre of rod |
| **Part (d):** eg Woman is a particle; The mass is a particle; The plank is a rigid rod | E1 | |
| | | **Total: 9** |4 A uniform plank is 10 m long and has mass 15 kg . It is placed on horizontal ground at the edge of a vertical river bank, so that 2 m of the plank is projecting over the edge, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{676e753d-1b80-413c-a4b9-21861db8dde5-3_250_1285_1361_388}
\begin{enumerate}[label=(\alph*)]
\item A woman of mass 50 kg stands on the part of the plank which projects over the river.
Find the greatest distance from the river bank at which she can safely stand.
\item The woman wishes to stand safely at the end of the plank which projects over the river.
Find the minimum mass which she should place on the other end of the plank so that she can do this.
\item State how you have used the fact that the plank is uniform in your solution.
\item State one other modelling assumption which you have made.
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2007 Q4 [9]}}