| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam on point of tilting |
| Difficulty | Standard +0.3 This is a standard M1 moments problem involving limiting equilibrium with a uniform beam. It requires taking moments about the pivot point and applying equilibrium conditions, but follows a well-established textbook pattern with straightforward calculations. The multi-part structure and need to interpret 'limiting equilibrium' adds slight complexity beyond the most basic moments questions, placing it slightly above average difficulty. |
| Spec | 6.04b Find centre of mass: using symmetry6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| (a) moments about \(P\): \(20g(3) + 50g(0.5) - mg(1.7) = 0\) | M2 | |
| \(1.7m = 60 + 25 = 85 \Rightarrow m = 50\) kg | M1 A1 | |
| (b) moments about \(P\): \((20 + x)g(3) + 50g(0.5) - 50g(2) = 0\) | M1 | |
| \(100 - 25 - 3(20 + x) = 0 \Rightarrow x = 5\) kg | M1 A1 | |
| (c) weight acts at the middle of the plank | B1 | (8 marks) |
**(a)** moments about $P$: $20g(3) + 50g(0.5) - mg(1.7) = 0$ | M2 |
$1.7m = 60 + 25 = 85 \Rightarrow m = 50$ kg | M1 A1 |
**(b)** moments about $P$: $(20 + x)g(3) + 50g(0.5) - 50g(2) = 0$ | M1 |
$100 - 25 - 3(20 + x) = 0 \Rightarrow x = 5$ kg | M1 A1 |
**(c)** weight acts at the middle of the plank | B1 | (8 marks)4.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{60b9db45-b48e-40a1-bd22-909e11877bc3-3_275_842_194_408}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
Figure 2 shows a uniform plank $A B$ of mass 50 kg and length 5 m which overhangs a river by 2 m . When a boy of mass 20 kg stands at $A$, his sister can walk to within 0.3 m of $B$, at which point the plank is in limiting equilibrium.
\begin{enumerate}[label=(\alph*)]
\item What is the mass of the girl?
\item Find the smallest extra weight which must be placed at $A$ to enable the girl to walk right to the end $B$.
\item How have you used the fact that the plank is uniform?
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [8]}}