| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Non-uniform beam on supports |
| Difficulty | Moderate -0.3 This is a standard M1 moments problem requiring equilibrium conditions (sum of forces and moments). Part (a) uses vertical equilibrium with equal reactions, part (b) takes moments about a point to find the centre of mass. The multi-step nature and 9 total marks elevate it slightly above the most routine questions, but the techniques are completely standard for M1 with no novel insight required. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_2}
A non-uniform plank of wood $AB$ has length 6 m and mass 90 kg. The plank is smoothly supported at its two ends $A$ and $B$, with $A$ and $B$ at the same horizontal level. A woman of mass 60 kg stands on the plank at the point $C$, where $AC = 2$ m, as shown in Fig. 2. The plank is in equilibrium and the magnitudes of the reactions on the plank at $A$ and $B$ are equal. The plank is modelled as a non-uniform rod and the woman as a particle. Find
\begin{enumerate}[label=(\alph*)]
\item the magnitude of the reaction on the plank at $B$, [2]
\item the distance of the centre of mass of the plank from $A$. [5]
\item State briefly how you have used the modelling assumption that
\begin{enumerate}[label=(\roman*)]
\item the plank is a rod,
\item the woman is a particle.
\end{enumerate} [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q3 [9]}}