| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particles at coordinate positions |
| Difficulty | Moderate -0.3 This is a straightforward M1 statics problem involving moments and equilibrium. Part (a) tests standard modelling assumptions (uniform rod, particle), while parts (b) and (c) require basic moment calculations about a point. The setup is clear, the mathematics is routine (taking moments, solving linear equations), and it's a typical textbook-style question with no novel insight required. Slightly easier than average due to its structured nature and standard techniques. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04c Composite bodies: centre of mass |
| Answer | Marks | Guidance |
|---|---|---|
| (a) (i) non-uniform rod | B2 | |
| (ii) particle | B1 | |
| (b) \(\text{resolve } \uparrow: 2R = 40g + 60g = 100g \therefore R = 50g\) | M1 A1 | |
| (c) \(\text{moments about } A: 40g(x) + 60g(4) - 50g(6) = 0\) | M1 A1 | |
| \(40gx = 300g - 240g = 60g \therefore x = 1.5 \text{ hence, c.o.m is } 1.5 \text{ m from } A\) | M1 A1 | (9 marks) |
(a) (i) non-uniform rod | B2 |
(ii) particle | B1 |
(b) $\text{resolve } \uparrow: 2R = 40g + 60g = 100g \therefore R = 50g$ | M1 A1 |
(c) $\text{moments about } A: 40g(x) + 60g(4) - 50g(6) = 0$ | M1 A1 |
$40gx = 300g - 240g = 60g \therefore x = 1.5 \text{ hence, c.o.m is } 1.5 \text{ m from } A$ | M1 A1 | (9 marks)\includegraphics{figure_1}
Figure 1 shows a plank $AB$ of mass 40 kg and length 6 m, which rests on supports at each of its ends. The plank is wedge-shaped, being thicker at end $A$ than at end $B$.
A woman of mass 60 kg stands on the plank at a distance of 2 m from $B$.
\begin{enumerate}[label=(\alph*)]
\item Suggest suitable modelling assumptions which can be made about
\begin{enumerate}[label=(\roman*)]
\item the plank,
\item the woman. [3 marks]
\end{enumerate}
Given that the reactions at each support are of equal magnitude,
\item find the magnitude of the reaction on the support at $A$, [2 marks]
\item calculate the distance of the centre of mass of the plank from $A$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [9]}}