| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particles at coordinate positions |
| Difficulty | Moderate -0.3 This is a standard M1 statics problem involving moments and reactions with a non-uniform beam. Parts (a) and (c) are bookwork requiring simple modeling statements. Parts (b) and (d) involve routine applications of resolving vertically and taking moments—standard textbook exercises with no novel problem-solving required. The 10 total marks reflect straightforward multi-part structure rather than conceptual difficulty. |
| Spec | 3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks |
|---|---|
| (i) rod | B1 |
| (ii) particle | B1 |
| Answer | Marks |
|---|---|
| resolve \(\uparrow\): \(R + 35g - 60g - 20g = 0\) | M1 |
| reaction at \(B = 45g\) N | A1 |
| Answer | Marks |
|---|---|
| non-uniform means weight not evenly distributed throughout plank i.e. c.o.m. not necessarily in middle of plank | B2 |
| Answer | Marks | Guidance |
|---|---|---|
| moments about \(A\): \(20gx + 60g(4) = 45g(6)\) | M2 A1 | |
| so \(x = 1.5\) m \(\Rightarrow\) c.o.m. is 1.5 m from \(A\) | A1 | (10) |
**Part (a):**
(i) rod | B1 |
(ii) particle | B1 |
**Part (b):**
resolve $\uparrow$: $R + 35g - 60g - 20g = 0$ | M1 |
reaction at $B = 45g$ N | A1 |
**Part (c):**
non-uniform means weight not evenly distributed throughout plank i.e. c.o.m. not necessarily in middle of plank | B2 |
**Part (d):**
moments about $A$: $20gx + 60g(4) = 45g(6)$ | M2 A1 |
so $x = 1.5$ m $\Rightarrow$ c.o.m. is 1.5 m from $A$ | A1 | (10)
---A non-uniform plank $AB$ of mass 20 kg and length 6 m is supported at both ends so that it is horizontal. When a woman of mass 60 kg stands on the plank at a distance of 2 m from $B$, the magnitude of the reaction at $A$ is 35g N.
\begin{enumerate}[label=(\alph*)]
\item Suggest a suitable model for
\begin{enumerate}[label=(\roman*)]
\item the plank, [2 marks]
\item the woman.
\end{enumerate}
\item Calculate the magnitude of the reaction at $B$, giving your answer in terms of $g$. [2 marks]
\item Explain briefly, in the context of the problem, the term 'non-uniform'. [2 marks]
\item Find the distance of the centre of mass of the plank from $A$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [10]}}