| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Non-uniform beam on supports |
| Difficulty | Moderate -0.8 This is a straightforward moments problem requiring only basic equilibrium principles (taking moments about a pivot) and standard calculations. Part (a) is a direct application of the moments formula, part (b) tests understanding of modelling assumptions, and part (c) extends the same principle with one additional unknown. All steps are routine for M1 students with no novel problem-solving required. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04a Centre of mass: gravitational effect6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass |
| Answer | Marks | Guidance |
|---|---|---|
| \(M(C): 25g \times 2 = 40g \times x\) → \(x = 1.25 \text{ m}\) | M1 A1 | (2 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Weight/mass acts at mid-point; or weight/mass evenly distributed (o.e.) | B1 | (1 mark) |
| Answer | Marks | Guidance |
|---|---|---|
| Solve: \(y = 0.4 \text{ m}\) | M1 A1 ↓ M1 A1 | (4 marks) |
## Part (a)
$M(C): 25g \times 2 = 40g \times x$ → $x = 1.25 \text{ m}$ | M1 A1 | (2 marks)
## Part (b)
Weight/mass acts at mid-point; or weight/mass evenly distributed (o.e.) | B1 | (1 mark)
## Part (c)
$M(C): 40g \times 1.4 = 15g \times y + 25g \times 2$
Solve: $y = 0.4 \text{ m}$ | M1 A1 ↓ M1 A1 | (4 marks)
**Total for Question 3: 8 marks**
---\includegraphics{figure_1}
A seesaw in a playground consists of a beam $AB$ of length $4$ m which is supported by a smooth pivot at its centre $C$. Jill has mass $25$ kg and sits on the end $A$. David has mass $40$ kg and sits at a distance $x$ metres from $C$, as shown in Figure 1. The beam is initially modelled as a uniform rod. Using this model,
\begin{enumerate}[label=(\alph*)]
\item find the value of $x$ for which the seesaw can rest in equilibrium in a horizontal position. [3]
\item State what is implied by the modelling assumption that the beam is uniform. [1]
\end{enumerate}
David realises that the beam is not uniform as he finds that he must sit at a distance $1.4$ m from $C$ for the seesaw to rest horizontally in equilibrium. The beam is now modelled as a non-uniform rod of mass $15$ kg. Using this model,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumii}{2}
\item find the distance of the centre of mass of the beam from $C$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2006 Q3 [8]}}