| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics A AS (Further Mechanics A AS) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particles at coordinate positions |
| Difficulty | Standard +0.3 This is a straightforward multi-part centre of mass question requiring standard formulas applied systematically. Part (i) uses the basic weighted average formula for particles, part (ii) requires finding lengths of wire segments and their midpoints (simple coordinate geometry), and part (iii) combines the results. All techniques are routine for Further Maths students with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (i) | (cid:167)x(cid:183) (cid:167)(cid:16)3(cid:183) (cid:167)0(cid:183) (cid:167)2(cid:183) (cid:167)5(cid:183)e |
| Answer | Marks |
|---|---|
| y (cid:32)2.4 | c |
| Answer | Marks |
|---|---|
| [4] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | Any correct method for at least 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (ii) | By symmetry, x (cid:32)1 |
| Answer | Marks |
|---|---|
| 3 | B1 |
| Answer | Marks |
|---|---|
| [4] | 2.4 |
| Answer | Marks |
|---|---|
| 1.1 | May be established from 1st |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (iii) | (cid:11)10m(cid:14)12m(cid:12)x (cid:32)10m(cid:11)0(cid:12)(cid:14)12m(cid:11)1(cid:12) |
| Answer | Marks |
|---|---|
| 11 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 1.1 | Method for combining (accept |
Question 5:
5 | (i) | (cid:167)x(cid:183) (cid:167)(cid:16)3(cid:183) (cid:167)0(cid:183) (cid:167)2(cid:183) (cid:167)5(cid:183)e
10m(cid:168) (cid:184)(cid:32)4m(cid:168) (cid:184)(cid:14)3m(cid:168) (cid:184)(cid:14)m(cid:168) (cid:184)(cid:14)2m(cid:168) (cid:184)
(cid:169)y(cid:185) (cid:169) 4 (cid:185) (cid:169)0(cid:185) (cid:169)0(cid:185) (cid:169)4(cid:185)
p
x (cid:32)0 S
y (cid:32)2.4 | c
M1
A1
A1
A1
[4] | 1.1
1.1
1.1
1.1 | Any correct method for at least 1
cpt
Allow 1 error including its
consequences
5 | (ii) | By symmetry, x (cid:32)1
12my (cid:32)5m(cid:117)2(cid:14)2m(cid:117)0(cid:14)5m(cid:117)2
5
y (cid:32)
3 | B1
M1
B1
A1
[4] | 2.4
3.3
1.1a
1.1 | May be established from 1st
principles.
Correct method using mid-points
Masses in the correct ratio
5 | (iii) | (cid:11)10m(cid:14)12m(cid:12)x (cid:32)10m(cid:11)0(cid:12)(cid:14)12m(cid:11)1(cid:12)
6
x (cid:32) (0.5454…)
11 | M1
A1
[2] | 3.1b
1.1 | Method for combining (accept
start again)
FT their (i), (ii)5 In this question, all coordinates refer to the axes shown in Fig. 5.1.
Fig. 5.1 shows a system of four particles with masses $4 m , 3 m , m$ and $2 m$ at the points $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D . These points have coordinates $( - 3,4 ) , ( 0,0 ) , ( 2,0 )$ and $( 5,4 )$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{be1851d6-af11-40e1-8a36-5938ee7864d4-5_436_817_513_639}
\captionsetup{labelformat=empty}
\caption{Fig. 5.1}
\end{center}
\end{figure}
(i) Calculate the coordinates of the centre of mass of the system of particles.
A thin uniform rigid wire of mass $12 m$ connects the points $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D with straight line sections, as shown in Fig. 5.2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{be1851d6-af11-40e1-8a36-5938ee7864d4-5_460_903_1338_573}
\captionsetup{labelformat=empty}
\caption{Fig. 5.2}
\end{center}
\end{figure}
(ii) Calculate the coordinates of the centre of mass of the wire.
The particles at $\mathrm { A } , \mathrm { B } , \mathrm { C }$ and D are now fixed to the wire to form a rigid object, $R$.\\
(iii) Calculate the $x$-coordinate of the centre of mass of $R$.
\hfill \mbox{\textit{OCR MEI Further Mechanics A AS Q5 [10]}}