| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Particles at coordinate positions |
| Difficulty | Moderate -0.8 This is a straightforward application of the centre of mass formula for discrete particles. Students simply substitute the given masses and coordinates into x̄ = Σ(mx)/Σm and ȳ = Σ(my)/Σm, requiring only arithmetic calculation with no problem-solving or conceptual insight needed. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass |
| Answer | Marks |
|---|---|
| 2 | 10mx = 1(3m) + 2(5m) + 5(2m) |
| Answer | Marks |
|---|---|
| y = 0.2 | M1 |
| Answer | Marks |
|---|---|
| [4] | 1.1 |
| Answer | Marks |
|---|---|
| 1.1 | Use of x ∑m = ∑ x m |
Question 2:
2 | 10mx = 1(3m) + 2(5m) + 5(2m)
x = 2.3
10my = 2(3m) + (−2)(5m) + 3(2m)
y = 0.2 | M1
A1
M1
A1
[4] | 1.1
1.1
1.1
1.1 | Use of x ∑m = ∑ x m
i i i
cao
Use of y ∑m = ∑ y m
i i i
cao2 The diagram shows a system of three particles of masses $3 m , 5 m$ and $2 m$ situated in the $x - y$ plane at the points $\mathrm { A } ( 1,2 ) , \mathrm { B } ( 2 , - 2 )$ and $\mathrm { C } ( 5,3 )$ respectively.\\
\begin{tikzpicture}[>=latex, x=1cm, y=1cm]
% Draw the background grid
\draw[dotted, gray!80, step=1] (0,-3) grid (6,4);
% Draw the axes
\draw[->, thick] (0,-3.2) -- (0,4.6) node[above] {$y$};
\draw[->, thick] (0,0) -- (6.8,0) node[right] {$x$};
% Origin label
\node[below left=1pt] at (0,0) {$0$};
% X-axis ticks and labels
\foreach \x in {2, 4, 6} {
\draw[thick] (\x, 0) -- (\x, -0.15) node[below] {$\x$};
}
% Y-axis ticks and labels
\foreach \y in {-2, 2, 4} {
\draw[thick] (0, \y) -- (-0.15, \y) node[left] {$\y$};
}
% Plot the points and their labels
% Point A
\fill (1,2) circle (1.5pt);
\node[above=2pt] at (1,2) {A $3m$};
% Point B
\fill (2,-2) circle (1.5pt);
\node[above=2pt] at (2,-2) {B $5m$};
% Point C
\fill (5,3) circle (1.5pt);
\node[above=2pt] at (5,3) {C $2m$};
\end{tikzpicture}
Determine the coordinates of the centre of mass of the system of particles.
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2021 Q2 [4]}}