| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Oblique collision, vector velocity form |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of momentum in two dimensions. Students apply the principle separately to each component (horizontal and vertical), leading to two simple linear equations that directly yield m and b. No problem-solving insight is required—just routine substitution into a standard formula. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03d Conservation in 2D: vector momentum |
| Answer | Marks | Guidance |
|---|---|---|
| \(6\begin{pmatrix}2\\4\end{pmatrix} + m\begin{pmatrix}3\\-2\end{pmatrix} = 6\begin{pmatrix}1\\3\end{pmatrix} + m\begin{pmatrix}7\\b\end{pmatrix}\) | M1 | Setting up momentum equation |
| Using \(x\)-components: \(12 + 3m = 6 + 7m\) | A1 | |
| \(6 = 4m\) | DM1 | |
| \(m = 1.5\) kg | A1 |
| Answer | Marks |
|---|---|
| Using \(y\)-components: \(24 + 1.5(-2) = 6(3) + 1.5b\) | M1 |
| Answer | Marks |
|---|---|
| \(b = 2\) | A1 |
# Question 3:
**(a)**
Conservation of momentum (component form):
$6\begin{pmatrix}2\\4\end{pmatrix} + m\begin{pmatrix}3\\-2\end{pmatrix} = 6\begin{pmatrix}1\\3\end{pmatrix} + m\begin{pmatrix}7\\b\end{pmatrix}$ | M1 | Setting up momentum equation
Using $x$-components: $12 + 3m = 6 + 7m$ | A1 |
$6 = 4m$ | DM1 |
$m = 1.5$ kg | A1 |
**(b)**
Using $y$-components: $24 + 1.5(-2) = 6(3) + 1.5b$ | M1 |
$24 - 3 = 18 + 1.5b$
$1.5b = 3$
$b = 2$ | A1 |3 Two particles, $A$ and $B$, are moving on a smooth horizontal plane when they collide. The mass of $A$ is 6 kg and the mass of $B$ is $m \mathrm {~kg}$. Before the collision, the velocity of $A$ is $\left[ \begin{array} { l } 2 \\ 4 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$ and the velocity of $B$ is $\left[ \begin{array} { r } 3 \\ - 2 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$. After the collision, the velocity of $A$ is $\left[ \begin{array} { l } 1 \\ 3 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$ and the velocity of $B$ is $\left[ \begin{array} { l } 7 \\ b \end{array} \right] \mathrm { ms } ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find $m$.
\item $\quad$ Find $b$.\\
(2 marks)\\
.......... $\_\_\_\_$\\
\includegraphics[max width=\textwidth, alt={}, center]{5d474771-fe32-47c6-8bf3-60ff7a25dd12-07_40_118_529_159}\\
\includegraphics[max width=\textwidth, alt={}, center]{5d474771-fe32-47c6-8bf3-60ff7a25dd12-07_39_117_623_159}
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2010 Q3 [6]}}