| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with vector velocities |
| Difficulty | Moderate -0.3 This is a straightforward application of conservation of momentum in two dimensions with coalescence. Part (a) requires setting up momentum conservation in the i-direction to find m (simple algebra), and part (b) uses the j-direction to find V. Both parts are direct substitution into the standard formula with no conceptual challenges or problem-solving required beyond routine mechanics. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(m\begin{bmatrix}4\\2\end{bmatrix}+3\begin{bmatrix}-1\\-1\end{bmatrix}=(m+3)\begin{bmatrix}1\\V\end{bmatrix}\) | M1 | Conservation of momentum equation with 3 terms |
| \(4m-3=m+3\) | A1 | Correct momentum equation |
| \(3m=6\) | M1 | Solving equation |
| \(m=2\) | A1 | Correct \(m\) from correct working; deduct one mark for using \(mg\) instead of \(m\) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(4-3=5V\) | M1 | Conservation of momentum equation for component containing \(V\) |
| A1 | Correct equation | |
| \(V=0.2\) | A1 | Correct \(V\) |
## Question 1:
**Part (a)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $m\begin{bmatrix}4\\2\end{bmatrix}+3\begin{bmatrix}-1\\-1\end{bmatrix}=(m+3)\begin{bmatrix}1\\V\end{bmatrix}$ | M1 | Conservation of momentum equation with 3 terms |
| $4m-3=m+3$ | A1 | Correct momentum equation |
| $3m=6$ | M1 | Solving equation |
| $m=2$ | A1 | Correct $m$ from correct working; deduct one mark for using $mg$ instead of $m$ |
**Part (b)**
| Working | Marks | Guidance |
|---------|-------|----------|
| $4-3=5V$ | M1 | Conservation of momentum equation for component containing $V$ |
| | A1 | Correct equation |
| $V=0.2$ | A1 | Correct $V$ |
---1 A particle of mass $m$ has velocity $\left[ \begin{array} { l } 4 \\ 2 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$. It then collides with a particle of mass 3 kg which has velocity $\left[ \begin{array} { l } - 1 \\ - 1 \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$. During the collision the particles coalesce and move with velocity $\left[ \begin{array} { l } 1 \\ V \end{array} \right] \mathrm { m } \mathrm { s } ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Show that $m = 2$.
\item Find $V$.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2005 Q1 [7]}}