| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Coalescence collision |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of momentum in two standard scenarios (coalescence and separate particles). Part (a) requires a single equation with opposite velocities, and part (b) is similarly direct. Both parts are routine textbook exercises requiring only recall of the momentum formula and basic algebra, making this easier than average for A-level. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(3 \times 4 + 2 \times (-4) = 5v\) | M1 A1 | Three term equation for conservation of momentum. Correct equation |
| \(4 = 5v\) | ||
| \(v = \frac{4}{5} = 0.8\) | A1 | Total: 3 — Correct speed (for use of \(mg\) instead of \(m\) deduct the first A1) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(3 \times 4 + 2 \times (-4) = 3 \times 0.4 + 2v\) | M1 A1 | Four term equation for conservation of momentum. Correct equation |
| \(4 = 1.2 + 2v\) | ||
| \(v = \frac{4 - 1.2}{2} = 1.4\) | A1 | Total: 3 — Correct speed (for use of \(mg\) instead of \(m\) deduct the first A1) |
## Question 1:
### Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| $3 \times 4 + 2 \times (-4) = 5v$ | M1 A1 | Three term equation for conservation of momentum. Correct equation |
| $4 = 5v$ | | |
| $v = \frac{4}{5} = 0.8$ | A1 | **Total: 3** — Correct speed (for use of $mg$ instead of $m$ deduct the first A1) |
### Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| $3 \times 4 + 2 \times (-4) = 3 \times 0.4 + 2v$ | M1 A1 | Four term equation for conservation of momentum. Correct equation |
| $4 = 1.2 + 2v$ | | |
| $v = \frac{4 - 1.2}{2} = 1.4$ | A1 | **Total: 3** — Correct speed (for use of $mg$ instead of $m$ deduct the first A1) |
---1 Two particles $A$ and $B$ have masses of 3 kg and 2 kg respectively. They are moving along a straight horizontal line towards each other. Each particle is moving with a speed of $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ when they collide.\\
\includegraphics[max width=\textwidth, alt={}, center]{965a176a-848c-478d-a748-80fc9dfe4399-2_225_579_676_660}
\begin{enumerate}[label=(\alph*)]
\item If the particles coalesce during the collision to form a single particle, find the speed of the combined particle after the collision.
\item If, after the collision, $A$ moves in the same direction as before the collision with speed $0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, find the speed of $B$ after the collision.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2007 Q1 [6]}}