| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Moderate -0.8 This is a straightforward two-part momentum conservation problem with standard collision scenarios. Part (a) requires simple application of conservation of momentum with one unknown, and part (b) involves a coalescence (perfectly inelastic collision) with again just one unknown. Both are routine textbook exercises requiring only direct substitution into the momentum equation with no problem-solving insight or multi-step reasoning needed. |
| Spec | 6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0.3 \times 4 + 0 = 0.3v + 0.2 \times 3\) | M1 | For attempt at use of conservation of momentum |
| Speed \(= 2 \text{ ms}^{-1}\) | A1 | |
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(0.2 \times 3 + 0 = (0.2 + m) \times 2\) | M1 | For attempt at use of conservation of momentum |
| \(m = 0.1\) | A1 | |
| Total: 2 |
## Question 1:
**Part (a):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.3 \times 4 + 0 = 0.3v + 0.2 \times 3$ | M1 | For attempt at use of conservation of momentum |
| Speed $= 2 \text{ ms}^{-1}$ | A1 | |
| | **Total: 2** | |
**Part (b):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.2 \times 3 + 0 = (0.2 + m) \times 2$ | M1 | For attempt at use of conservation of momentum |
| $m = 0.1$ | A1 | |
| | **Total: 2** | |
---1 Two particles $P$ and $Q$, of masses 0.3 kg and 0.2 kg respectively, are at rest on a smooth horizontal plane. $P$ is projected at a speed of $4 \mathrm {~ms} ^ { - 1 }$ directly towards $Q$. After $P$ and $Q$ collide, $Q$ begins to move with a speed of $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $P$ after the collision.\\
After the collision, $Q$ moves directly towards a third particle $R$, of mass $m \mathrm {~kg}$, which is at rest on the plane. The two particles $Q$ and $R$ coalesce on impact and move with a speed of $2 \mathrm {~ms} ^ { - 1 }$.
\item Find $m$.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2022 Q1 [4]}}