| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.8 This is a straightforward M1 collision problem requiring direct application of conservation of momentum to find m, then using the impulse-momentum theorem (impulse = change in momentum). Both parts involve standard formulas with clear given values and minimal algebraic manipulation—easier than average A-level maths questions. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| (a) | Conservation of momentum: \(4m - 6 = m + 9\) → \(m = 5\) | M1 A1 A1 |
| (b) | Impulse = change in momentum = \(3 \times 3 - (3 \times -2) = 15\) | M1 A1 |
| [5 marks total] |
| **Part** | **Answer/Working** | **Marks** | **Guidance** |
|----------|-------------------|----------|-------------|
| (a) | Conservation of momentum: $4m - 6 = m + 9$ → $m = 5$ | M1 A1 A1 | (3 marks) |
| (b) | Impulse = change in momentum = $3 \times 3 - (3 \times -2) = 15$ | M1 A1 | (2 marks) |
| | | | **[5 marks total]** |\begin{enumerate}
\item Two particles $B$ and $C$ have mass $m \mathrm {~kg}$ and 3 kg respectively. They are moving towards each other in opposite directions on a smooth horizontal table. The two particles collide directly. Immediately before the collision, the speed of $B$ is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the speed of $C$ is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. In the collision the direction of motion of $C$ is reversed and the direction of motion of $B$ is unchanged. Immediately after the collision, the speed of $B$ is $1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the speed of $C$ is $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\end{enumerate}
Find\\
(a) the value of $m$,\\
(b) the magnitude of the impulse received by $C$.\\
\hfill \mbox{\textit{Edexcel M1 2011 Q1 [5]}}