| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find mass |
| Difficulty | Moderate -0.8 This is a straightforward M1 collision problem requiring direct application of impulse formula (part a) and conservation of momentum (part b). All values are given, requiring only substitution into standard formulas with careful attention to sign conventions—simpler than average A-level questions which typically require more problem-solving or multi-step reasoning. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| \(I = 4(5-1) = 16 \text{ Ns}\) | M1 A1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Notes |
| CLM: \(4 \times 5 - m \times 3 = 4 \times 1 + m \times 2\) | M1 A1 | |
| \(\Rightarrow m = 3.2\) | DM1 A1 (4) | |
| or \(16 = m(3+2)\) | M1 A1 | |
| \(\Rightarrow m = 3.2\) | DM1 A1 (4) | Total: 6 |
## Question 1:
### Part (a)
| Working | Marks | Notes |
|---------|-------|-------|
| $I = 4(5-1) = 16 \text{ Ns}$ | M1 A1 (2) | |
### Part (b)
| Working | Marks | Notes |
|---------|-------|-------|
| CLM: $4 \times 5 - m \times 3 = 4 \times 1 + m \times 2$ | M1 A1 | |
| $\Rightarrow m = 3.2$ | DM1 A1 (4) | |
| **or** $16 = m(3+2)$ | M1 A1 | |
| $\Rightarrow m = 3.2$ | DM1 A1 (4) | **Total: 6** |
---\begin{enumerate}
\item Two particles $A$ and $B$ have masses 4 kg and $m \mathrm {~kg}$ respectively. They are moving towards each other in opposite directions on a smooth horizontal table when they collide directly. Immediately before the collision, the speed of $A$ is $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the speed of $B$ is $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Immediately after the collision, the direction of motion of $A$ is unchanged and the speed of $A$ is $1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(a) Find the magnitude of the impulse exerted on $A$ in the collision.
\end{enumerate}
Immediately after the collision, the speed of $B$ is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(b) Find the value of $m$.\\
\hfill \mbox{\textit{Edexcel M1 2008 Q1 [6]}}