| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Session | Specimen |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision followed by wall impact |
| Difficulty | Standard +0.3 This is a standard M2 collision problem with multiple parts requiring conservation of momentum, Newton's experimental law, and inequality reasoning. While it involves several steps and 'show that' proofs, the techniques are routine for M2 students and follow predictable patterns without requiring novel insight or complex problem-solving beyond applying standard formulas. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(3mu - 2mu = 2mw - mv\) | M1 A1 | |
| \(4eu = w + v\) | M1 A1 | |
| Solve \(w = \frac{1}{3}(1 + 4e)u\) | M1 A1 | (6) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| \(v = \frac{1}{3}(8e-1)u\) | M1 A1 | |
| \(v > 0 \Rightarrow e > \frac{1}{8}\) | A1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Notes |
| Rebound speed of \(B = \frac{1}{6}(1+4e)u\) | B1 | |
| 2nd collision \(\Rightarrow \frac{1}{6}(1+4e)u > \frac{1}{3}(8e-1)u\) | M1 | |
| \(1 + 4e > 16e - 2\), \(\quad 3 > 12e\) | ||
| \(e < \frac{1}{4}\) | M1 A1 | (4) |
## Question 8:
### Part (a):
| Answer/Working | Marks | Notes |
|---|---|---|
| $3mu - 2mu = 2mw - mv$ | M1 A1 | |
| $4eu = w + v$ | M1 A1 | |
| Solve $w = \frac{1}{3}(1 + 4e)u$ | M1 A1 | **(6)** |
### Part (b):
| Answer/Working | Marks | Notes |
|---|---|---|
| $v = \frac{1}{3}(8e-1)u$ | M1 A1 | |
| $v > 0 \Rightarrow e > \frac{1}{8}$ | A1 | **(3)** |
### Part (c):
| Answer/Working | Marks | Notes |
|---|---|---|
| Rebound speed of $B = \frac{1}{6}(1+4e)u$ | B1 | |
| 2nd collision $\Rightarrow \frac{1}{6}(1+4e)u > \frac{1}{3}(8e-1)u$ | M1 | |
| $1 + 4e > 16e - 2$, $\quad 3 > 12e$ | | |
| $e < \frac{1}{4}$ | M1 A1 | **(4)** |8. A particle $A$ of mass $m$ is moving with speed $3 u$ on a smooth horizontal table when it collides directly with a particle $B$ of mass $2 m$ which is moving in the opposite direction with speed $u$. The direction of motion of $A$ is reversed by the collision. The coefficient of restitution between $A$ and $B$ is $e$.
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of $B$ immediately after the collision is $\frac { 1 } { 3 } ( 1 + 4 e ) u$.\\
(6)
\item Show that $e > \frac { 1 } { 8 }$.\\
(3)
Subsequently $B$ hits a wall fixed at right angles to the line of motion of $A$ and $B$. The coefficient of restitution between $B$ and the wall is $\frac { 1 } { 2 }$. After $B$ rebounds from the wall, there is a further collision between $A$ and $B$.
\item Show that $e < \frac { 1 } { 4 }$.\\
(4)
END
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q8 [13]}}