| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Three-particle sequential collisions |
| Difficulty | Standard +0.3 This is a standard M2 momentum and collisions question requiring systematic application of conservation of momentum and coefficient of restitution formula across two collisions. While it has multiple parts and requires careful algebraic manipulation, it follows a predictable structure with no novel insights needed—students who have practiced collision problems will recognize the standard approach immediately. The 'show that' parts provide target answers, reducing problem-solving demand. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| \(u = 8v\) | M1 A1, A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(k = 3\) | M1 A1ft, A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(y = \frac{9}{8}v = e = \frac{3}{4}\) ★ | M1 A1ft, M1, A1 | cso; 4 marks |
| (d) \(y = \frac{9}{8}v > v \Rightarrow\) further collision between \(P\) and \(Q\) | M1 A1 | 2 marks; 12 marks total |
(a) NEL: $3v - (-v) = eu$
$u = 8v$ | M1 A1, A1 | 3 marks
(b) LM: $8mv = -mv + 3kmv$ fit their u
$(m \times (u) = -mv + 3kmv)$
$k = 3$ | M1 A1ft, A1 | 3 marks
(c) LM: $9mv = -3mv + 11mv$ fit their k
NEL: $2y = e \times 3v$
$y = \frac{9}{8}v = e = \frac{3}{4}$ ★ | M1 A1ft, M1, A1 | cso; 4 marks
(d) $y = \frac{9}{8}v > v \Rightarrow$ further collision between $P$ and $Q$ | M1 A1 | 2 marks; 12 marks total
**A1 is cso – watch out for incorrect statements re. velocity**
---A particle $P$ of mass $m$ is moving in a straight line on a smooth horizontal table. Another particle $Q$ of mass $km$ is at rest on the table. The particle $P$ collides directly with $Q$. The direction of motion of $P$ is reversed by the collision. After the collision, the speed of $P$ is $v$ and the speed of $Q$ is $3v$. The coefficient of restitution between $P$ and $Q$ is $\frac{1}{2}$.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $v$ only, the speed of $P$ before the collision. [3]
\item Find the value of $k$. [3]
\end{enumerate}
After being struck by $P$, the particle $Q$ collides directly with a particle $R$ of mass $11m$ which is at rest on the table. After this second collision, $Q$ and $R$ have the same speed and are moving in opposite directions. Show that
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item the coefficient of restitution between $Q$ and $R$ is $\frac{1}{4}$, [4]
\item there will be a further collision between $P$ and $Q$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2007 Q4 [12]}}