| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Direct collision with speed relationships |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law. Part (a) involves straightforward algebraic manipulation to show a given result, and part (b) requires calculating kinetic energies before and after—both are routine applications of well-practiced formulas with no novel insight needed. Slightly easier than average due to the 'show that' structure guiding students to the answer. |
| 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 |
|---|---|---|
| LM NEL: \(12mu + 6mu = 4mx + 12meu\) | B1 M1 A1 | |
| \(4eu - x = eu\) | ||
| Eliminating \(x\) to obtain equation in \(e\) | DM1 | |
| Leading to \(e = \frac{3}{4}\) ★ | A1 cso | [5] |
| Answer | Marks | Guidance |
|---|---|---|
| \(x = 3eu\) or \(\frac{9}{4}u\) or \(4.5u - 3eu\) | B1 | seen or implied in (b) |
| M1 A1 ft | ||
| Loss in KE \(= \frac{1}{2}4m(3u)^2 + \frac{1}{2}3m(2u)^2 - \frac{1}{2}4m\left(\frac{9}{4}u\right)^2 - \frac{1}{2}3m(3u)^2\) | fit their \(x\) | |
| \(= 24mu^2 - 23\frac{5}{8}mu^2 - \frac{3}{8}mu^2 = 0.375mu^2\) | A1 | [4] [9] |
**Part (a):**
LM NEL: $12mu + 6mu = 4mx + 12meu$ | B1 M1 A1 |
$4eu - x = eu$ | |
Eliminating $x$ to obtain equation in $e$ | DM1 |
Leading to $e = \frac{3}{4}$ ★ | A1 cso | [5]
**Part (b):**
$x = 3eu$ or $\frac{9}{4}u$ or $4.5u - 3eu$ | B1 | seen or implied in (b)
| M1 A1 ft |
Loss in KE $= \frac{1}{2}4m(3u)^2 + \frac{1}{2}3m(2u)^2 - \frac{1}{2}4m\left(\frac{9}{4}u\right)^2 - \frac{1}{2}3m(3u)^2$ | | fit their $x$
$= 24mu^2 - 23\frac{5}{8}mu^2 - \frac{3}{8}mu^2 = 0.375mu^2$ | A1 | [4] [9]2. A particle $A$ of mass $4 m$ is moving with speed $3 u$ in a straight line on a smooth horizontal table. The particle $A$ collides directly with a particle $B$ of mass $3 m$ moving with speed $2 u$ in the same direction as $A$. The coefficient of restitution between $A$ and $B$ is $e$. Immediately after the collision the speed of $B$ is $4 e u$.
\begin{enumerate}[label=(\alph*)]
\item Show that $e = \frac { 3 } { 4 }$.
\item Find the total kinetic energy lost in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2008 Q2 [9]}}