| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision with unchanged direction |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's experimental law (restitution). Part (a) uses momentum conservation with an inequality constraint, parts (b) and (c) apply standard formulas. While multi-step, it follows textbook methods without requiring novel insight—slightly easier than average due to its routine nature. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Momentum: \(36m - 24m = 9mv_A + 4mv_B\) | \(9v_A + 4v_B = 12\) | M1 A1 A1 |
| \(v_A > 0\), so \(4v_B < 12\) | \(v_B < 3\) | M1 A1 |
| (b) \((v_B - v_A)(-6-4) = -e\) | \(e = (v_B - v_A)/10\) | M1 A1 |
| Now \(v_B - v_A < v_B < 3\), so \(e < \frac{3}{10}\) | M1 A1 A1 | |
| (c) If \(e = 0\), \(v_B = v_A\) | \(13v_A = 12\) | \(v_A = v_B = \frac{12}{13} \text{ ms}^{-1}\) |
**(a)** Momentum: $36m - 24m = 9mv_A + 4mv_B$ | $9v_A + 4v_B = 12$ | M1 A1 A1 |
$v_A > 0$, so $4v_B < 12$ | $v_B < 3$ | M1 A1 |
**(b)** $(v_B - v_A)(-6-4) = -e$ | $e = (v_B - v_A)/10$ | M1 A1 |
Now $v_B - v_A < v_B < 3$, so $e < \frac{3}{10}$ | M1 A1 A1 |
**(c)** If $e = 0$, $v_B = v_A$ | $13v_A = 12$ | $v_A = v_B = \frac{12}{13} \text{ ms}^{-1}$ | M1 M1 A1 A1 | 14 marksTwo smooth spheres $A$ and $B$, of equal radius and masses $9m$ and $4m$ respectively, are moving towards each other along a straight line with speeds 4 ms$^{-1}$ and 6 ms$^{-1}$ respectively. They collide, after which the direction of motion of $A$ remains unchanged.
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of $B$ after the impact cannot be more than 3 ms$^{-1}$. [5 marks]
\end{enumerate}
The coefficient of restitution between $A$ and $B$ is $e$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that $e < \frac{3}{10}$. [5 marks]
\item Find the speeds of $A$ and $B$ after the impact in the case when $e = 0$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q7 [14]}}