| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Standard +0.3 This is a standard M1 mechanics question on collisions and impulse-momentum. Parts (a)-(c) involve straightforward application of impulse-momentum theorem and conservation of momentum with clear given values. Part (d) requires tracking multiple objects' positions over time, which adds some complexity but follows standard kinematics. The question is slightly above average difficulty due to the multi-stage collision scenario and the need to carefully track directions and positions, but all techniques are routine M1 content with no novel problem-solving required. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(8m + m = 8 \text{ ms}^{-1}\) | M1 A1 | 2 marks |
| (b) Momentum: \(2m(6) = 2mv_A + 8m\) giving \(v_A = 2 \text{ ms}^{-1}\) | M1 A1 A1 | 3 marks |
| (c) \(8m - 11m = mv_B\) giving \(v_B = -3\), i.e. \(3 \text{ ms}^{-1}\) in reverse direction | M1 A1 A1 | 3 marks |
| (d) B has moved \(3 \text{ m in } \frac{3}{8} \text{ s}\), during which time A has moved \(0.75 \text{ m}\) so A and B are \(2.25 \text{ m}\) apart. Let \(d\) = required distance: | M1 A1 | |
| \(d + 3 = (2.25 - d) + 2\) giving \(2d = 6.75 - 3d\) so \(d = 1.35 \text{ m}\) | M1 A1 A1 | 5 marks |
| (e) Modelled as particles, so width of spheres is negligible | B1 | total: 15 |
(a) $8m + m = 8 \text{ ms}^{-1}$ | M1 A1 | 2 marks
(b) Momentum: $2m(6) = 2mv_A + 8m$ giving $v_A = 2 \text{ ms}^{-1}$ | M1 A1 A1 | 3 marks
(c) $8m - 11m = mv_B$ giving $v_B = -3$, i.e. $3 \text{ ms}^{-1}$ in reverse direction | M1 A1 A1 | 3 marks
(d) B has moved $3 \text{ m in } \frac{3}{8} \text{ s}$, during which time A has moved $0.75 \text{ m}$ so A and B are $2.25 \text{ m}$ apart. Let $d$ = required distance: | M1 A1 |
$d + 3 = (2.25 - d) + 2$ giving $2d = 6.75 - 3d$ so $d = 1.35 \text{ m}$ | M1 A1 A1 | 5 marks
(e) Modelled as particles, so width of spheres is negligible | B1 | total: 15$A$, $B$ and $C$ are three small spheres of equal radii and masses $2m$, $m$ and $5m$ respectively. They are placed in a straight line on a smooth horizontal surface. $A$ is projected with speed 6 ms$^{-1}$ towards $B$, which is at rest. When $A$ hits $B$ it exerts an impulse of magnitude $8m$ Ns on $B$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed with which $B$ starts to move. [2 marks]
\item Show that the speed of $A$ after it collides with $B$ is 2 ms$^{-1}$. [3 marks]
\end{enumerate}
After travelling 3 m, $B$ hits $C$, which is then travelling towards $B$ at $2.2$ ms$^{-1}$. $C$ is brought to rest by this impact.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that the direction of $B$'s motion is reversed and find its new speed. [3 marks]
\item Find how far $B$ now travels before it collides with $A$ again. [6 marks]
\item State a modelling assumption that you have made about the spheres. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [15]}}