| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Standard +0.3 This is a standard M1 impulse-momentum question with straightforward application of conservation principles. Part (a) uses impulse-momentum theorem directly, part (b) requires showing a given result and simple deduction, and part (c) involves setting up an inequality for a second collision. All steps follow routine procedures with no novel insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks |
|---|---|
| (a) New momentum of \(B = -3km + 7km = 4km\), so speed \(= 4 \text{ ms}^{-1}\) | M1 A1 A1 |
| (b) \(5m - 3km = mv_A + 4km\) | M1 A1 |
| \(v_A = 5 - 7k < 0\) as \(k > 1\) | |
| so speed \(= (7k - 5) \text{ ms}^{-1}\) and direction is reversed | M1 A1 |
| (c) \(B\)'s speed is now increased by \(\frac{u}{k}\) and its direction changed | M1 |
| so must have \(\frac{u}{k} - 4 > 7k - 5\) | M1 A1 A1 |
| \(\frac{u}{k} > 7k - 1\) | |
| \(u > k(7k - 1)\) | |
| Total: 12 marks |
(a) New momentum of $B = -3km + 7km = 4km$, so speed $= 4 \text{ ms}^{-1}$ | M1 A1 A1 |
(b) $5m - 3km = mv_A + 4km$ | M1 A1 |
| $v_A = 5 - 7k < 0$ as $k > 1$ | |
| so speed $= (7k - 5) \text{ ms}^{-1}$ and direction is reversed | M1 A1 |
(c) $B$'s speed is now increased by $\frac{u}{k}$ and its direction changed | M1 |
| so must have $\frac{u}{k} - 4 > 7k - 5$ | M1 A1 A1 |
| $\frac{u}{k} > 7k - 1$ | |
| $u > k(7k - 1)$ | |
| | **Total: 12 marks**Two small smooth spheres $A$ and $B$, of equal radius but masses $m$ kg and $km$ kg respectively, where $k > 1$, move towards each other along a straight line and collide directly. Immediately before the collision, $A$ has speed 5 ms$^{-1}$ and $B$ has speed 3 ms$^{-1}$. In the collision, the impulse exerted by $A$ on $B$ has magnitude $7km$ Ns.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $B$ after the impact. [3 marks]
\item Show that the speed of $A$ immediately after the collision is $(7k - 5)$ ms$^{-1}$ and deduce that the direction of $A$'s motion is reversed. [5 marks]
\end{enumerate}
$B$ is now given a further impulse of magnitude $mu$ Ns, as a result of which a second collision between it and $A$ occurs.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that $u > k(7k - 1)$. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [12]}}