| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Coalescence collision |
| Difficulty | Standard +0.3 This is a standard M1 collision problem combining impulse-momentum with friction. Part (a) requires systematic application of impulse and conservation of momentum (two equations, two unknowns), while parts (b) and (c) involve routine friction and SUVAT calculations. The multi-part structure and 12 marks indicate moderate length, but all techniques are core M1 material with no novel insight required, making it slightly easier than average. |
| Spec | 3.03r Friction: concept and vector form6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(10000(u_A - 10) = 84000\) | \(u_A = 18.4 \text{ m s}^{-1}\) | M1 A1 A1 |
| \(7000(u_B + 10) = 84000\) | \(u_B = 2 \text{ m s}^{-1}\) | M1 A1 A1 |
| (b) Resisting force \(= \mu R = 0.15 \times 17000g = 24990 \text{ N}\) | M1 A1 A1 | |
| (c) \(v = u + at\): \(0 = 10 - 0.15gt\) | \(t = 6.80 \text{ s}\) | M1 A1 A1 |
(a) $10000(u_A - 10) = 84000$ | $u_A = 18.4 \text{ m s}^{-1}$ | M1 A1 A1
$7000(u_B + 10) = 84000$ | $u_B = 2 \text{ m s}^{-1}$ | M1 A1 A1
(b) Resisting force $= \mu R = 0.15 \times 17000g = 24990 \text{ N}$ | M1 A1 A1
(c) $v = u + at$: $0 = 10 - 0.15gt$ | $t = 6.80 \text{ s}$ | M1 A1 A1 | **12 marks**Two railway trucks $A$ and $B$, of masses 10 000 kg and 7 000 kg respectively, are moving towards each other along a horizontal straight track. The trucks collide, and in the collision $A$ exerts an impulse on $B$ of magnitude 84 000 Ns. Immediately after the collision, the trucks move together with speed 10 ms$^{-1}$. Modelling the trucks as particles,
\begin{enumerate}[label=(\alph*)]
\item find the speed of each truck immediately before the collision. [6 marks]
\end{enumerate}
When the trucks are moving together along the track, the coefficient of friction between them and the track is 0.15. Assuming that no other resisting forces act on the trucks, calculate
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the magnitude of the resisting force on the trucks, [3 marks]
\item the time taken after the collision for the trucks to come to rest. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [12]}}