| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Session | Specimen |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Standard +0.3 This is a standard M1 collision question requiring repeated application of conservation of momentum across multiple collisions. Parts (i) and (ii) are routine calculations, part (iii) tests conceptual understanding of relative velocities, and part (iv) requires tracking momentum through the system. While multi-step, it follows predictable patterns with no novel insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(0.3 \times 3.2 = 0.3 \times 0.8 + 0.4 \times b\) | M1, A1, A1 | For using conservation of momentum; For correct LHS; For correct RHS |
| Hence \(b = 1.8\) so \(B\)'s speed is 1.8 m s\(^{-1}\) | A1 | For correct value 1.8 correctly obtained |
| Subtotal: 4 marks | ||
| (ii) \(0.4 \times 1.8 - 3.2 m = -0.4 \times 3.1 - 0.4 m\) | M1, A1 | For momentum equn with at least one relevant negative sign; For correct LHS |
| Hence \(m = 0.7\) | A1, A1 | For correct RHS; For correct value 0.4 correctly obtained |
| Subtotal: 4 marks | ||
| (iii) \(0.4 \times 3.1 + 0.3 \times 0.8\), so net momentum of A and B is towards the left and therefore they can't both move towards the right after the impact | B1 | For correctly explained application of momentum conservation |
| Subtotal: 1 mark | ||
| (iv) Total momentum of all three particles is leftwards | M1 | For reasoning based on the total momentum |
| Hence A ends up moving left, as if it moves right after all collisions so do B and C | A1 | For correct conclusion regarding direction |
| Total momentum left is at most 1.4a | M1 | For use of the idea that \(a \geq b \geq c\) |
| Hence \(1.4a \geq 0.7 \times 3.2 - 0.3 \times 3.2\), so the speed of A is at least 0.914 m s\(^{-1}\) | A1 | For correct conclusion |
| Subtotal: 4 marks | ||
| Total: 13 marks |
**(i)** $0.3 \times 3.2 = 0.3 \times 0.8 + 0.4 \times b$ | M1, A1, A1 | For using conservation of momentum; For correct LHS; For correct RHS
Hence $b = 1.8$ so $B$'s speed is 1.8 m s$^{-1}$ | A1 | For correct value 1.8 correctly obtained
| | **Subtotal: 4 marks**
**(ii)** $0.4 \times 1.8 - 3.2 m = -0.4 \times 3.1 - 0.4 m$ | M1, A1 | For momentum equn with at least one relevant negative sign; For correct LHS
Hence $m = 0.7$ | A1, A1 | For correct RHS; For correct value 0.4 correctly obtained
| | **Subtotal: 4 marks**
**(iii)** $0.4 \times 3.1 + 0.3 \times 0.8$, so net momentum of A and B is towards the left and therefore they can't both move towards the right after the impact | B1 | For correctly explained application of momentum conservation
| | **Subtotal: 1 mark**
**(iv)** Total momentum of all three particles is leftwards | M1 | For reasoning based on the total momentum
Hence A ends up moving left, as if it moves right after all collisions so do B and C | A1 | For correct conclusion regarding direction
Total momentum left is at most 1.4a | M1 | For use of the idea that $a \geq b \geq c$
Hence $1.4a \geq 0.7 \times 3.2 - 0.3 \times 3.2$, so the speed of A is at least 0.914 m s$^{-1}$ | A1 | For correct conclusion
| | **Subtotal: 4 marks**
| | **Total: 13 marks**\includegraphics{figure_5}
Three uniform spheres $A$, $B$ and $C$ have masses 0.3 kg, 0.4 kg and $m$ kg respectively. The spheres lie in a smooth horizontal groove with $B$ between $A$ and $C$. Sphere $B$ is at rest and spheres $A$ and $C$ are each moving with speed $3.2 \text{ m s}^{-1}$ towards $B$ (see diagram). Air resistance may be ignored.
\begin{enumerate}[label=(\roman*)]
\item $A$ collides with $B$. After this collision $A$ continues to move in the same direction as before, but with speed $0.8 \text{ m s}^{-1}$. Find the speed with which $B$ starts to move. [4]
\item $B$ and $C$ then collide, after which they both move towards $A$, with speeds of $3.1 \text{ m s}^{-1}$ and $0.4 \text{ m s}^{-1}$ respectively. Find the value of $m$. [4]
\item The next collision is between $A$ and $B$. Explain briefly how you can tell that, after this collision, $A$ and $B$ cannot both be moving towards $C$. [1]
\item When the spheres have finished colliding, which direction is $A$ moving in? What can you say about its speed? Justify your answers. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q6 [13]}}