| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Moderate -0.3 This is a standard two-collision momentum problem requiring straightforward application of conservation of momentum twice in sequence. The calculations are routine with simple numbers, though students must carefully track which collision they're analyzing. Slightly easier than average due to the direct application of a single principle with no conceptual complications. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Inclusion of \(P\) is automatically M0 | M0 | Inclusion of 0.1 (unless a MR) is automatically M0 |
| \(0.1 \times 1.5 + 0.3u + 0.6 \times 0.8 = 0.1 \times 1.5 + (0.3)(0.6) \times 1\) | ||
| \(u = 1.4\) | Use of 0.6 or \(v\)(ii) instead of 1.5 is valid |
## Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Inclusion of $P$ is automatically M0 | M0 | Inclusion of 0.1 (unless a MR) is automatically M0 |
| $0.1 \times 1.5 + 0.3u + 0.6 \times 0.8 = 0.1 \times 1.5 + (0.3)(0.6) \times 1$ | | |
| $u = 1.4$ | | Use of 0.6 or $v$(ii) instead of 1.5 is valid |
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\includegraphics[max width=\textwidth, alt={}, center]{b7f05d10-9d3c-4098-846d-ca6511c75c5d-2_135_917_274_575}
Three particles $P , Q$ and $R$ have masses $0.1 \mathrm {~kg} , 0.3 \mathrm {~kg}$ and 0.6 kg respectively. The particles travel along the same straight line on a smooth horizontal table and have velocities $1.5 \mathrm {~ms} ^ { - 1 } , 1.1 \mathrm {~ms} ^ { - 1 }$ and $0.8 \mathrm {~ms} ^ { - 1 }$ respectively (see diagram). $P$ collides with $Q$ and then $Q$ collides with $R$. In the second collision $Q$ and $R$ coalesce and subsequently move with a velocity of $1 \mathrm {~ms} ^ { - 1 }$.\\
(i) Find the speed of $Q$ immediately before the second collision.\\
(ii) Calculate the change in momentum of $P$ in the first collision.
\hfill \mbox{\textit{OCR M1 2013 Q1 [6]}}