| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Multiple sequential collisions |
| Difficulty | Moderate -0.8 This is a straightforward M1 momentum question with standard collision scenarios. Part (i) uses conservation of momentum with the special condition that speeds are unchanged (perfectly elastic collision), requiring simple algebraic manipulation. Part (ii) is another direct application of conservation of momentum. Both parts are routine textbook exercises requiring only recall and application of standard formulas, with no novel problem-solving insight needed. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Before momentum \(= +/-(0.4u - 0.3 \times 8)\) | B1 | Accept inclusion of \(g\), including final A1 |
| \(0.4u - 0.3 \times 8 = -0.4u + 0.3 \times 8\) | M1 | Uses momentum cons. 4 non-zero terms |
| A1ft | ft candidates "before" expression | |
| \(u = 6\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| After momentum \(= +/-9m\) | B1 | No marks if \(g\) included, even if apparently cancelled |
| \(0.3 \times 8 - 3m = 9m\) | M1 | Uses momentum conservation 3 non-zero terms |
| A1ft | ft candidates "after" expression | |
| \(m = 0.2\) | A1 |
## Question 2:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Before momentum $= +/-(0.4u - 0.3 \times 8)$ | B1 | Accept inclusion of $g$, including final A1 |
| $0.4u - 0.3 \times 8 = -0.4u + 0.3 \times 8$ | M1 | Uses momentum cons. 4 non-zero terms |
| | A1ft | ft candidates "before" expression |
| $u = 6$ | A1 | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| After momentum $= +/-9m$ | B1 | No marks if $g$ included, even if apparently cancelled |
| $0.3 \times 8 - 3m = 9m$ | M1 | Uses momentum conservation 3 non-zero terms |
| | A1ft | ft candidates "after" expression |
| $m = 0.2$ | A1 | |
---2\\
\includegraphics[max width=\textwidth, alt={}, center]{8b79facc-e37f-45c3-95c0-9f2a30ca8fe4-2_138_1118_680_463}
Three particles $P , Q$ and $R$ with masses $0.4 \mathrm {~kg} , 0.3 \mathrm {~kg}$ and $m \mathrm {~kg}$ are moving along the same straight line on a smooth horizontal surface. $P$ and $Q$ are moving towards each other with speeds $u \mathrm {~ms} ^ { - 1 }$ and $8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively. $R$ has speed $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and is moving in the same direction as $Q$ (see diagram).\\
(i) Immediately after the collision between $P$ and $Q$ their directions of motion have been reversed, but their speeds are unchanged. Calculate $u$.
The next collision is between $Q$ and $R$. After the collision between $Q$ and $R$, particle $Q$ is at rest and $R$ has speed $9 \mathrm {~ms} ^ { - 1 }$.\\
(ii) Calculate $m$.\\
\includegraphics[max width=\textwidth, alt={}, center]{8b79facc-e37f-45c3-95c0-9f2a30ca8fe4-2_547_1506_1521_251}
Two travellers $A$ and $B$ make the same journey on a long straight road. Each traveller walks for part of the journey and rides a bicycle for part of the journey. They start their journeys at the same instant, and they end their journeys simultaneously after travelling for $T$ hours. $A$ starts the journey cycling at a steady $20 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ for 1 hour. $A$ then leaves the bicycle at the side of the road, and completes the journey walking at $5 \mathrm {~km} \mathrm {~h} ^ { - 1 }$. $B$ begins the journey walking at a steady $4 \mathrm {~km} \mathrm {~h} ^ { - 1 }$. When $B$ finds the bicycle where $A$ left it, $B$ cycles at $15 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ to complete the journey (see diagram).\\
\hfill \mbox{\textit{OCR M1 2015 Q2 [8]}}