| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find final speed |
| Difficulty | Moderate -0.8 This is a straightforward momentum conservation problem with clearly stated conditions. Part (i) requires a single application of conservation of momentum with all values given explicitly, including that P's final speed is simply 1.1 m/s. Part (ii) is basic kinematics (distance = relative speed × time). No problem-solving insight needed, just routine application of standard M1 formulas. |
| Spec | 6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Total momentum before \(= 0.3 \times 2.2 + 0.5 \times 0.8\) | B1 | Allow inclusion of \(g\) |
| Mom P after \(= 0.3 \times 2.2/2\) | B1 | \(0.33\), accept \(0.33g\) and negative term |
| \(0.3 \times 2.2 + 0.5 \times 0.8 = 0.3 \times 2.2/2 + 0.5v\) | M1 | Allow \(0.33g = 0.5gv - 0.5g \times 0.8\) |
| \(v = 1.46 \text{ ms}^{-1}\) | A1 [4] | Allow from inclusion of \(g\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(PQ = 3 \times 1.46 - 3 \times 2.2/2\) | M1 | \(3(1.46 - 2.2/2)\) Accept \(3 \times 1.46 - 2.2/2\) |
| \(PQ = 1.08 \text{ m}\) | A1 [2] |
# Question 1:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Total momentum before $= 0.3 \times 2.2 + 0.5 \times 0.8$ | B1 | Allow inclusion of $g$ |
| Mom P after $= 0.3 \times 2.2/2$ | B1 | $0.33$, accept $0.33g$ and negative term |
| $0.3 \times 2.2 + 0.5 \times 0.8 = 0.3 \times 2.2/2 + 0.5v$ | M1 | Allow $0.33g = 0.5gv - 0.5g \times 0.8$ |
| $v = 1.46 \text{ ms}^{-1}$ | A1 **[4]** | Allow from inclusion of $g$ |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $PQ = 3 \times 1.46 - 3 \times 2.2/2$ | M1 | $3(1.46 - 2.2/2)$ Accept $3 \times 1.46 - 2.2/2$ |
| $PQ = 1.08 \text{ m}$ | A1 **[2]** | |
---1 Particles $P$ and $Q$, of masses 0.3 kg and 0.5 kg respectively, are moving in the same direction along the same straight line on a smooth horizontal surface. $P$ is moving with speed $2.2 \mathrm {~ms} ^ { - 1 }$ and $Q$ is moving with speed $0.8 \mathrm {~ms} ^ { - 1 }$ immediately before they collide. In the collision, the speed of $P$ is reduced by $50 \%$ and its direction of motion is unchanged.\\
(i) Calculate the speed of $Q$ immediately after the collision.\\
(ii) Find the distance $P Q$ at the instant 3 seconds after the collision.
\hfill \mbox{\textit{OCR M1 2012 Q1 [6]}}