| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2011 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision followed by wall impact |
| Difficulty | Moderate -0.3 This is a standard M2 collision question requiring routine application of conservation of momentum, coefficient of restitution formula, and impulse-momentum theorem. All parts follow textbook procedures with no novel problem-solving required, making it slightly easier than average for A-level. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Answer/Working | Marks |
| ia | If reversed \(2.9 + 2 = e(3 + 1.5)\) | M1 |
| \(e > 1\) impossible | A1 | |
| [2] | May be seen in ia | |
| b | \(2.9 - 2 = e(3 + 1.5)\) | M1 |
| \(e = 0.2\) | A1 | |
| [2] | ||
| ii | \(3m - 0.2 \times 1.5 = 2m + 0.2 \times 2.9\) | A1 |
| \(m = 0.88\) | A1 | |
| [3] | ||
| iii | \(0.68 = 0.2v + 0.2 \times 2.9\) | M1 |
| \(v = 0.5\) | A1 | |
| \(e = 0.5/2.9\) | M1 | Separation speed not 2.9. Allow 5/29 |
| \(e = 0.172\) | A1 | |
| [4] |
| **Part** | **Answer/Working** | **Marks** | **Guidance** |
|----------|-------------------|----------|-------------|
| ia | If reversed $2.9 + 2 = e(3 + 1.5)$ | M1 | Award B1 if no explicit numerical justification |
| | $e > 1$ impossible | A1 | |
| | | [2] | May be seen in ia |
| b | $2.9 - 2 = e(3 + 1.5)$ | M1 | |
| | $e = 0.2$ | A1 | |
| | | [2] | |
| ii | $3m - 0.2 \times 1.5 = 2m + 0.2 \times 2.9$ | A1 | Conservation of momentum. Accept with $g$ included consistently. Do not award if $g$ used. |
| | $m = 0.88$ | A1 | |
| | | [3] | |
| iii | $0.68 = 0.2v + 0.2 \times 2.9$ | M1 | Impulse = change in momentum |
| | $v = 0.5$ | A1 | |
| | $e = 0.5/2.9$ | M1 | Separation speed not 2.9. Allow 5/29 |
| | $e = 0.172$ | A1 | |
| | | [4] | |4 Two small spheres $A$ and $B$ are moving towards each other along a straight line on a smooth horizontal surface. $A$ has speed $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $B$ has speed $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ before they collide directly. The direction of motion of $B$ is reversed in the collision. The speeds of $A$ and $B$ after the collision are $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $2.9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ respectively.
\begin{enumerate}[label=(\roman*)]
\item (a) Show that the direction of motion of $A$ is unchanged by the collision.\\
(b) Calculate the coefficient of restitution between $A$ and $B$.
The mass of $B$ is 0.2 kg .
\item Find the mass of $A$.\\
$B$ continues to move at $2.9 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and strikes a vertical wall at right angles. The wall exerts an impulse of magnitude 0.68 N s on $B$.
\item Calculate the coefficient of restitution between $B$ and the wall.
\end{enumerate}
\hfill \mbox{\textit{OCR M2 2011 Q4 [11]}}