| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2005 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Three-particle sequential collisions |
| Difficulty | Standard +0.3 This is a standard M2 momentum/collisions question requiring routine application of conservation of momentum, coefficient of restitution formula, and impulse calculation. Part (iii) requires comparing velocities after coalescence but involves straightforward algebra. Slightly above average difficulty due to the three-particle setup and coalescence, but all techniques are standard textbook exercises. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03c Momentum in 2D: vector form6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(5m = mu + 4m\) | M1 | cons. of mom. |
| \(u = 1\) | A1 | |
| \(e = (2-1)/5\) | M1 | |
| \(e = \frac{3}{5}\) | A1 | 4 |
| (ii) \(l = 4m\) | B1 | |
| \(\rightarrow\) | B1 | 2 |
| (iii) \(4m = 5mv\) | M1 | |
| \(v = \frac{4}{5}\) | A1 | |
| \(\frac{4}{5} < 1\) | B1 | 3 |
(i) $5m = mu + 4m$ | M1 | cons. of mom.
$u = 1$ | A1 |
$e = (2-1)/5$ | M1 |
$e = \frac{3}{5}$ | A1 | 4 |
(ii) $l = 4m$ | B1 |
$\rightarrow$ | B1 | 2 | to the right
(iii) $4m = 5mv$ | M1 |
$v = \frac{4}{5}$ | A1 |
$\frac{4}{5} < 1$ | B1 | 3 | 94\\
\includegraphics[max width=\textwidth, alt={}, center]{35477eb8-59e0-4de6-889c-1f5841f65eec-3_168_956_246_593}
Three smooth spheres $A , B$ and $C$, of equal radius and of masses $m \mathrm {~kg} , 2 m \mathrm {~kg}$ and $3 m \mathrm {~kg}$ respectively, lie in a straight line and are free to move on a smooth horizontal table. Sphere $A$ is moving with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ when it collides directly with sphere $B$ which is stationary. As a result of the collision $B$ starts to move with speed $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Find the coefficient of restitution between $A$ and $B$.\\
(ii) Find, in terms of $m$, the magnitude of the impulse that $A$ exerts on $B$, and state the direction of this impulse.
Sphere $B$ subsequently collides with sphere $C$ which is stationary. As a result of this impact $B$ and $C$ coalesce.\\
(iii) Show that there will be another collision.
\hfill \mbox{\textit{OCR M2 2005 Q4 [9]}}