| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2009 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Oblique and successive collisions |
| Type | Condition for further/no further collision |
| Difficulty | Standard +0.3 This is a standard M2 momentum question involving two successive collisions with straightforward application of impulse-momentum theorem and coefficient of restitution. Part (i) requires basic impulse calculation, part (ii) needs conservation of momentum plus restitution equation followed by comparing final velocities—all routine techniques for M2 with no novel insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| \(I = 0.9 = 6×0.2 - v × 0.2\) | M1 | needs to be mass 0.2 |
| \(v = 1.5\) | A1 A1 3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.6 = (c - b)/6\) | M1 A1 | restitution (allow 1.5 for M1) |
| \(6 \times 0.2 = 0.2b + 0.1c\) | M1 A1 | momentum (allow 1.5 for M1) |
| \(b = 2.8\) | A1 | |
| \(0.4 \times 5 + 0.2 \times 1.5 = 0.4a + 0.2 \times 6\) | M1 | 1st collision (needs their 1.5 for M1) |
| \(I = 0.9 = -0.4a - 0.4 \times 5\) | A1 | |
| \(a = 2.75\) | A1 | |
| \(2.75 < 2.8\) | M1 | compare v's of A and B (calculated) |
| no further collision | A1 10 |
### Part (i)
$I = 0.9 = 6×0.2 - v × 0.2$ | M1 | needs to be mass 0.2
$v = 1.5$ | A1 A1 3 |
### Part (ii)
$0.6 = (c - b)/6$ | M1 A1 | restitution (allow 1.5 for M1)
$6 \times 0.2 = 0.2b + 0.1c$ | M1 A1 | momentum (allow 1.5 for M1)
$b = 2.8$ | A1 |
$0.4 \times 5 + 0.2 \times 1.5 = 0.4a + 0.2 \times 6$ | M1 | 1st collision (needs their 1.5 for M1)
$I = 0.9 = -0.4a - 0.4 \times 5$ | A1 |
$a = 2.75$ | A1 |
$2.75 < 2.8$ | M1 | compare v's of A and B (calculated)
no further collision | A1 10 | | 136 Two uniform spheres, $A$ and $B$, have the same radius. The mass of $A$ is 0.4 kg and the mass of $B$ is 0.2 kg . The spheres $A$ and $B$ are travelling in the same direction in a straight line on a smooth horizontal surface, $A$ with speed $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, and $B$ with speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, where $v < 5$. A collides directly with $B$ and the impulse between them has magnitude 0.9 Ns . Immediately after the collision, the speed of $B$ is $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(i) Calculate $v$.\\
$B$ subsequently collides directly with a stationary sphere $C$ of mass 0.1 kg and the same radius as $A$ and $B$. The coefficient of restitution between $B$ and $C$ is 0.6 .\\
(ii) Determine whether there will be a further collision between $A$ and $B$.
\hfill \mbox{\textit{OCR M2 2009 Q6 [13]}}