| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Range of coefficient of restitution |
| Difficulty | Moderate -0.3 This is a standard two-part collision problem requiring application of conservation of momentum and Newton's law of restitution. Part (i) involves routine algebraic manipulation of two simultaneous equations to find velocities in terms of u and e. Part (ii) requires setting up and solving a simple inequality. While it involves multiple steps, the techniques are entirely standard for M2 collision problems with no novel insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact |
| Answer | Marks |
|---|---|
| 6 (i) | 0.4 g = 50e/0.8 |
| Answer | Marks |
|---|---|
| v = 1.6(0) ms −1 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| A1 | [5] | Uses T = λ × /L (e = 0.064) |
| Answer | Marks |
|---|---|
| (ii) | PE gain to reach O = 0.4 g × 0.82 |
| Answer | Marks |
|---|---|
| energy | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| A1 | [3] | From initial position, (3.28J) |
| At initial position, (0.4625J) | 8 | |
| Page 6 | Mark Scheme | Syllabus |
| GCE A LEVEL – October/November 2013 | 9709 | 53 |
Question 6:
--- 6 (i) ---
6 (i) | 0.4 g = 50e/0.8
Moves down = 0.044 m
0.4 × 1.5 2 /2 + 0.4 g × 0.044 +
50(0.82–0.8) 2 /(2 × 0.8)
=0.4v2 /2 + 50 × 0.064 2 /(2 × 0.8)
v = 1.6(0) ms −1 | M1
A1
M1
A1
A1 | [5] | Uses T = λ × /L (e = 0.064)
(0.8 + 0.064 – 0.82)
Sets up 2EE/2KE/PE equation
(ii) | PE gain to reach O = 0.4 g × 0.82
KE + EE = 0.4 × 1.5 2 /2
+50(0.82 – 0.8) 2 /(2 × 0.8)
Shows by evaluation that insufficient
energy | B1
M1
A1 | [3] | From initial position, (3.28J)
At initial position, (0.4625J) | 8
Page 6 | Mark Scheme | Syllabus | Paper
GCE A LEVEL – October/November 2013 | 9709 | 53Two particles $A$ and $B$ have masses $3m$ and $2m$ respectively. Initially $A$ is at rest and $B$ is moving with speed $u$ in a straight line towards $A$. The coefficient of restitution between the particles is $e$.
\begin{enumerate}[label=(\roman*)]
\item Find the speeds of the particles immediately after the collision.
\item Find the condition on $e$ for $A$ to be moving faster than $B$ after the collision.
\end{enumerate}
[8]
\hfill \mbox{\textit{CAIE M2 2013 Q6 [8]}}