| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Mechanics (Further AS Paper 2 Mechanics) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Direct collision with speed relationships |
| Difficulty | Standard +0.3 This is a standard Further Maths mechanics collision problem requiring conservation of momentum and coefficient of restitution equations. The setup is straightforward with given masses, speeds, and e-value. Part (a) is scaffolded ('show that'), part (b) is routine calculation, and part (c) requires basic conceptual understanding of friction effects. Slightly above average difficulty due to being Further Maths content, but the problem-solving is algorithmic with no novel insight required. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| CoM: \(2 \times 4 - 2 \times 3 = 2v_C + 3v_D\) | M1 | Forms equation using conservation of momentum |
| \(2v_C + 3v_D = 2\) | M1 | Forms equation using coefficient of restitution |
| \(v_C - v_D = -0.6(-2-4)\) | A1 | Obtains two correct equations |
| \(v_C - v_D = -3.6\), \(5v_D = 9.2\), \(v_D = 1.84 = 1.8 \text{ m s}^{-1}\) to 2 sf | R1 | Completes rigorous argument using both conservation of energy and CoR to find speed of \(D\) to specified accuracy. Only award if completely correct solution, clear, easy to follow and contains no slips |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(1.84 - v_C = 3.6\), \(v_C = -1.76\) | M1 | Forms equation to find velocity of \(C\) |
| Speed of \(C = 1.8 \text{ m s}^{-1}\) to 2 sf | A1 | Obtains correct speed for \(C\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| The introduction of friction will not affect my answer to (b) because the collision is instantaneous. | E1 | Gives a valid explanation e.g. collision is instantaneous, no distance travelled, no work done, no energy lost to friction during collision |
| Therefore answer to part (b) is not affected by the introduction of friction | R1 | Depends on E1 above |
## Question 5:
### Part 5(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| CoM: $2 \times 4 - 2 \times 3 = 2v_C + 3v_D$ | M1 | Forms equation using conservation of momentum |
| $2v_C + 3v_D = 2$ | M1 | Forms equation using coefficient of restitution |
| $v_C - v_D = -0.6(-2-4)$ | A1 | Obtains two correct equations |
| $v_C - v_D = -3.6$, $5v_D = 9.2$, $v_D = 1.84 = 1.8 \text{ m s}^{-1}$ to 2 sf | R1 | Completes rigorous argument using both conservation of energy and CoR to find speed of $D$ to specified accuracy. Only award if completely correct solution, clear, easy to follow and contains no slips |
### Part 5(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $1.84 - v_C = 3.6$, $v_C = -1.76$ | M1 | Forms equation to find velocity of $C$ |
| Speed of $C = 1.8 \text{ m s}^{-1}$ to 2 sf | A1 | Obtains correct speed for $C$ |
### Part 5(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| The introduction of friction will not affect my answer to (b) because the collision is instantaneous. | E1 | Gives a valid explanation e.g. collision is instantaneous, no distance travelled, no work done, no energy lost to friction during collision |
| Therefore answer to part (b) is not affected by the introduction of friction | R1 | Depends on E1 above |
---5 Two small smooth discs, $C$ and $D$, have equal radii and masses of 2 kg and 3 kg respectively.
The discs are sliding on a smooth horizontal surface towards each other and collide directly.
Disc $C$ has speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and disc $D$ has speed $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ as they collide.
The coefficient of restitution between $C$ and $D$ is 0.6
The diagram shows the discs, viewed from above, before the collision.\\
\includegraphics[max width=\textwidth, alt={}, center]{18522f4c-4aa2-4ef5-898f-5ad2b06e287c-06_343_712_868_753}
5
\begin{enumerate}[label=(\alph*)]
\item Show that the speed of $D$ immediately after the collision is $1.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, correct to 2 significant figures.\\
5
\item Find the speed of $C$ immediately after the collision.\\[0pt]
[2 marks]\\
5
\item In fact the horizontal surface on which the discs are sliding is not smooth.\\
Explain how the introduction of friction will affect your answer to part (b).\\[0pt]
[2 marks]\\
Turn over for the next question
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics Q5 [4]}}