| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Mechanics (Further AS Paper 2 Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision with unchanged direction |
| Difficulty | Standard +0.3 This is a standard A-level mechanics collision problem requiring conservation of momentum and Newton's law of restitution. The multi-part structure guides students through the solution systematically, and all techniques are routine applications of standard formulas with straightforward algebra. Slightly easier than average due to the scaffolding and lack of conceptual subtlety. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| \(e = \frac{3.5 + 2.5}{5 - 3} = 3\), impossible since \(e \leq 1\), hence sphere \(A\) cannot reverse direction | M1 | Uses formula for \(e\) and substitutes four velocities |
| R1 | Obtains \(e = 3\) or \(v_A = 3.5 - 2e\) and uses \(e \leq 1\) to deduce sphere \(A\) cannot reverse direction |
| Answer | Marks | Guidance |
|---|---|---|
| \(e = \frac{3.5 - 2.5}{5 - 3} = \frac{1}{2}\) | R1 | Deduces \(e = \frac{1}{2}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Conservation of momentum: \(5m + 0.6(3) = 2.5m + 0.6(3.5)\) | M1 | Forms conservation of momentum equation with at least two terms correct |
| \(2.5m = 0.3\) | A1 | Forms fully correct momentum equation |
| Mass of sphere \(A = 0.12\) kg | A1 | Must include units |
## Question 7(a)(i):
$e = \frac{3.5 + 2.5}{5 - 3} = 3$, impossible since $e \leq 1$, hence sphere $A$ cannot reverse direction | M1 | Uses formula for $e$ and substitutes four velocities
| R1 | Obtains $e = 3$ or $v_A = 3.5 - 2e$ **and** uses $e \leq 1$ to deduce sphere $A$ cannot reverse direction
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## Question 7(a)(ii):
$e = \frac{3.5 - 2.5}{5 - 3} = \frac{1}{2}$ | R1 | Deduces $e = \frac{1}{2}$
---
## Question 7(b):
Conservation of momentum: $5m + 0.6(3) = 2.5m + 0.6(3.5)$ | M1 | Forms conservation of momentum equation with at least two terms correct
$2.5m = 0.3$ | A1 | Forms fully correct momentum equation
Mass of sphere $A = 0.12$ kg | A1 | Must include units
---7 Two smooth, equally sized spheres, $A$ and $B$, are moving in the same direction along a straight line on a smooth horizontal surface, as shown in the diagram below.\\
\includegraphics[max width=\textwidth, alt={}, center]{78120346-4a16-4545-925a-d6fab4b750e9-06_314_465_420_849}
The spheres subsequently collide.\\
Immediately after the collision, $A$ has speed $2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and $B$ has speed $3.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
The coefficient of restitution between the spheres is $e$
7
\begin{enumerate}[label=(\alph*)]
\item (i) Show that $A$ does not change its direction of motion as a result of the collision.\\
7 (a) (ii) Find the value of $e$\\
7
\item Given that the mass of $B$ is 0.6 kg , find the mass of $A$
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2023 Q7 [6]}}