| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Mechanics (Further AS Paper 2 Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Derive dimensions from formula |
| Difficulty | Moderate -0.5 This is a straightforward dimensional analysis question requiring students to equate dimensions of terms in an equation. Part (a) involves basic manipulation (since y and x have same dimensions, k must be dimensionless), and part (b) asks for a standard deduction. While it's a Further Maths mechanics question, the dimensional analysis itself is routine and requires no problem-solving insight—just systematic application of a standard technique. |
| Spec | 6.01c Dimensional analysis: error checking |
| Answer | Marks | Guidance |
|---|---|---|
| \([y] = [x] - \frac{[k][x^2]}{[u^2]}\) | M1 | Applies dimensional analysis, condone use of \([k] = k\) |
| \(L = L - \frac{[k]L^2}{(LT^{-1})^2}\) | A1 | Uses correct dimensions for \(u\) and either \(x\) or \(y\) |
| \([k] = LT^{-2}\) | A1 | Obtains \([k] = LT^{-2}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(k\) represents an acceleration | E1 | Deduces that \(LT^{-2}\) represents an acceleration |
## Question 6(a):
$[y] = [x] - \frac{[k][x^2]}{[u^2]}$ | M1 | Applies dimensional analysis, condone use of $[k] = k$
$L = L - \frac{[k]L^2}{(LT^{-1})^2}$ | A1 | Uses correct dimensions for $u$ and either $x$ or $y$
$[k] = LT^{-2}$ | A1 | Obtains $[k] = LT^{-2}$
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## Question 6(b):
$k$ represents an acceleration | E1 | Deduces that $LT^{-2}$ represents an acceleration
---6 A ball is thrown with speed $u$ at an angle of $45 ^ { \circ }$ to the horizontal from a point $O$
When the horizontal displacement of the ball is $x$, the vertical displacement of the ball above $O$ is $y$ where
$$y = x - \frac { k x ^ { 2 } } { u ^ { 2 } }$$
6
\begin{enumerate}[label=(\alph*)]
\item Use dimensional analysis to find the dimensions of $k$\\
6
\item State what can be deduced about $k$ from the dimensions that you found in part (a).
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2023 Q6 [4]}}