| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Mechanics (Further Paper 3 Mechanics) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Find exponents with partial constraints |
| Difficulty | Standard +0.3 This is a straightforward dimensional analysis question requiring students to equate dimensions on both sides of an equation. Part (a) is trivial recall (force = MLT^-2), and part (b) involves setting up and solving simple simultaneous equations from dimension matching. While it's a Further Maths mechanics question, dimensional analysis is a standard technique with no conceptual subtlety or problem-solving insight required—just methodical application of a learned procedure. |
| Spec | 6.01a Dimensions: M, L, T notation6.01d Unknown indices: using dimensions |
| Answer | Marks | Guidance |
|---|---|---|
| 5(a) | States MLT–2 | 1.2 |
| Subtotal | 1 | |
| Q | Marking Instructions | AO |
| Answer | Marks |
|---|---|
| 5(b) | Uses dimensional analysis notation |
| Answer | Marks | Guidance |
|---|---|---|
| Must not use units. | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone use of units. | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| α = 1 and β = 2 | 2.2a | R1 |
| Subtotal | 3 | |
| Question total | 4 | |
| Q | Marking Instructions | AO |
Question 5:
--- 5(a) ---
5(a) | States MLT–2 | 1.2 | B1 | MLT–2
Subtotal | 1
Q | Marking Instructions | AO | Marks | Typical Solution
--- 5(b) ---
5(b) | Uses dimensional analysis notation
to form an equation.
Must not use units. | 3.3 | M1 | [F] = [k][r]α[v]β
MLT–2 = ML–2 × Lα × LβT–β
1 = –2 + α + β
α + β = 3
–2 = –β
β = 2
α = 1
Obtains either α = 1 or β = 2
Condone use of units. | 1.1a | M1
Completes a reasoned argument
using dimensions to show that
α = 1 and β = 2 | 2.2a | R1
Subtotal | 3
Question total | 4
Q | Marking Instructions | AO | Marks | Typical SolutionWhen a sphere of radius $r$ metres is falling at $v$ m s$^{-1}$ it experiences an air resistance force $F$ newtons.
The force is to be modelled as
$$F = kr^\alpha v^\beta$$
where $k$ is a constant with units kg m$^{-2}$
\begin{enumerate}[label=(\alph*)]
\item State the dimensions of $F$
[1 mark]
\item Use dimensional analysis to find the value of $\alpha$ and the value of $\beta$
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Mechanics 2024 Q5 [4]}}