| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Mechanics (Further Paper 3 Mechanics) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Find exponents with partial constraints |
| Difficulty | Standard +0.3 Part (a) is straightforward recall of Hooke's law to find dimensions of k (MT^-2). Part (b) is a standard dimensional analysis problem requiring equating powers of M, L, T - a routine Further Maths technique with no conceptual difficulty, though it requires careful algebraic manipulation across three simultaneous equations. |
| Spec | 6.01a Dimensions: M, L, T notation6.01d Unknown indices: using dimensions |
| Answer | Marks | Guidance |
|---|---|---|
| 4(a) | Determines the correct dimensions | |
| of stiffness, CAO. | 1.2 | B1 |
| Total | 1 | |
| Q | Marking Instructions | AO |
| Answer | Marks |
|---|---|
| 4(b) | Formulates the problem using |
| Answer | Marks | Guidance |
|---|---|---|
| two dimensions correct. | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| c (PI) | 2.2a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| and c | 1.1b | A1 |
| Total | 3 | |
| Question total | 4 | |
| Q | Marking Instructions | AO |
Question 4:
--- 4(a) ---
4(a) | Determines the correct dimensions
of stiffness, CAO. | 1.2 | B1 | MT−2
Total | 1
Q | Marking Instructions | AO | Marks | Typical Solution
--- 4(b) ---
4(b) | Formulates the problem using
dimensional analysis with at least
two dimensions correct. | 3.3 | M1 | T = M a ( L T − 2 ) b ( M T − 2 ) c
a + c = 0
b = 0
− 2 b − 2 c = 1
1
c = −
2
1
a =
2
Compares dimensions to deduce
three equations in terms of a, b and
c (PI) | 2.2a | M1
Obtains the correct values of a, b
and c | 1.1b | A1
Total | 3
Question total | 4
Q | Marking Instructions | AO | Marks | Typical SolutionA spring has stiffness $k$
\begin{enumerate}[label=(\alph*)]
\item Determine the dimensions of $k$ [1 mark]
\item One end of the spring is attached to a fixed point. A particle of mass $m$ kg is attached to the other end of the spring.
The particle is set into vertical motion and moves up and down, taking $t$ seconds to complete one oscillation.
A possible model for $t$ is
$$t = pm^a g^b k^c$$
where $p$ is a dimensionless constant and $g \text{ m s}^{-2}$ is the acceleration due to gravity.
Find the values of $a$, $b$ and $c$ for this model to be dimensionally consistent.
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Mechanics 2021 Q4 [4]}}