| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Major (Further Mechanics Major) |
| Year | 2024 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Elastic string equilibrium and statics |
| Difficulty | Moderate -0.3 Parts (a)-(c) are straightforward applications of Hooke's law (F=kx), elastic potential energy (½kx²), and dimensional analysis basics. Part (d) requires systematic dimensional analysis but follows a standard method taught in Further Mechanics. The question is slightly easier than average A-level because it's highly structured with clear steps and uses standard formulas, though the dimensional analysis component elevates it slightly above pure recall. |
| Spec | 6.01a Dimensions: M, L, T notation6.01d Unknown indices: using dimensions6.02e Calculate KE and PE: using formulae6.02h Elastic PE: 1/2 k x^2 |
| Answer | Marks |
|---|---|
| 2 (a) | 2g =k(0.05) |
| k =40g or 392 (N m−1) | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 2.2a | Use of F = kx with F =2gor F = 2 and correct extension |
| Answer | Marks |
|---|---|
| 2 (b) | Energy stored = 1(k)(0.05)2 |
| Answer | Marks |
|---|---|
| =0.05g or 0.49 (J) | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.2 |
| 1.1 | Use of E= 1kx2 with correct extension (0.05) and their k from |
| Answer | Marks | Guidance |
|---|---|---|
| 2(c) | [k]=MT −2 | B1 |
| [1] | 2.5 | [M][T−2] (or other incorrect forms) is B0 but condone if |
| Answer | Marks |
|---|---|
| 2(d) | [v]=LT −1 |
| Answer | Marks |
|---|---|
| α=−0.5, γ=0.5 | B1 |
| Answer | Marks |
|---|---|
| [4] | 1.2 |
| Answer | Marks |
|---|---|
| 1.1 | soi – allow incorrect notation provided intention is clear |
Question 2:
--- 2 (a) ---
2 (a) | 2g =k(0.05)
k =40g or 392 (N m−1) | M1
A1
[2] | 1.1
2.2a | Use of F = kx with F =2gor F = 2 and correct extension
(0.05) soi
--- 2 (b) ---
2 (b) | Energy stored = 1(k)(0.05)2
2
=0.05g or 0.49 (J) | M1
A1
[2] | 1.2
1.1 | Use of E= 1kx2 with correct extension (0.05) and their k from
2
part (a) soi
--- 2(c) ---
2(c) | [k]=MT −2 | B1
[1] | 2.5 | [M][T−2] (or other incorrect forms) is B0 but condone if
replaced with the correct answer – must be using capital letters
(so MUST be MT −2and nothing else)
--- 2(d) ---
2(d) | [v]=LT −1
LT −1 =M α L β (MT −2) γ
β=1
α=−0.5, γ=0.5 | B1
M1
A1
A1
[4] | 1.2
2.1
1.1
1.1 | soi – allow incorrect notation provided intention is clear
Setting up an equation in M, L and T using their [k] from part (c)
with [m], [v] and [a] all correct – allow incorrect notation
provided intention is clear
www (so must come from a correct equation)
www (so must come from a correct equation)One end of a light spring is attached to a fixed point. A mass of 2 kg is attached to the other end of the spring.
The spring hangs vertically in equilibrium. The extension of the spring is 0.05 m.
\begin{enumerate}[label=(\alph*)]
\item Find the stiffness of the spring. [2]
\item Find the energy stored in the spring. [2]
\item Find the dimensions of stiffness of a spring. [1]
\end{enumerate}
A particle P of mass $m$ is performing complete oscillations with amplitude $a$ on the end of a light spring with stiffness $k$. The spring hangs vertically and the maximum speed $v$ of P is given by the formula
$$v = Cm^{\alpha}a^{\beta}k^{\gamma},$$
where C is a dimensionless constant.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Use dimensional analysis to determine $\alpha$, $\beta$, and $\gamma$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Major 2024 Q2 [9]}}