| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics B AS (Further Mechanics B AS) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Elastic string equilibrium and statics |
| Difficulty | Easy -1.2 This is a straightforward elastic string equilibrium problem requiring only basic application of Hooke's law and force balance. Part (a) involves simple vertical equilibrium with two strings (2T = mg, T = kx), requiring just two equations to solve for k. Part (b) tests conceptual understanding of energy dissipation but requires no calculation. Both parts are routine applications of standard mechanics principles with no problem-solving insight needed. |
| Spec | 6.02g Hooke's law: T = k*x or T = lambda*x/l6.02h Elastic PE: 1/2 k x^2 |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | Use of 𝑇 = 𝑘𝑥 |
| Answer | Marks | Guidance |
|---|---|---|
| 2𝑘 ×0.1 = 5𝑔 | M1 | 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑘 = 245 (N m−1) | A1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | The string may have been stretched beyond its | |
| elastic limit | E1 | 2.2b |
| elastic collision, oe | OR there is always energy |
| Answer | Marks |
|---|---|
| [1] | OR Air resistance |
Question 1:
1 | (a) | Use of 𝑇 = 𝑘𝑥 | B1 | 3.3 | Where k is stiffness | Needs to be used, so we
need to see 0.1k used for T
2𝑘 ×0.1 = 5𝑔 | M1 | 3.4 | Or 0.1x = 2.5g (coming
from considering the
tension in one string).
𝑘 = 245 (N m−1) | A1 | 1.1 | Accept 25g | Units not necessary
[3]
(b) | The string may have been stretched beyond its
elastic limit | E1 | 2.2b | OR mass may have had non-
elastic collision, oe | OR there is always energy
loss in any oscillation
[1] | OR Air resistance1 A small object of mass 5 kg is attached to one end of each of two identical parallel light elastic strings. The upper ends of both strings are attached to a horizontal ceiling.\\
The object hangs in equilibrium at R , with the extension of each string being 0.1 m , as shown in Fig. 1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4acb019b-e630-4766-9d7f-39bc0e174ba1-2_620_394_580_242}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
\begin{enumerate}[label=(\alph*)]
\item Find the stiffness of each string.
One of the strings is now removed and the object initially falls downwards. The object does not return to R at any point in the subsequent motion.
\item Suggest a reason why the object does not return to $R$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics B AS 2019 Q1 [4]}}