| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics B AS (Further Mechanics B AS) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Bungee jumping problems |
| Difficulty | Standard +0.3 This is a standard energy conservation problem with elastic potential energy. Part (i)(A) involves setting up GPE = EPE and simplifying to the given equation (routine but multi-step). Part (i)(B) is straightforward algebra. Part (ii) requires qualitative reasoning about air resistance effects, which is slightly less routine but still accessible. Overall slightly easier than average A-level mechanics. |
| Spec | 6.02g Hooke's law: T = k*x or T = lambda*x/l6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (i) | (A) |
| Answer | Marks |
|---|---|
| X2 (cid:32)256 AG | C |
| Answer | Marks |
|---|---|
| [3] | I |
| Answer | Marks |
|---|---|
| 1.1 | Equating GPE lost to EPE gained |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (i) | (B) |
| Answer | Marks |
|---|---|
| = 4 m. | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 3.2a | For 20(cid:16)X |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (ii) | The EPE term would be less than the GPE term |
| Answer | Marks |
|---|---|
| be less than 20 [so she would be safe]. | E1 |
| [1] | 3.2b |
Question 3:
3 | (i) | (A) | 1
20(cid:117)576(cid:32) (cid:117)90X2 E
2
2(cid:117)20(cid:117)576
X2 (cid:32)
90
X2 (cid:32)256 AG | C
M1
A1
E1
[3] | I
3.1b
1.1
1.1 | Equating GPE lost to EPE gained
For one side correct
All correct and convincing working
3 | (i) | (B) | P
S
Natural length required is 20(cid:16)X
= 4 m. | M1
A1
[2] | 1.1
3.2a | For 20(cid:16)X
For this mark answer must refer to natural
length
3 | (ii) | The EPE term would be less than the GPE term
because of the air resistance. This would mean that
when natural length is 4 m, the stretched length would
be less than 20 [so she would be safe]. | E1
[1] | 3.2b3 A young woman wishes to make a bungee jump. One end of an elastic rope is attached to her safety harness. The other end is attached to the bridge from which she will jump.
She calculates that the stretched length of the rope at the bottom of her motion should be 20 m , she knows that her weight is 576 N and the stiffness of the elastic rope is $90 \mathrm { Nm } ^ { - 1 }$. She has to calculate the unstretched length of rope required to perform the jump safely.
She models the situation by assuming the following.
\begin{itemize}
\item The rope is of negligible mass.
\item Air resistance may be neglected.
\item She is a particle.
\item She moves vertically downwards from rest.
\item Her starting point is level with the fixed end of the rope.
\item The length she calculates for the rope does not include any extra for attaching the ends.
\begin{enumerate}[label=(\roman*)]
\item (A) Show that the greatest extension of the rope, $X$, satisfies the equation $X ^ { 2 } = 256$.\\
(B) Hence determine the natural length of rope she needs.
\item To remain safe she wishes to be sure that, if air resistance is taken into account, the stretched length of the rope of natural length determined in part (i) will not be more than 20 m . Advise her on this point.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics B AS Q3 [6]}}