| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Mechanics (Further AS Paper 2 Mechanics) |
| Year | 2023 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Bungee jumping problems |
| Difficulty | Challenging +1.2 This is a standard Further Maths mechanics problem requiring energy conservation with elastic potential energy. Part (a) involves setting up and solving a quadratic equation using EPE = ½(λ/L)x², which is routine for FM students. Part (b) requires brief conceptual reasoning about modelling assumptions. The multi-step nature and FM content place it above average difficulty, but it follows a well-practiced template without requiring novel insight. |
| 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 |
|---|---|---|
| GPE \(= mgh = 70(9.8)(80) = 54880\) J | B1 | Accept \(5600g\) or \(54936\) or \(56000\) |
| EPE \(= \frac{\lambda x^2}{2l} = \frac{2800(80-L)^2}{2L}\) | B1 | Recalls and uses EPE formula correctly, uses \(x = 80 - L\) |
| \(\frac{2800(80-L)^2}{2L} = 54880\), since \(L < 80\), \(L = 40.3\), hence \(L = 40\) | M1 | Applies conservation of energy using GPE and EPE in terms of \(L\) |
| \(L = 40\) | A1 | AWRT 40 to 2 sig fig |
| Answer | Marks | Guidance |
|---|---|---|
| If Omar is not modelled as a particle then his height must be considered | E1 | Explains that if Omar is not modelled as a particle then height must be considered |
| \(40\) m would therefore be too long, and Omar would end up in the water, hence \(L < 40\) | E1 | Infers that length found in part (a) would be too long |
## Question 8(a):
GPE $= mgh = 70(9.8)(80) = 54880$ J | B1 | Accept $5600g$ or $54936$ or $56000$
EPE $= \frac{\lambda x^2}{2l} = \frac{2800(80-L)^2}{2L}$ | B1 | Recalls and uses EPE formula correctly, uses $x = 80 - L$
$\frac{2800(80-L)^2}{2L} = 54880$, since $L < 80$, $L = 40.3$, hence $L = 40$ | M1 | Applies conservation of energy using GPE and EPE in terms of $L$
$L = 40$ | A1 | AWRT 40 to 2 sig fig
---
## Question 8(b):
If Omar is not modelled as a particle then his height must be considered | E1 | Explains that if Omar is not modelled as a particle then height must be considered
$40$ m would therefore be too long, and Omar would end up in the water, hence $L < 40$ | E1 | Infers that length found in part (a) would be too long
---8 In this question use $g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$
Omar, a bungee jumper of mass 70 kg , has his ankles attached to one end of an elastic cord.
The other end of the cord is attached to a bridge which is 80 metres above the surface of a river.
Omar steps off the bridge at the point where the cord is attached and falls vertically downwards.
The cord can be modelled as a light elastic string of natural length $L$ metres and modulus of elasticity 2800 N
Model Omar as a particle.
8
\begin{enumerate}[label=(\alph*)]
\item Given that Omar just reaches the surface of the river before being pulled back up, find the value of $L$
Fully justify your answer.\\
8
\item If Omar is not modelled as a particle, explain the effect of revising this assumption on your answer to part (a).
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2023 Q8 [7]}}