| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Mechanics (Further Paper 3 Mechanics) |
| Year | 2024 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hooke's law and elastic energy |
| Type | Vertical elastic string: released from rest at natural length or above (string initially slack) |
| Difficulty | Standard +0.3 This is a standard elastic string energy problem with straightforward applications of EPE = λx²/(2l), conservation of energy, and force comparison. All parts follow routine procedures taught in Further Maths mechanics with no novel insight required, making it slightly easier than average. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.02j Conservation with elastics: springs and strings |
| Answer | Marks | Guidance |
|---|---|---|
| 6(a) | Uses the EPE formula with their | |
| extension. | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone missing units. | 1.1b | A1 |
| Subtotal | 2 | |
| Q | Marking Instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 6(b) | Uses GPE formula with their AB | 1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| Condone missing units. | 1.1b | A1 |
| Subtotal | 2 | |
| Q | Marking Instructions | AO |
| Answer | Marks |
|---|---|
| 6(c) | Forms a three-term energy |
| Answer | Marks | Guidance |
|---|---|---|
| Condone sign errors. | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| their energies. | 1.1b | A1F |
| Answer | Marks | Guidance |
|---|---|---|
| Must include units. | 3.2b | A1 |
| Subtotal | 3 | |
| Q | Marking Instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 6(d) | Obtains 3.6 for tension at C | 1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| tension. | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| with their calculations. | 2.4 | R1 |
| Subtotal | 3 | |
| Question total | 10 | |
| Q | Marking Instructions | AO |
Question 6:
--- 6(a) ---
6(a) | Uses the EPE formula with their
extension. | 1.1a | M1 | 18×1.52
EPE= =6.75 J
2×3
Obtains 6.75 or 6.8
Condone missing units. | 1.1b | A1
Subtotal | 2
Q | Marking Instructions | AO | Marks | Typical Solution
--- 6(b) ---
6(b) | Uses GPE formula with their AB | 1.1a | M1 | GPE = 0.25 × 9.8 × 1.5
= 3.675 J
= 3.7 J (to 2sf)
Obtains AWRT 3.7
Condone missing units. | 1.1b | A1
Subtotal | 2
Q | Marking Instructions | AO | Marks | Typical Solution
--- 6(c) ---
6(c) | Forms a three-term energy
equation using their EPE and GPE.
Condone sign errors. | 3.3 | M1 | 1
6.75 – 3.675 = × 0.25v2
2
v2 = 24.6
v = 5.0 m s–1
Forms a correct equation using
their energies. | 1.1b | A1F
Obtains 5 or 5.0
Must include units. | 3.2b | A1
Subtotal | 3
Q | Marking Instructions | AO | Marks | Typical Solution
--- 6(d) ---
6(d) | Obtains 3.6 for tension at C | 1.1a | B1 | 18×0.6
T= =3.6 N
3
Resultant force = T – mg
= 3.6 – 0.25 × 9.8
= 1.15 N
Resultant force is upwards and the
particle is moving upwards, so
speed is increasing.
Finds the resultant force or
acceleration of the particle at C or
compares the value of mg with the
tension. | 3.3 | M1
Explains that this force is upwards
and so the speed is increasing or
an explanation that is consistent
with their calculations. | 2.4 | R1
Subtotal | 3
Question total | 10
Q | Marking Instructions | AO | Marks | Typical SolutionIn this question use $g = 9.8$ m s$^{-2}$
A light elastic string has natural length 3 metres and modulus of elasticity 18 newtons.
One end of the elastic string is attached to a particle of mass 0.25 kg
The other end of the elastic string is attached to a fixed point $O$
The particle is released from rest at a point $A$, which is 4.5 metres vertically below $O$
\begin{enumerate}[label=(\alph*)]
\item Calculate the elastic potential energy of the string when the particle is at $A$
[2 marks]
\item The point $B$ is 3 metres vertically below $O$
Calculate the gravitational potential energy gained by the particle as it moves from $A$ to $B$
[2 marks]
\item Find the speed of the particle at $B$
[3 marks]
\item The point $C$ is 3.6 metres vertically below $O$
Explain, showing any calculations that you make, why the speed of the particle is increasing the first time that the particle is at $C$
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Mechanics 2024 Q6 [10]}}