AQA Further Paper 3 Mechanics 2022 June — Question 8 8 marks

Exam BoardAQA
ModuleFurther Paper 3 Mechanics (Further Paper 3 Mechanics)
Year2022
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAdvanced work-energy problems
TypeElastic string horizontal surface projection
DifficultyStandard +0.8 This is a multi-stage work-energy problem requiring students to analyze motion with friction across different surfaces, apply conservation of energy principles multiple times, and critically evaluate a real-world claim. While the individual calculations are standard Further Maths mechanics, the question requires careful tracking of energy transformations through multiple phases and thoughtful physical reasoning for part (c), placing it moderately above average difficulty.
Spec6.02i Conservation of energy: mechanical energy principle
8
  1. Use an energy method to find the maximum speed of the crate.
    8
  2. Use an energy method to find the total distance travelled by the crate.
    8
  3. A student claims that in reality the crate is unlikely to travel more than 5.3 metres in total. Comment on the validity of this claim. \includegraphics[max width=\textwidth, alt={}, center]{0afe3ff2-0af5-4aeb-98c5-1346fa803388-12_2488_1732_219_139}
Question 8(a):
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(R + 240\sin 30° = 60 \times 9.8\); \(R = 468\)B1 Obtains correct value of or expression for normal reaction force
\(240\cos 30° \times 5 - 0.4 \times 468 \times 5 = \dfrac{1}{2} \times 60v^2\)M1 Forms three-term energy equation with at least two correct terms. Condone consistent wrong use of trigonometry within solution.
\(600\sqrt{3} - 936 = 30v^2\); \(103.23 = 30v^2\)A1F Correct energy equation. Follow through use of \(R = 60g\)
\(v = 1.8549... = 1.9 \text{ ms}^{-1}\)A1 Uses energy method to obtain maximum speed, AWRT 1.9. Condone missing units.
Total: 4 marks
Question 8(b):
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(103.23 = 0.4 \times 588 \times d\); \(103.23 = 235.2 \times d\); \(d = 0.44\); Crate travels 5.4 metresM1 Forms energy equation to find additional distance using speed/energy from part (a). Must use normal reaction as 588.
Final answer given to 2 sf with correct unitsA1 Obtains correct total distance. Final answer must be given to 2 sf and with correct units.
Total: 2 marks
Question 8(c):
AnswerMarks Guidance
Answer/WorkingMark Guidance
As air resistance has been ignored it is unlikely that the crate will travel as far as the 5.4 metres predictedE1 States that air resistance has been ignored
Hence the student's claim is quite reasonableE1 Makes reasoned comment on student's claim based on answer to part (b) and impact of air resistance
Total: 2 marks
## Question 8(a):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $R + 240\sin 30° = 60 \times 9.8$; $R = 468$ | B1 | Obtains correct value of or expression for normal reaction force |
| $240\cos 30° \times 5 - 0.4 \times 468 \times 5 = \dfrac{1}{2} \times 60v^2$ | M1 | Forms three-term energy equation with at least two correct terms. Condone consistent wrong use of trigonometry within solution. |
| $600\sqrt{3} - 936 = 30v^2$; $103.23 = 30v^2$ | A1F | Correct energy equation. Follow through use of $R = 60g$ |
| $v = 1.8549... = 1.9 \text{ ms}^{-1}$ | A1 | Uses energy method to obtain maximum speed, AWRT 1.9. Condone missing units. |

**Total: 4 marks**

---

## Question 8(b):

| Answer/Working | Mark | Guidance |
|---|---|---|
| $103.23 = 0.4 \times 588 \times d$; $103.23 = 235.2 \times d$; $d = 0.44$; Crate travels 5.4 metres | M1 | Forms energy equation to find additional distance using speed/energy from part (a). Must use normal reaction as 588. |
| Final answer given to 2 sf with correct units | A1 | Obtains correct total distance. Final answer must be given to 2 sf and with correct units. |

**Total: 2 marks**

---

## Question 8(c):

| Answer/Working | Mark | Guidance |
|---|---|---|
| As air resistance has been ignored it is unlikely that the crate will travel as far as the 5.4 metres predicted | E1 | States that air resistance has been ignored |
| Hence the student's claim is quite reasonable | E1 | Makes reasoned comment on student's claim based on answer to part (b) and impact of air resistance |

**Total: 2 marks**

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8
\begin{enumerate}[label=(\alph*)]
\item Use an energy method to find the maximum speed of the crate.\\

8
\item Use an energy method to find the total distance travelled by the crate.\\

8
\item A student claims that in reality the crate is unlikely to travel more than 5.3 metres in total. Comment on the validity of this claim.\\

\includegraphics[max width=\textwidth, alt={}, center]{0afe3ff2-0af5-4aeb-98c5-1346fa803388-12_2488_1732_219_139}
\end{enumerate}

\hfill \mbox{\textit{AQA Further Paper 3 Mechanics 2022 Q8 [8]}}
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