| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Mechanics (Further AS Paper 2 Mechanics) |
| Year | 2019 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Particle on slope then horizontal |
| Difficulty | Standard +0.3 This is a straightforward energy and work-done problem requiring standard mechanics techniques: calculating PE and KE changes, finding resistance force from work-energy principle, then checking if motion continues. While it involves multiple parts and careful arithmetic with the 50° angle, it follows a predictable template with no novel insight required. Slightly easier than average A-level due to clear structure and standard method application. |
| Spec | 6.02a Work done: concept and definition6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks |
|---|---|
| 6(a) | Forms an expression for PE and at |
| Answer | Marks | Guidance |
|---|---|---|
| Must include 15sin/cos(40°/50°) | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| expressions | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| appropriate signs | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| energy AWRT 4000 J | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 6(b)(i) | Translates problem into an | |
| equation to find F | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| figs before rounding | 1.1b | A1 |
| Answer | Marks |
|---|---|
| 6(b)(ii) | Translates problem into an |
| Answer | Marks | Guidance |
|---|---|---|
| move from B to C | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| at B | 1.1b | A1F |
| Answer | Marks | Guidance |
|---|---|---|
| CSO | 2.2b | E1 |
| Total | 9 | |
| Q | Marking Instructions | AO |
Question 6:
--- 6(a) ---
6(a) | Forms an expression for PE and at
least one expression for KE
Must include 15sin/cos(40°/50°) | 3.1b | M1 | PE at A
mgh=40g(15sin500)=4504
KE at A
1 1
mv2 = (40)(1)2 =20
2 2
KE at B
1 1
mv2 = (40)(5)2 =500
2 2
Loss in energy
4504 + 20 – 500 = 4000 J (to 2 sf)
Obtains three fully correct energy
expressions | 1.1b | A1
Evaluates ‘their’ change in energy
using three energy terms with
appropriate signs | 1.1a | M1
Obtains the correct change in
energy AWRT 4000 J | 1.1b | A1
--- 6(b)(i) ---
6(b)(i) | Translates problem into an
equation to find F | 3.1b | M1 | Change in energy = force x distance
4024 = 15F
F = 268.2…. N
F = 270 N (to 2 sf)
Obtains F = 270 when rounded to
two significant figures AG
Must use their rounded or
unrounded energy value from part
(a)
Must show F to more than two sig
figs before rounding | 1.1b | A1
--- 6(b)(ii) ---
6(b)(ii) | Translates problem into an
equation and finds distance
travelled along BC
Or
Calculates total energy needed to
move from B to C | 3.4 | M1 | KE at B = force x distance travelled
500 = 270d
d = 1.85
1.85 < 2
If Martin’s size is negligible then he
does not reach the end of the slide
If Martin’s size is not negligible then
he might reach the end of the slide
Compares their value of d with
distance BC
Or
Compares their energy with the KE
at B | 1.1b | A1F
Infers correctly whether Martin
reaches the point C or not
CSO | 2.2b | E1
Total | 9
Q | Marking Instructions | AO | Marks | Typical SolutionIn this question use $g = 9.8\,\text{m}\,\text{s}^{-2}$
Martin, who is of mass 40 kg, is using a slide.
The slide is made of two straight sections $AB$ and $BC$.
The section $AB$ has length 15 metres and is at an angle of $50°$ to the horizontal.
The section $BC$ has length 2 metres and is horizontal.
\includegraphics{figure_6}
Martin pushes himself from $A$ down the slide with initial speed $1\,\text{m}\,\text{s}^{-1}$
He reaches $B$ with speed $5\,\text{m}\,\text{s}^{-1}$
Model Martin as a particle.
\begin{enumerate}[label=(\alph*)]
\item Find the energy lost as Martin slides from $A$ to $B$.
[4 marks]
\item Assume that a resistance force of constant magnitude acts on Martin while he is moving on the slide.
\begin{enumerate}[label=(\roman*)]
\item Show that the magnitude of this resistance force is approximately 270 N
[2 marks]
\item Determine if Martin reaches the point $C$.
[3 marks]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Mechanics 2019 Q6 [9]}}