| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Mechanics (Further Paper 3 Mechanics) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Vertical circle with peg/obstacle |
| Difficulty | Challenging +1.8 This Further Maths mechanics problem requires understanding of energy conservation and geometry of a string wrapping around a peg. Part (a) tests diagram interpretation (straightforward), while part (c) demands setting up energy equations with the constraint that the string goes slack at a specific angle, requiring careful geometric analysis and solving a transcendental equation. The multi-step reasoning and geometric insight needed elevate this above standard mechanics questions, though the techniques themselves are well-established. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05e Radial/tangential acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| 7(a) | States that the 60 angle is too | |
| small | 2.3 | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| the string becomes slack | 2.3 | E1 |
| Total | 2 | |
| Q | Marking Instructions | AO |
| Answer | Marks |
|---|---|
| 7(b) | Draws a diagram that shows the |
| Answer | Marks | Guidance |
|---|---|---|
| level than the final level shown. | 2.3 | B1 |
| Total | 1 | |
| Q | Marking Instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 7(c) | Introduces a variable for the mass | |
| and uses it in an equation | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Newton’s second law. | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| v 2 | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| for v | 3.4 | M1 |
| Obtains a correct energy equation | 1.1b | A1 |
| Deduces the correct angle | 2.2a | A1 |
| Total | 6 | |
| Question total | 9 | |
| Q | Marking Instructions | AO |
Question 7:
--- 7(a) ---
7(a) | States that the 60 angle is too
small | 2.3 | E1 | The 60 angle is too small
The sphere must start at a higher
level than where the string
becomes slack
States that the initial position must
be higher than the point at which
the string becomes slack | 2.3 | E1
Total | 2
Q | Marking Instructions | AO | Marks | Typical Solution
--- 7(b) ---
7(b) | Draws a diagram that shows the
initial position more accurately,
where the sphere starts at higher
level than the final level shown. | 2.3 | B1
Total | 1
Q | Marking Instructions | AO | Marks | Typical Solution
--- 7(c) ---
7(c) | Introduces a variable for the mass
and uses it in an equation | 1.1b | B1 | Let mass = m and speed when the
string becomes slack = v
m v 2
m g c o s 6 0 =
0 . 6
v 2 = 0 . 6 g c o s 6 0
Take GPE as zero at the bar
1
mgh= m0.6gcos60+mg0.6cos60
2
h=0.45
0.45
cos= =0.3
1.5
= 73
Resolves radially at the point where
the string becomes slack and uses
Newton’s second law. | 3.3 | M1
Obtains correct expression for v or
v 2 | 1.1b | A1
Forms a three term energy
equation and substitutes their value
for v | 3.4 | M1
Obtains a correct energy equation | 1.1b | A1
Deduces the correct angle | 2.2a | A1
Total | 6
Question total | 9
Q | Marking Instructions | AO | Marks | Typical SolutionA light string has length 1.5 metres.
A small sphere is attached to one end of the string.
The other end of the string is attached to a fixed point O
A thin horizontal bar is positioned 0.9 metres directly below O
The bar is perpendicular to the plane in which the sphere moves.
The sphere is released from rest with the string taut and at an angle $\alpha$ to the downward vertical through O
The string becomes slack when the angle between the two sections of the string is 60°
Ben draws the diagram below to show the initial position of the sphere, the bar and the path of the sphere.
\includegraphics{figure_7}
\begin{enumerate}[label=(\alph*)]
\item State two reasons why Ben's diagram is not a good representation of the situation.
[2 marks]
\item Using your answer to part (a), sketch an improved diagram.
[1 mark]
\item Find $\alpha$, giving your answer to the nearest degree.
[6 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Further Paper 3 Mechanics 2021 Q7 [9]}}