| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2020 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Variable mass or unknown mass |
| Difficulty | Standard +0.3 This is a standard AS-level mechanics pulley problem requiring Newton's second law applied to a two-body system. Part (a) involves routine equation setup and algebraic manipulation to reach a given result. Parts (b) and (c) require straightforward reasoning about constraints and using SUVAT equations. The question is slightly easier than average due to the 'show that' scaffold in part (a) and the standard nature of all techniques required. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks |
|---|---|
| 16(a) | Models the motion of the container |
| Answer | Marks | Guidance |
|---|---|---|
| the equation correct. | 3.3 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Forms fully correct equation | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| particle | 3.3 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑎𝑎 𝑚𝑚. | 2.1 | R1 |
| Subtotal | 4 | ∴ 𝑎𝑎 = � � 𝘨𝘨 |
| Answer | Marks | Guidance |
|---|---|---|
| 16(b) | Deduces correct limits | |
| Condone | 2.2a | B1 |
| Answer | Marks |
|---|---|
| Subtotal | 1 |
| Answer | Marks |
|---|---|
| 16(c) | Uses appropriate constant |
| Answer | Marks | Guidance |
|---|---|---|
| acceleration | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Calculates correct value for | 1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑎𝑎 𝑚𝑚 | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Condone 0.1 | 3.2a | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 4 | 𝑚𝑚 = 4+𝘨𝘨 = 0.10 |
| Answer | Marks |
|---|---|
| 16(d) | Describes any valid assumption not |
| Answer | Marks | Guidance |
|---|---|---|
| with the load | 3.5b | E1 |
| Answer | Marks |
|---|---|
| Subtotal | 1 |
| Question Total | 10 |
Question 16:
--- 16(a) ---
16(a) | Models the motion of the container
and load with at least one side of
the equation correct. | 3.3 | M1 | 𝑇𝑇−(𝑚𝑚+2)𝘨𝘨 = (𝑚𝑚+2)𝑎𝑎
5𝘨𝘨−𝑇𝑇 = 5𝑎𝑎
5𝘨𝘨−(𝑚𝑚+2)𝘨𝘨 = (5+2+ 𝑚𝑚)𝑎𝑎
(3−𝑚𝑚)𝘨𝘨= (7+𝑚𝑚)𝑎𝑎
3−𝑚𝑚
Forms fully correct equation | 1.1b | A1
Forms fully correct equation for
particle | 3.3 | B1
Completes a rigorous argument by
eliminating and rearranging to
express in terms of AG
𝑇𝑇
𝑎𝑎 𝑚𝑚. | 2.1 | R1
Subtotal | 4 | ∴ 𝑎𝑎 = � � 𝘨𝘨
𝑚𝑚 +7
--- 16(b) ---
16(b) | Deduces correct limits
Condone | 2.2a | B1 | 0 < 𝑚𝑚 < 3
0 ≤ 𝑚𝑚 < 3
Subtotal | 1
--- 16(c) ---
16(c) | Uses appropriate constant
acceleration equation to find the
acceleration | 3.4 | M1 | 1 2
𝑎𝑎 =𝑢𝑢𝑡𝑡+ 𝑎𝑎𝑡𝑡
Using 2 and
𝑎𝑎 =2 ,𝑢𝑢 = 0 𝑡𝑡 = 1
𝑎𝑎 = 4
3−𝑚𝑚
4 = � � 𝘨𝘨
𝑚𝑚 +7
kg
3𝘨𝘨−28
Calculates correct value for | 1.1b | A1
𝑎𝑎
Forms equation for in terms of
using their value
𝑎𝑎 𝑚𝑚 | 3.4 | M1
𝑎𝑎
Solves to find AWRT 0.10
Condone 0.1 | 3.2a | A1
𝑚𝑚.
Subtotal | 4 | 𝑚𝑚 = 4+𝘨𝘨 = 0.10
--- 16(d) ---
16(d) | Describes any valid assumption not
related to those assumptions
already stated in the question.
Eg The particle is at least 2m
above the ground
Eg The particle does not collide
with the load | 3.5b | E1 | I assumed that the top of the
container does not reach the pulley
Subtotal | 1
Question Total | 10A simple lifting mechanism comprises a light inextensible wire which is passed over a smooth fixed pulley.
One end of the wire is attached to a rigid triangular container of mass 2 kg, which rests on horizontal ground.
A load of $m$ kg is placed in the container.
The other end of the wire is attached to a particle of mass 5 kg, which hangs vertically downwards.
The mechanism is initially held at rest as shown in the diagram below.
\includegraphics{figure_16}
The mechanism is released from rest, and the container begins to move upwards with acceleration $a\text{ m s}^{-2}$
The wire remains taut throughout the motion.
\begin{enumerate}[label=(\alph*)]
\item Show that
$$a = \left(\frac{3 - m}{m + 7}\right)g$$ [4 marks]
\item State the range of possible values of $m$. [1 mark]
\item In this question use $g = 9.8\text{ m s}^{-2}$
The load reaches a height of 2 metres above the ground 1 second after it is released.
Find the mass of the load. [4 marks]
\item Ignoring air resistance, describe one assumption you have made in your model. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 2020 Q16 [10]}}