| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Horizontal road towing |
| Difficulty | Moderate -0.8 This is a straightforward M1 mechanics question requiring standard application of Newton's second law to a two-body system. Part (a) involves basic F=ma calculations with given values, part (b) uses elementary kinematics (v=u+at, s=ut+½at²), and part (c) asks for a simple conceptual explanation. All techniques are routine with no problem-solving insight required, making it easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Newton's 2nd law for whole system: \(P - 200 - 300 = (1200 + 1000) \times 0.8\) | M1 A1 | Correct equation with all terms |
| \(P - 500 = 1760\) | A1 | |
| \(P = 2260 \text{ N}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Apply Newton's 2nd law to caravan: \(T - 300 = 1000 \times 0.8\) | M1 A1 | Equation for caravan only |
| \(T = 300 + 800 = 1100 \text{ N}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(v = u + at \Rightarrow 15 = 7 + 0.8t\) | M1 A1 | Correct use of suvat |
| \(t = \frac{8}{0.8} = 10 \text{ s}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(s = ut + \frac{1}{2}at^2 = 7\times10 + \frac{1}{2}\times0.8\times100\) | M1 A1 | Or other valid suvat method |
| \(s = 70 + 40 = 110 \text{ m}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Resistance forces vary with speed (e.g. air resistance increases as speed increases) | B1 | Accept equivalent correct physical reasoning |
# Question 3:
## Part (a)(i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Newton's 2nd law for whole system: $P - 200 - 300 = (1200 + 1000) \times 0.8$ | M1 A1 | Correct equation with all terms |
| $P - 500 = 1760$ | A1 | |
| $P = 2260 \text{ N}$ | A1 | |
## Part (a)(ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Apply Newton's 2nd law to caravan: $T - 300 = 1000 \times 0.8$ | M1 A1 | Equation for caravan only |
| $T = 300 + 800 = 1100 \text{ N}$ | A1 | |
## Part (b)(i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $v = u + at \Rightarrow 15 = 7 + 0.8t$ | M1 A1 | Correct use of suvat |
| $t = \frac{8}{0.8} = 10 \text{ s}$ | A1 | |
## Part (b)(ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $s = ut + \frac{1}{2}at^2 = 7\times10 + \frac{1}{2}\times0.8\times100$ | M1 A1 | Or other valid suvat method |
| $s = 70 + 40 = 110 \text{ m}$ | A1 | |
## Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Resistance forces vary with speed (e.g. air resistance increases as speed increases) | B1 | Accept equivalent correct physical reasoning |3 A car, of mass 1200 kg , tows a caravan, of mass 1000 kg , along a straight horizontal road. The caravan is attached to the car by a horizontal tow bar, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{f30b02da-a41e-44cb-b45f-9e6a3a9d0528-06_277_901_484_584}
Assume that a constant resistance force of magnitude 200 newtons acts on the car and a constant resistance force of magnitude 300 newtons acts on the caravan. A constant driving force of magnitude $P$ newtons acts on the car in the direction of motion. The car and caravan accelerate at $0.8 \mathrm {~ms} ^ { - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find $P$.
\item Find the magnitude of the force in the tow bar that connects the car to the caravan.
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item Find the time that it takes for the speed of the car and caravan to increase from $7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ to $15 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
\item Find the distance that they travel in this time.
\end{enumerate}\item Explain why the assumption that the resistance forces are constant is unrealistic.\\
(1 mark)
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2011 Q3 [13]}}