| Exam Board | AQA |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2010 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Train with coupled trucks/carriages |
| Difficulty | Moderate -0.8 This is a standard connected particles problem requiring systematic application of F=ma to each component. Parts (a)-(c) involve straightforward force diagrams and single-body calculations, while (d) requires considering the whole system. The multi-part structure and 4-step progression is typical, but each step follows directly from Newton's second law with no conceptual challenges or novel problem-solving required. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution |
6 A small train at an amusement park consists of an engine and two carriages connected to each other by light horizontal rods, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{fe8c1ea4-cf4d-4741-8af5-03e8c2c88559-4_190_1038_420_493}
The engine has mass 2000 kg and each carriage has mass 500 kg .
The train moves along a straight horizontal track. A resistance force of magnitude 400 newtons acts on the engine, and resistance forces of magnitude 300 newtons act on each carriage. The train is accelerating at $0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram to show the horizontal forces acting on Carriage 2.
\item Show that the magnitude of the force that the rod exerts on Carriage 2 is 550 newtons.
\item Find the magnitude of the force that the rod attached to the engine exerts on Carriage 1.
\item A forward driving force of magnitude $P$ newtons acts on the engine. Find $P$.
\end{enumerate}
\hfill \mbox{\textit{AQA M1 2010 Q6 [9]}}