| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2020 |
| Session | Specimen |
| Marks | 6 |
| Topic | Forces, equilibrium and resultants |
| Type | Connected particles via tow-bar on horizontal surface |
| Difficulty | Moderate -0.8 This is a straightforward mechanics problem requiring application of Newton's second law to a two-body system. Part (a) uses F=ma on the whole system with given acceleration. Parts (b) and (c) repeat the process with changed resistance values. All steps are routine calculations with no conceptual challenges or novel problem-solving required—significantly easier than average A-level questions. |
| Spec | 3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
Two trucks, $S$ and $T$, of masses 8000 kg and 10000 kg respectively, are pulled along a straight, horizontal track by a constant, horizontal force of $P$ N. A resistive force of 600 N acts on $S$ and a resistive force of 450 N acts on $T$. The coupling between the trucks is light and horizontal (see diagram).
\includegraphics{figure_8}
The acceleration of the system is 0.3 ms$^{-2}$ in the direction of the pulling force of magnitude $P$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of $P$. [2]
\end{enumerate}
Truck $S$ is now subjected to an extra resistive force of 1800 N. The pulling force, $P$, does not change.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Calculate the new acceleration of the trucks. [2]
\item Calculate the force in the coupling between the trucks. [2]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2020 Q8 [6]}}