| Exam Board | SPS |
|---|---|
| Module | SPS SM Mechanics (SPS SM Mechanics) |
| Year | 2021 |
| Session | September |
| Marks | 12 |
| Topic | Newton's laws and connected particles |
| Type | Car towing trailer, horizontal |
| Difficulty | Moderate -0.3 This is a standard connected particles mechanics problem requiring Newton's second law applications and SUVAT equations. Parts (a)-(c) involve routine force calculations and kinematics with clearly defined steps. The proportional resistance condition is straightforward to apply, and part (d) tests basic understanding of modeling assumptions. While it requires careful bookkeeping across multiple parts, it demands no novel insight beyond textbook methods, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03k Connected particles: pulleys and equilibrium |
A car of mass $1200 \text{ kg}$ pulls a trailer of mass $400 \text{ kg}$ along a straight horizontal road. The car and trailer are connected by a tow-rope modelled as a light inextensible rod. The engine of the car provides a constant driving force of $3200 \text{ N}$. The horizontal resistances of the car and the trailer are proportional to their respective masses. Given that the acceleration of the car and the trailer is $0.4 \text{ m s}^{-2}$,
\begin{enumerate}[label=(\alph*)]
\item find the resistance to motion on the trailer, [4]
\item find the tension in the tow-rope. [3]
\end{enumerate}
When the car and trailer are travelling at $25 \text{ m s}^{-1}$ the tow-rope breaks. Assuming that the resistances to motion remain unchanged,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the distance the trailer travels before coming to a stop, [4]
\item state how you have used the modelling assumption that the tow-rope is inextensible. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Mechanics 2021 Q3 [12]}}