7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f2737a11-4a15-41e9-9f87-31a705a8948b-18_326_1107_246_479}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
A car of mass 1200 kg is towing a trailer of mass 600 kg up a straight road, as shown in Figure 4.
The road is inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 12 }\)
The driving force produced by the engine of the car is 3000 N .
The car moves with acceleration \(0.75 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
The non-gravitational resistance to motion of
- the car is modelled as a constant force of magnitude \(2 R\) newtons
- the trailer is modelled as a constant force of magnitude \(R\) newtons
The car and the trailer are modelled as particles.
The tow bar between the car and trailer is modelled as a light rod that is parallel to the direction of motion.
Using the model,
- show that the value of \(R\) is 60
- find the tension in the tow bar.
When the car and trailer are moving at a speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the tow bar breaks.
Given that the non-gravitational resistance to motion of the trailer remains unchanged, - use the model to find the further distance moved by the trailer before it first comes to rest.