4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{dceb2432-117c-40fe-bf3d-782beeb42e41-12_360_1004_246_534}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
A car is travelling round a circular track. The track is banked at an angle \(\alpha\) to the horizontal, as shown in Figure 4.
The car and driver are modelled as a particle.
The car moves round the track with constant speed in a horizontal circle of radius \(r\).
When the car is moving with speed \(\frac { 1 } { 2 } \sqrt { g r }\) round the circle, there is no sideways friction between the tyres of the car and the track.
- Show that \(\tan \alpha = \frac { 1 } { 4 }\)
The sideways friction between the tyres of the car and the track has coefficient of friction \(\mu\), where \(\mu < 4\)
The maximum speed at which the car can move round the circle without slipping sideways is \(V\).
- Find \(V\) in terms of \(\mu , r\) and \(g\).