The road in the example 14 above is constructed as per the requir… - Vidyadip

Question

The road in the example $14$ above is constructed as per the requirements. The coefficient of static friction between the tyres of a vehicle on this road is $0.8,$ will there be any lower speed limit? By how much can the upper speed limit exceed in this case?
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Answer

Data: $r=72 m , \theta=78^{\circ} 4^{\prime}, \mu_{ s }=0.8, g =10 m / s ^2 \tan \theta=\tan 78^{\circ} 4^{\prime}=5$
$v_{\min }=\sqrt{r g\left(\frac{\tan \theta-\mu_{ s }}{1+\mu_{ s } \tan \theta}\right)}$
$ = \sqrt{(72)(10)\left(\frac{5-0.8}{1+(0.8)(5)}\right)}$
$=\sqrt{720 \times \frac{4.2}{5}}=\sqrt{144 \times 4.2}=12 \times 2.049$
$=24.588 m / s =88.52 km / h $
This will be the lower limit or minimum speed on this track.
Since the track is heavily banked, $\theta>45^{\circ}$, there is no upper limit or maximum speed on this track.

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