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Question
A road is constructed as per the given 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?
(Given: r = 72 m, vo = 216 km/h, w = 10 m, θ = 78°4', h = 9.805 m)
Solution
Given:
μs = 0.8
r = 72 m
θ = 78°4'
g = 10 m/s2
tan θ = tan 78°4' = 5
Vmin = `sqrt("rg"[("tan"theta - mu_"s")/(1 + mu_"s" "tan"theta)])`
= `sqrt(72xx10((5 - 0.8)/(1 + 0.8 xx 5)))`
`= sqrt(720xx4.2/(4+1)`
`= sqrt(3024/5)`
`=sqrt(144xx4.2)`
= 12 × 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, θ > 45°, there is no upper limit or maximum speed on this track.
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