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प्रश्न
A road is constructed part of a racing tracks to be designed with radius of curvature 72 m. We are not recommending the vehieles to drive faster than 216 kmph.. 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)
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उत्तर
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(72 xx 10((5 - 0.8)/(1 + 0.8 xx 5)))`
`= sqrt(720 xx 4.2/(4 + 1)`
`= sqrt(3024/5)`
`= sqrt(144 xx 4.2)`
= 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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