find vmax and vmin when the road is blanked with Vsafe=36km/hr,R=20m, µ=0.4
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Radius (r) = 20 m.
Speed (v) = 36 km/hr = 10 m/s.
Coefficient of the Static Friction(u)= 0.4
tan α = v²/rg
⇒ α = tan⁻(1/2)
Therefore, Sin α = 1/√5 and Cosα = 2/√5
Using the Formula,
V max. = \sqrt{\frac{rg(Sin\alpha + uCos\alpha)}{Cos\alpha - uSin\alpha}
On Solving it,
V max. = 15 m/s. = 54 km/hr.
V min. = \sqrt{\frac{rg(Sin\alpha - uCos\alpha)}{Cos\alpha + uSin\alpha}
On Solving, V min. = 14 km/hr.
Therefore, Possible speeds of the Vehicle so that it neither slips down nor skids up is 14 km/hr to 54 km/hr.
Hope it helps.
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