Question

A turn of radius 20 m is banked for the vehicles going at a speed of 36 km/h. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up?

Answer 1

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.

Answer 2

Answer:

Explanation:

See pic