What will be the maximum speed of a car on a road turn of radius 30 m if the coefficient of friction between the tyres and the road is 0.4 (Take g = 9.8 m/s²)

Concept:

The maximum speed of a car on a turn can be determined using the concept of centripetal force and frictional force. The frictional force provides the necessary centripetal force to keep the car in a circular path.

The maximum speed, v_max, can be calculated using the formula:

v_max = √(μ × g × r)

Calculation:

Radius of road turn, r = 30 m

Coefficient of friction, μ = 0.4

Acceleration due to gravity, g = 9.8 m/s2

We have,

⇒ v_max = √(0.4 × 9.8 m/s² × 30 m)

⇒ v_max = √(117.6)

⇒ v_max = 10.84 m/s

∴ The maximum speed of the car on the road turn is 10.84 m/s.