Question

Derive on expression for maximum safety speed with which a vehicle should move along a curved harizontal road

Answer 1

Answer:

Expression for maximum safety speed on horizontal curve road:

i. Consider a vehicle of mass m moving with speed v along a horizontal curve of radius r.

ii. While taking a turn, vehicle performs circular motion. Centripetal force is provided by the frictional force between tyres and road.

iii. Centripetal force is given by, FCP = mv2 r iv. Frictional force between road and tyres of wheel is given by, Fs = μN where, μ = coefficient of friction between tyres of wheels and road. N = normal reaction acting on vehicle in upward direction. But, N = mg This is maximum speed of vehicle.

Significance:

i. The maximum safe speed of a vehicle on a curve road depends upon friction between tyres and road. ii. Friction depends on the nature of the surface and presence of oil or water on the road.

iii. If friction is not sufficient to provide centripetal force, the vehicle is likely to skid off the road.