Question

derive the equation for a maximum speed on a road of radius r​

Answer 1

Answer:

Gravitational attraction force – mg

Frictional force (f) – acting between car’s tire and road, and parallel to the slope of a road

Normal force (N)- It is a reaction force of the gravitational force exerted by the road on a car

Centripetal force (mv2r) - acting towards the center of the circular path followed by the car.

Let’s take inclination angle A of the road

This is an expression for a maximum speed of a car on a banked road in a circular motion.

Note: (1) Roads are banked to prevent high-speed cars from skidding.

(2) If a car is moving at a speed more than mentioned above, it will skid.

(3) If the force of friction is not strong enough, the vehicle will skid. Also, note that friction acts downwards along the road, as the car tends to skid up.

Explanation: