Overturning of Vehicle
When a car moves in a circular path with speed more than the maximum speed, then it overturns and its inner wheel leaves the ground first.
Weight of the car = mg
Speed of the car = v
Radius of the circular path = r
Distance between the center of wheels of the car = 2a
Height of the center of gravity (G) of the car from the road level = h
Reaction on the inner wheels of the car by the ground = R1
Reaction on the outer wheels of the car by the ground = R2
When a car moves in a circular path, horizontal force F provides the required centripetal force.
For rotational equilibrium, by taking the moment of forces R1, R2, and F about G,
As there is no vertical motion so
By solving (8), (9) and (10)
It is clear from (11) that if v increases, value of R1 decreases and for R1 = 0,
i.e., the maximum speed of a car without overturning on a flat road is given by