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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.
 
36821.png
Fig. 6
 
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 R1R2, and F about G,
 
 
As there is no vertical motion so
 
 
By solving (8), (9) and (10)
 
36809.png
 
It is clear from (11) that if v increases, value of R1 decreases and for R1 = 0,
36797.png or 36791.png
 
i.e., the maximum speed of a car without overturning on a flat road is given by
36785.png




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