Answer:
The maximum speed of the car should be 13.7 m/s
Explanation:
For the car to travel at a maximum safe speed , the frictional force acting should be maximum and at the same time should provide the necessary centripetal force.
Let 'k' (=0.3502) be the coefficient of friction and 'N' be the normal force acting on the surface.
Then ,
N = mg , where 'm' is the mass of the body and 'g'(=9.8) is the acceleration due to gravity.
∴ Maximum frictional force , f = kN = kmg
Centripetal force that should act on the car to move with maximum possible speed is -
, where 'v' is the velocity of the car and 'r'(=55m) is the radius of circular path.
Equating the 2 forces , we get -
∴
Substituting all the values , we get -
v = 13.7 m/s.