Answer :
a) The banking angle should be = 37.22°.
b) The normal force acting on the car is 5852.94 N.
The frictional force acting on the car is 4445.84 N.
What is banking of roads?
Banking of roads is the practice of raising the outer borders of curving roads over the inner edge in order to give vehicles the necessary centripetal force to make a turn safely.
Given that:
steady speed: v = 22 m/s.
radius of curvature: r = 65 m.
acceleration due to gravity: g = 9.8 m/s^2.
Hence, banking angle = tan⁻¹(v²/rg)
= tan⁻¹(22²/(65×9.8))
= 37.22°
b) at the proper banking angle,
The normal force acting on the car = mg cosθ
= 750 × 9.8 × cos 37.22° N.
= 5852.94 N.
The frictional force acting on the car= mg sinθ
= 750 × 9.8 × sin 37.22° N.
= 4445.84 N.
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