A car has to move on a level turn of radius 45 m. If the coefficient of static friction between the tyre and the road is 2.0, find the maximum speed the car can take without skidding.
Let the mass of the car be M. The forces on the car are
(a) weight Mg downward
(b) normal force N by the road upward
(c) friction fs by the road towards the centre
The car is going on a horizontal circle of radius R, so it is accelerating. The acceleration is towards the centre and its magnitude is v2R, where v is the speed. For vertical direction, acceleration = 0. Resolving the forces in vertical and horizontal directions and applying Newton's laws, we have
N = mg
and fs = Mv2R.
As we are looking for the maximum speed for no skidding, it is a case of limiting friction and hence
fs = μs N = μs Mg.
So, we have
μs Mg = Mv2R
or, v2 = μsgR.
Putting the values, v=√
= 30 m/s