Question

A car of mass 1000 kg moves on a circular track of radius 20 m, if the coefficient of friction is 0.64 then the maximum velocity with which the car can move is

Answer 1

The weight of the car is (1000 kg) x (9.80) = 9800 N.
The maximum force of friction between the tires and the road is $F_{fr}\le {\mu }_s{F}_N$
So $F_{fr}\le$(.64)(9800 N) = 6272 N
This causes a centripetal acceleration of:
F = ma
6272 N = (1000 kg) x a
a = 6.272 m/$s^2$
Since, $a=\frac{v^2}{r}$,
$6.272=\frac{v^2}{20m}$,
v = 11.2 m/s.