Question

A car with mass 2000 kg drives around a flat circular track of radius 28.0 m. The coefficient of friction between the car tires and the track is 0.830. How fast can the car go around the track without losing traction?

Answer 1

Answer:

15 m/s

Explanation:

Let g = 9.81 m/s2. We can calculate the car weight and also the normal force acting on it

W = N = mg = 2000*9.81 = 19620 N

So the maximum static friction force on the car is

$F_f = N\mu = 19620 * 0.83 = 16284.6$

Which is also the greatest centripetal force that can act on the car without making it slip. From here we can calculate the greatest centripetal acceleration according to Newton's 2nd law

$a_c = F_f/m = 16284.6 / 2000 = 8.1423 m/s^2$

From here we can calculate the maximum linear speed that car can have

$a_c = v^2/r$

where r is the radius of circular track

$v^2 = a_c*r = 8.1423 * 28 = 227.984$

$v = \sqrt{227.9844} = 15 m/s$