A 1200 kg car surrounds an 80 meter radius curve. If the coefficient of friction between the tires and the road is 0.65, what maximum speed should the car have to not leave the curve to : a. 23 m / s

b. 10 mph

c. 62 km / h

d. 6.3 m / s

Answer: a) 23 m/s

Explanation: In order to solve this problem we have to consider the circular movement where the friction force change de direcion of the velocty to keep a circular trajectory.

By using Second Newton law, we have:

F=m*acentripeta

μ*N = m*v^2/r where N (equal to mg) is the normal force and μ is the coefficient of friction. r is the redius of the trajectory.

so

the maximun speed permited to keep a circular trajectory is calculated as:

v = (μ*r*g) ^1/2 = (0.65*80m*9.8 m/s^2) ^1/2=22.57 m/s