Question

4. A 14000N car traveling at 25m/s rounds a curve of radius 200m. Find the following: a. The centripetal acceleration of the car.   


b. The force that maintains centripetal acceleration.


c. The minimum coefficient of static friction between the tires and road that will allow the car to round the curve safely.

Answer 1

Given

14000 N car traveling at v = 25 m/s ,

radius of the curve is r = 200 m

mass of the car is m = W/g = 14000 N/(10 m/s^2) = 1400 kg

a) we know that the centripetal acceleration or radial acceleration is a_rad = v^2/r

   a_rad = 25^2/200 m/s^2 = 3.125 m/s2

b) The centripetal force acts always towards the center , whose magnitude is

   F_c = m*v^2/r
mass of the car is m = W/g = 14000 N/(10 m/s^2) = 1400 kg
   F_c = 1400*25^2/200 N
  
   F_c = 4375 N

c)

here the centripetal force equal to the frictional force

  
   F_c = F_f
  
   m*v^2/r = mue_s*F_N

   m*v^2/r = mue_s*m*g

   v^2/r = mue_s*g

   mue_s = v^2/r*g

   mue_s = 25^2/(200*10)

   mue-s = 0.3125
The minimum coefficient of static friction between the tires and road that will allow the car to round the curve safely is mue_s = 0.3125