Question

Calculate the maximum deceleration of a car that is heading down a 9° slope (one that makes an angle of 9° with the horizontal) under the following road conditions. You may assume that the weight of the car is evenly distributed on all four tires and that the static coefficient of friction is involved--that is, the tires are not allowed to slip during the deceleration

Answer 1

from the force diagram ,

F_n = mg cos9

frictional force is given as

f_f = u F_n

f_f = mgcos9

force equation for motion downward is given as

mg Sin9 - f_f = ma                       eq-1

Torque equation is given as

f_f R = Ia/R

f_f = (0.5) m R² (a/R²)

f_f = (0.5) m a                       eq-2

using eq-1 and eq-2

mg Sin9 - (0.5) m a = ma

mg Sin9 = 1.5 ma

a = 2g Sin9/3