a car is traveling at 100km at 5 degree incline when its bra

a car is traveling at 100km/ at 5 degree incline when its brakes become locked. determine the stopping distance of the car knowing that the coefficient of kinetic friction between the tires and the road is .65

Problem 29.

12.28 A car is traveling at 100 km/h along a straight, level road when its brakes become locked. Determine the stopping distance of the car knowing that the coefficient of kinetic friction between the tires and the road is 0.65 12.29 Solve Prob. 12.28 if the car is traveling down a 5° incline

Solution

Let m be the mass of the car
Let be the constant road slope angle to horizontal
Let be the coefficient of friction between road and tires.
Let a be the acceleration of the car while braking and velocity greater than zero.

adjust velocity to standard units
100km/hr (1000m/km / 3600 s/hr) = 27.8 m/s

Normal force of the road on the car
Fn = mgcos

Friction force of the road on the car
Ff = Fn
Ff = mgcos

Weight Force acting parallel to the road in direction of motion
Fg = mgsin

Net force acting on the car
F = Fg - Ff
F = mgsin - mgcos
F = mg(sin - cos)

comparing to basic equation
F = ma
a = g(sin - cos)
a = 9.81(sin5 - 0.65cos5)
a = -5.5 m/s²

kinematic equation

vf² = vi² + 2ad
d = (vf² - vi²) / 2a

d = (0² - 27.8²) / 2(-5.5)
d = 70 m