Final answer:
The magnitude of the braking acceleration of the car is 3.92 m/s². The normal force on each rear wheel is 2516.67 N. The normal force on each front wheel is 4400 N.
Step-by-step explanation:
To find the magnitude of the braking acceleration of the car, we need to use the formula:
a = μk * g
where μk is the coefficient of kinetic friction between the tires and the road, and g is the acceleration due to gravity (9.8 m/s²). In this case, μk = 0.40, so:
a = 0.40 * 9.8 = 3.92 m/s²
To find the normal force on each rear wheel, we can use the formula:
NR = (m * g) / (L + d)
where m is the mass of the car, g is the acceleration due to gravity, L is the separation between the front and rear axles, and d is the distance from the center of mass to the front axle. In this case, m = 11 kN = 11000 N (remember to convert to Newtons), g = 9.8 m/s², L = 4.2 m, and d = 1.8 m, so:
NR = (11000 * 9.8) / (4.2 + 1.8) = 2516.67 N
To find the normal force on each front wheel, we can use a similar formula:
NF = (m * g) / (L - d)
where the variables have the same meanings. In this case:
NF = (11000 * 9.8) / (4.2 - 1.8) = 4400 N
The braking force on each rear wheel can be found using the formula:
FR = NR * μk
where NR is the normal force on each rear wheel and μk is the coefficient of kinetic friction. In this case:
FR = 2516.67 * 0.40 = 1006.67 N
Finally, the braking force on each front wheel can be found using a similar formula:
FF = NF * μk
where NF is the normal force on each front wheel and μk is the coefficient of kinetic friction. In this case:
FF = 4400 * 0.40 = 1760 N