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In Figure, the driver of a car on a horizontal road makes an emergency stop by applying the brakes so that all four wheels lock and skid along the road. The coefficient of kinetic friction between tires and road is 0.40. The separation between the front and rear axles is L=4.2 m, and the center of mass of the car is located at distance d=1.8 m behind the front axle and distance h=0.75 m above the road. The car weighs 11kN. Find the magnitude of (a) the braking acceleration of the car, (b) the normal force on each rear wheel, (c) the normal force on each front wheel, (d) the braking force on each rear wheel, and (e) the braking force on each front wheel. (Hint: Although the car is not in translational equilibrium, it is in rotational equilibrium.)

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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

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