A 1550 kg automobile has a wheel base (the distance between the axles) of 3.00 m. The center of mass of the automobile is on the center line at a point 1.10 m behind the front axle. Find the force exerted by the ground on each wheel.

force on each rear wheel
___ kN (upward)
force at each front wheel
___ kN (upward)

To find the forces exerted by the ground on each wheel of the automobile, we need to consider the weight of the car and its distribution.

Let's start by calculating the weight of the car. The weight (W) is given by the mass (m) multiplied by the acceleration due to gravity (g).

W = m * g

Given that the mass of the car is 1550 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate:

W = 1550 kg * 9.8 m/s^2
W ≈ 15,190 N

The weight of the car is approximately 15,190 Newtons.

Now, let's consider the distribution of weight. The center of mass of the car is located 1.10 m behind the front axle. Since the wheelbase is given as 3.00 m, we can assume that the front axle is located at a distance of 1.50 m from the center line.

To find the weight distribution between the front and rear wheels, we can consider the lever principle. The weight is distributed proportionally to the distances from the center of mass to each axle.

Let's denote the force at each rear wheel as F_r and the force at each front wheel as F_f.

Using the lever principle, we can set up the following equation:

F_r * 1.50 m = F_f * (1.50 m + 1.10 m)

Simplifying the equation:

F_f = 1.50 m * F_r / (1.50 m + 1.10 m)
F_f = 1.50 m * F_r / (2.60 m)

Now, we know that the sum of the forces at the front and rear wheels must equal the weight of the car:

F_r + F_f = 15,190 N

Substituting the value of F_f from the previous equation:

F_r + (1.50 m * F_r / (2.60 m)) = 15,190 N

Simplifying and solving for F_r:

(2.60 m * F_r) + (1.50 m * F_r) = 15,190 N * (2.60 m)
4.10 m * F_r = 39,494 N
F_r = 39,494 N / 4.10 m
F_r ≈ 9,644.88 N

Therefore, the force exerted by the ground on each rear wheel is approximately 9,644.88 N (upward).

Finally, we can substitute this value into the equation for F_f to find the force exerted by the ground on each front wheel:

F_f = 1.50 m * 9,644.88 N / (2.60 m)
F_f ≈ 5,542.88 N

Therefore, the force exerted by the ground on each front wheel is approximately 5,542.88 N (upward).