An automobile with a mass of 1310 kg has 3.10 m between the front and rear axles. Its center of gravity is located 1.78 m behind the front axle. The automobile is on level ground.
(a) Determine the magnitude of the force from the ground on each front wheel (assuming equal forces on the front wheels).
N
(b) Determine the magnitude of the force from the ground on each rear wheel (assuming equal forces on the rear wheels).
N
It is easy. Draw the force diagram.
1) the sum of the vertical forces is zero. You have two forces upwards on the front wheels (both the same), two forces up on the rear wheels (both the same), and the weight downward.
2*Ff+2*fb-W=0
2) Sum moments about any point. I will choose the front wheels..
W(1.78)-2fb*3.10=0 Solve for fb.
Now, go back to the first equation and solve for ff. Remember w is mg.
To determine the magnitude of the force from the ground on each wheel, we can start by calculating the weight (mg) and the weight distribution of the automobile.
(a) Magnitude of the force from the ground on each front wheel:
To find the weight of the automobile, we can use the formula W = mg, where W represents weight, m represents mass, and g represents the acceleration due to gravity (approximately 9.8 m/s²).
W = (mass of the automobile) × (acceleration due to gravity)
W = 1310 kg × 9.8 m/s²
W ≈ 12818 N
Next, we need to determine the weight distribution between the front and rear axles. Since the center of gravity is located 1.78 m behind the front axle, the distance between the center of gravity and the front axle is (3.10 m - 1.78 m) = 1.32 m.
To find the weight distribution on the front axle, we need to divide the weight by the distance between the center of gravity and the front axle, and then multiply it by the distance between the front and rear axles.
Front weight distribution = (Weight / distance between center of gravity and front axle) × distance between front and rear axles
Front weight distribution = (12818 N / 1.32 m) × 3.10 m
Front weight distribution ≈ 94489 N
Since there are two front wheels, we can divide the weight distribution by 2 to find the force from the ground on each front wheel.
Magnitude of the force from the ground on each front wheel = Front weight distribution / 2
Magnitude of the force from the ground on each front wheel ≈ 47244.5 N
Therefore, the magnitude of the force from the ground on each front wheel is approximately 47244.5 N.
(b) Magnitude of the force from the ground on each rear wheel:
To find the weight distribution on the rear axle, we can subtract the front weight distribution from the total weight.
Rear weight distribution = Total weight - Front weight distribution
Rear weight distribution ≈ 12818 N - 94489 N
Rear weight distribution ≈ -81671 N
Since the weight distribution on the rear axle is negative, it means that there is an upward force acting on the rear wheels.
Magnitude of the force from the ground on each rear wheel = (-Rear weight distribution / 2)
Magnitude of the force from the ground on each rear wheel ≈ 40835.5 N (assuming equal forces on the rear wheels).
Therefore, the magnitude of the force from the ground on each rear wheel is approximately 40835.5 N.