a) Force on each front wheel: F1 = 2777.677 N.
b) Force on each rear wheel: F2 = 3893.123 N.
let's determine the magnitude of the force from the ground on each wheel of the automobile.
Given:
Mass of the automobile (m) = 1360 kg
Distance between the front and rear axles (L) = 3.05 m
Distance of the center of gravity from the front axle (d) = 1.78 m
Solution:
a) Force on each front wheel:
To determine the force on each front wheel, we can use the principle of moments. The sum of the moments about any point must be zero. Let's take the rear axle as the point of reference.
ΣM_rear_axle = 0
The forces acting on the automobile are:
Weight of the automobile (W) = mg = 1360 kg * 9.81 m/s² = 13248.6 N (acting downwards at the center of gravity)
Force on each front wheel (F1) (acting upwards)
Force on each rear wheel (F2) (acting upwards)
The moment due to the weight of the automobile is:
M_weight = Wd = 13248.6 N * 1.78 m = 23461.07 N·m
The moment due to the force on each front wheel is:
M_F1 = 2F1L/2 = F1L
Since the forces on the front wheels are assumed to be equal, we can divide the total moment by 2.
The total moment about the rear axle must be zero, so:
M_weight - M_F1 + M_F2 = 0
Substituting the expressions for the moments:
23461.07 N·m - F1L + F2L = 0
Solving for F1:
F1 = (23461.07 N·m) / L - F2/2
b) Force on each rear wheel:
The force on each rear wheel can be determined using the equation for equilibrium of forces in the vertical direction.
ΣF_y = 0
The forces acting on the automobile in the vertical direction are:
Weight of the automobile (W) = 13248.6 N (acting downwards)
Force on each front wheel (F1) (acting upwards)
Force on each rear wheel (F2) (acting upwards)
Substituting the forces:
W - 2F1 - 2F2 = 0
Substituting the expression for F1 from part (a):
W - 2((23461.07 N·m) / L - F2/2) - 2F2 = 0
Simplifying and solving for F2:
F2 = (23461.07 N·m) / L + 9324.35 N