A truck is driving over a scale at a weigh station. When the front wheels drive over the scale, the scale reads 5800 N. When the rear wheels drive over the scale, it reads 6500 N. The distance between the front and rear wheels is 3.20 m. Determine the distance between the front wheels and the truck's center of gravity.

A. 1.69 m
B. 1.50 m
C. 1.59 m
D. 1.72 m

To find the distance between the front wheels and the truck's center of gravity, we use the principle of moments (torque) about one point on the truck.

Let's denote the total weight of the truck by W, and the distance from the front wheels to the truck's center of gravity by x. The distance between the front and rear wheels is given as 3.20 m.

We have the following reads from the scale:

When the front wheels are on the scale: 5800 N

When the rear wheels are on the scale: 6500 N

Assuming the truck is stationary and in equilibrium, the sum of the moments about the front wheels gives:

Moment about front wheels: (6500 N) x (3.20 m)

Moment = Total Weight (W) x x + (5800 N) x (3.20 m)

Combining the two moments about the front wheels, we get:

W x x = (6500 N) x (3.20 m) - (5800 N) x (3.20 m)

First, we need to find the total weight of the truck:

W = 6500 N + 5800 N = 12300 N

Now, substituting W and the distances:

12300 N x x = 6500 N x 3.20 m

12300 N x x = 20800 Nm

Simplifying for x:

x = 20800 Nm / 12300 N

x ≈ 1.69 m

The correct answer is 1.69 m.