When only the front wheels of an automobile are on a platform scale, the scale balances at 7.9 kN; when only the rear wheels are on the scale, it balances at 6.2 kN. What is the weight of the automobile?

How far is its center of mass behind the front axle? The distance between the axles is 3.0 m.

I got the first part 14.1 kN

I just need help with the distance of center of mass behind the front axle.

Lick a butt, that will probably help.

for the center of mass asume that xm for rear wheel is zero so you just do

center of mass = (x1m1+x2m2)/(m1+m2)
let ur x2m2 be zero so plug ur number n finally subtract ur value from the length if the axles.

damn, 2chainz

To find the weight of the automobile, we can use the principle of weight distribution.

When only the front wheels are on the platform scale, the scale balances at 7.9 kN. This means that the total weight of the front wheels is 7.9 kN.

Similarly, when only the rear wheels are on the scale, the scale balances at 6.2 kN. This means that the total weight of the rear wheels is 6.2 kN.

Since the weight of the automobile is distributed between the front and rear wheels, the total weight of the automobile is the sum of the weights on the front and rear wheels.

Total weight of the automobile = Weight on front wheels + Weight on rear wheels
Total weight of the automobile = 7.9 kN + 6.2 kN
Total weight of the automobile = 14.1 kN

Therefore, the weight of the automobile is 14.1 kN.

To find the distance of the center of mass behind the front axle, we can use the concept of weight distribution.

Given that the distance between the axles is 3.0 m, we need to find the distance of the center of mass (COM) from the front axle.

Let's assume the distance of the COM from the front axle is x.

The weight distribution of the automobile can be expressed as follows:
Weight on front wheels / Weight on rear wheels = Distance of COM from rear axle / Distance of COM from front axle

We know the weight on the front wheels is 7.9 kN and the weight on the rear wheels is 6.2 kN.

Therefore, we can write the equation as:
7.9 kN / 6.2 kN = (3.0 m - x) / x

Simplifying the equation:
7.9 / 6.2 = (3.0 - x) / x
1.27 = (3.0 - x) / x

Cross-multiplying:
1.27x = 3.0 - x
2.27x = 3.0
x = 3.0 / 2.27

Hence, the distance of the center of mass behind the front axle is approximately 1.32 meters (or 132 cm).