To determine the location of the center of mass of a car,the car is driven over a scale on a horizontal floor.When the front wheels are over the scale,the weight recorded by the scale is 5800 N,and when the rear wheels are over the scale,the scale reads 6500 N.The distance between the front and rear wheels is measured to be 3.20 m.How far behind the front wheels is the center of mass located?
A)0.845 m
B)1.50 m
C)1.59 m
D)1.69 m
E)1.72 m

Question

Quizplus · Accepted Answer

The center of mass can be found using the principle of moments. The total weight of the car is the sum of the weights recorded by the scale when the front and rear wheels are on it, which is 5800 N + 6500 N = 12300 N. Let $x$ be the distance from the front wheels to the center of mass. The moment about the front wheels when the rear wheels are on the scale is equal to the total weight times the distance of the center of mass from the front wheels, which must equal the moment produced when the rear wheels are on the scale (6500 N times the distance between the wheels, 3.20 m). So, we have $12300N \cdot x = 6500N \cdot 3.20m$. Solving for $x$ gives $x = \frac{6500N \cdot 3.20m}{12300N} = 1.69m$.

To Determine the Location of the Center of Mass of a Car,the