To determine the location of the center of mass (or center of gravity) 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) 1.72 m
B) 1.50 m
C) 0.845 m
D) 1.69 m
E) 1.59 m

Question

To determine the location of the center of mass (or center of gravity) 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)  1.72 m
B)  1.50 m
C)  0.845 m
D)  1.69 m
E)  1.59 m

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, which is 5800 N + 6500 N = 12300 N. The moment about the point where the front wheels touch the scale (taking this point as the pivot) is equal to the moment about the point where the rear wheels touch the scale. Using the formula for the center of mass (distance to the center of mass * total weight = weight on one side * distance from that side), we get $x \times 12300 = 6500 \times 3.20$. Solving for $x$ gives $x = \frac{6500 \times 3.20}{12300} = 1.69$ meters.

To Determine the Location of the Center of Mass (Or