A car drives over a weigh scale. When the two front wheels are on the scale, the weight measured is 6000 N. When the rear two wheels are on the scale, the weight measured is 7500 N. How far from the front wheels is the car's centre of mass if the wheels are 3.5 m apart?
A)0.7 m
B)1.56 m
C)1.94 m
D)2.8 m

Question

Quizplus · Accepted Answer

The car's total weight is the sum of the weights measured by the scale when the front and rear wheels are on it, which is 6000 N + 7500 N = 13500 N. To find the distance from the front wheels to the car's center of mass, we can use the principle of moments. Let $x$ be the distance from the front wheels to the center of mass. The moment about the rear wheels when the front wheels are on the scale is $6000 \times 3.5$. This should equal the total weight times the distance from the center of mass to the rear wheels ($13500 \times (3.5 - x)$). Solving for $x$ gives $x = 1.94$ m.

A Car Drives Over a Weigh Scale