Question

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

Answer 1

Explanation:

It is given that,

When the front wheels are over the scale, the weight recorded by the scale is 5800 N, F₁ = 5800 N

When the rear wheels are over the scale, the scale reads 6500 N, F₂ = 6500

The distance between the front and rear wheels is measured to be 3.20 m, x₂ = 3.2 m

We need to find the location of center of mass behind the front wheels. Let the center of is located at a distance of x₁. Thus balancing the torques we get :

$5800\times x_2=6500\times (3.2-x_2)$

On solving the above equation we get, x₂ = 1.69 m

So, the center of mass is located at a distance of 1.69 meters behind the front wheels.