Question

The CM of an empty 1150-kg car is 2.35 m behind the front of the car. How far from the front of the car will the CM be when two people sit in the front seat 2.75 m from the front of the car, and three people sit in the back seat 3.85 m from the front? Assume that each person has a mass of 80.0 kg.

Answer 1

Let the new centre of mass be at a distance from the front of the car.

For it to be the centre of mass, the first moments of the masses at this point should be totally equal to zero, i.e, their sum should be zero.

The first moment of the masses about this point will the product of the masses and the distance of their location to the centre of mass.

Putting in our values, we get

Hence, the new centre of mass is behind the front of the car.