Question

The center of mass of an empty automobile is 2.5m (pretend the empty automobile's mass is 0kg). 2 100kg people are 2.8m from the front bumper. One 50kg person is 4m from the front bumper. How far behind the front bumper is the center of mass?

How would I work through this problem?

Answer 1

Given

center of mass of the car is at 2.5 m

let 2,m1 = 100 kg people are at x1 = 2.8 m from front bumper and

m2 = 50 kg person is at x2 = 4 m from front bumper

let the referance position is front bumper then the center of mass of the system is

   Xcm = m1*x1+m2*x2/(m1+m2)

   Xcm = (200*2.8+50*4)/(200+50)

   Xcm = 3.04 m

the center of mass is (3.04-2.50)m = 0.54 m behind the front bumper