Question

A 10 cm tall 3 kg hat sits on a 15 cm tall 10 kg cat which sits on a 50 cm tall 25 kg dog. If we can approximate each body’s center of mass to be at each’s geometric center (that is, one-half the height above the previous body), where is the center of mass vertically for this system as measured from the floor?

Answer 1

While calculating center of mass of a system of extended objects, we can replace each exended object with a point mass at their respective center of mass.

Mass of dog = m1=25 kg. Vertical position of center of mass of dog=y1=50/2 = 25 cm.

Mass of cat = m2=10 kg. Vertical position of center of mass of cat=y2=50+15/2=57.5 cm.

Mass of hat = m3=3 kg. Vertical position of center of mass of hat=y3=50+15+10/2=70 cm.

So, vertical position of center of mass of the entire system = (m1y1+m2y2+m3y3)/(m1+m2+m3)

= (25*25+10*57.5+3*70)/(25+10+3)=37.105 cm.