Question

You are on a 20 meter long boat, it weights 1000 kg, and you weigh 100 kg. Consider the system of you and the boat together. (Assume the boat slides on the water without friction, the boat’s center of mass is at its center, and your center of mass is the same height as the boat’s center of mass).

a)   If you are at one end of the boat, how far from the center of the boat is the system’s center of mass?

b)   How far does the system’s center of mass move (with respect to the water) if you walk from one end of the boat to the other?

c)   Now consider the system of you, the boat, and the anchor of the boat. The anchor is 100 kg (ignore buoyancy of the anchor and weight of the rope from which it hangs) and is hanging in the water 10 meters directly below the center of the boat. Now you are at one end of the boat, how far is the boat’s center from the center of mass of this system?

Answer 1

1)
The location of the center of mass is, as seen from the right side of the boat:
CM = (1000*10 + 100*20)/(1100) = 10.90 m
From the center of the boat the center of mass is 10.9 - 10 = 0.9 m

2) the location of the center of mass will not change, as long as there is no force on the system from the outside.

3)
The location of the center of mass is, as seen from righ side of the boat :
Cm = (1000*10+100*20+ 10*100)/(1000+100+100) = 10.83 m
From the center of the boat the center of mass is 10.83 - 10 = 0.83 m