Question

A square uniform raft, 20 m by 20 m , of mass 6400 kg , is used as a ferryboat.

a)If three cars, each of mass 1150 kg , occupy the NE, SE, and SW corners, determine the coordinates of the CM of the loaded ferryboat relative to the center of the raft. Take the origin to be at the CM of the raft.

Answer 1

It should be slightly SE of the center of the raft.

If we assume the masses are point masses so that the CG of each car sits on the edge of the raft.

if our assumed baseline is the east edge of the raft we get

x = 6400[10] + 1150[0] + 1150[0] + 1150[20] / (6400 + 3(1150))
x = 8.83 m

we would get the exact same formula and distance if the south side of our raft were the baseline.

10- 8.83 = 1.17

The CG is 1.17 m east and 1.17 m south of the center of the raft.

d = √(2(1.17)²)
d = 1.655m SE of the raft center.