Question

A square uniform raft, 18.1m by 18.1m, of mass 6229kg, is used as a ferryboat. If three cars, each of mass 1176kg, occupy the NE, SE, and SW corners, determine the CM of the loaded ferryboat. Use east as the positive x-axis, north as the positive y-axis and the centre of the raft as the origin.

Y coordinate?

X Coordinate

Answer 1

Break the problem down. Start with the NE and SW cars. If they were the only cars on the raft and the raft was weightless then the CM is right in the center of the raft, isn't it.

Now add the third car. It is the balanced between the line joining it (the third car) and the centre of gravity of the first two cars (which incidently is where the raft's weight is.

So what's at the origin? The mass of the raft, the Centre of mass of the NE and SW cars.

The total mass at the origin is 2*1176 + 6229 = 8581 kg

Now we need to balance what's at the origin and at the SE corner. The distance to the origin from the SE corner is

x^2 + x^2 = 18.1^2
2x^2 = 327.61
x=12.79
Let y be the distance from the origin to the final CM.

8581*y = 1176*(12.8 - y)
8588y = 14002 - 1158y
y = 2.04 meters.

The distance to the SE car is 12.8 -2.04 = 10.75 m along the line joining the car in the SW corner to the origin