Finding the Center of Mass for a Loaded Ferryboat on a Square Raft

[fiziks09]

Homework Statement

A square uniform raft, 18m by 18m of mass 6200kg is used as a ferry boat. if three cars each of mass 1350 kg occupy the NE, SE, and SW corners, determine the Centre of mass of the loaded ferryboat relative to the centre of the raft

Homework Equations

Center of mass (CM) = $$\sum mixi/M$$
where M = m1 + m2...mn

The Attempt at a Solution

The centre of mass i think, is going to be two-dimensional i.e x-axis and y-axis
So i drew my co-ordinate system and came up with the following

CM(x-axis) = 1350(18) + 1350(18) +1350(-18)/3(1350)+6200 = 2.3i

The -18 is for the SW car where x is negative.

CM(y-axis) = 1350(18) + 1350(-18) +1350(-18)/3(1350) + 6200= -2.3j

i have two -18's coz for the SW and NW where y is negative..

I used 18 as the distance for all three cars since the raft is 18m by 18m. But my solution is wrong. Please any help will be very appreciated. Thanks

 

[Doc Al]

I used 18 as the distance for all three cars since the raft is 18m by 18m.

Put the origin of your coordinate system in the center of the raft.

 

[fiziks09]

Okay... i already had that in mind while drawing up that solution. Am i missing something??

 

[Doc Al]

Okay... i already had that in mind while drawing up that solution. Am i missing something??

There are 4 masses involved--the raft and the three cars. Measured from the center of the raft, what are their coordinates?

 

[fiziks09]

There are 4 masses involved--the raft and the three cars. Measured from the center of the raft, what are their coordinates?

Well i think that

the raft has (0,0)
the NE car has (18,18)
the SE car has (18,-18)
the SW car has (-18,-18)

 

[Doc Al]

Well i think that

the raft has (0,0)

Good.

the NE car has (18,18)
the SE car has (18,-18)
the SW car has (-18,-18)

No. 18m is the length of the sides of the raft. What's the distance from the center to the sides?

 

[fiziks09]

ohh.. that would be half the distance right?... which is 9m

 

[Doc Al]

ohh.. that would be half the distance right?... which is 9m

Yes, now you're cooking. So redo your calculations.

 

[fiziks09]

yeah its perfectly okay now.. Thanks a bunch for figuring it out.