Determining Maximum Distance Using Center of Mass

[UrbanXrisis]

question is http://home.earthlink.net/~urban-xrisis/clip003.jpg

I'm guessing that the center of mass has to be in the edge. I'm not sure how to set it up so that I can find the most distance. any ideas?

 

[whozum]

the CM of the system is definitely on the edge. The blocks on the table are of equal mass and length, if the CM of the system is exactly on the edge, what do you know about how much mass is on the table relative to how much total mass there is?

 

[UrbanXrisis]

they should be equal?

 

[whozum]

The mass hanging over the edge = The mass on the table, the center of mass of the whole system is on the edge means the mass to the right balances the mass to the left. If both blocks weigh the same, the only thing that isn't symmetric is the position of L. if half the mass hangs over the edge, then how much of the total length hangs over the edge? (they are the same mass, length, and density)

 

[UrbanXrisis]

total length is 2L so half is hanging off, that means the length of L is hanging off?

 

[whozum]

No, total length means the length from the leftest point on the lower block to the rightest point on the right block. If half the mass is hanging off and half is on, then how much of the length is hanging off? They are uniform blocks.

Try simplifying the system to just one block and figure it out that way.

 

[UrbanXrisis]

3L/4?
is that it?