Figure 4: Two Blocks Stacked
Now let's add a second block between the table and the first block. We
want to arrange things so that both blocks are exactly balanced.
To do this, we'll position
the original block atop the second block exactly as it was originally
positioned on the table--halfway off. And we'll position the second block one
quarter of the way off of the table.
Let's make sure that this really balances. The first (top) block is clearly
balanced, since it is positioned on the second block exactly as it was
positioned before--halfway off. But what about the second (bottom) block?
The center of gravity of the second block will be the average of the centers of
gravity of the two blocks considered separately. Using our coordinate system,
this average is:
| cg2 := ((cg1 + 1/4) - 1/4) / 2; |
Since cg2 is 0, we know that the bottom block is also balanced perfectly.
Be sure that you understand why this computation for the center of gravity of
the second block makes sense.
Click here for the answer
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah