[ T ] Suppose that N equal uniform rectangular blocks are stacked one on top of the other, allowing for some overhang. Archimedes’ law of the lever implies that the stack of N blocks is stable as long as the center of mass of the top ( N − 1 ) blocks lies at the edge of the bottom block. Let x denote the position of the edge of the bottom block, and think of its position as relative to the center of the next-to—bottom block. This implies that ( N − 1 ) x = ( 1 2 − x ) or x = 1 / ( 2 N ) . Use this expression to compute the maximum overhang (the position of the edge of the top block over the edge of the bottom block.) See the following figure.
[ T ] Suppose that N equal uniform rectangular blocks are stacked one on top of the other, allowing for some overhang. Archimedes’ law of the lever implies that the stack of N blocks is stable as long as the center of mass of the top ( N − 1 ) blocks lies at the edge of the bottom block. Let x denote the position of the edge of the bottom block, and think of its position as relative to the center of the next-to—bottom block. This implies that ( N − 1 ) x = ( 1 2 − x ) or x = 1 / ( 2 N ) . Use this expression to compute the maximum overhang (the position of the edge of the top block over the edge of the bottom block.) See the following figure.
[T] Suppose that N equal uniform rectangular blocks are stacked one on top of the other, allowing for some overhang. Archimedes’ law of the lever implies that the stack of N blocks is stable as long as the center of mass of the top
(
N
−
1
)
blocks lies at the edge of the bottom block. Let x denote the position of the edge of the bottom block, and think of its position as relative to the center of the next-to—bottom block. This implies that
(
N
−
1
)
x
=
(
1
2
−
x
)
or
x
=
1
/
(
2
N
)
. Use this expression
to compute the maximum overhang (the position of the edge of the top block over the edge of the bottom block.) See the following figure.
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