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Physics 112  HW #12 Solutions
Spring 2006
1174
Any group of contiguous blocks starting with the top block must have its combined CM
supported by the next block (or table) just below. Imagine
building from the top down
.
(a) Start with 2 blocks. The CM
1
(
) of the top block (#1) can
be out as far as the edge of block #2, so block #1 can overhang
by L/2. The CM
12
of the two blocks combined can be as far out
as the edge of the table, an additional L/4 to the left of CM
1
. So
block #2 can overhang the table by this additional L/4 and block
#1 by a total of L/2 + L/4 = 3L/4
.
(b)
Add block #3. Place blocks #1 and 2 on top of block #3 so
that CM
12
is at the right edge of block #3. (Block #3 takes the
place of the table from part (a).) How far to the left of CM
12
is
the CM
123
of the 3 blocks combined? This is like starting with a
12
and adding a point mass
m (block #3) a distance L/2 to the left of CM
12
. CM
123
is
2m(0) + m(L/2)
2m + m
= L/6 to the left of CM
12
, and this point can be
as far out as the edge of the table. So block #1 overhangs the
table by L/2 + L/4 + L/6 = 11L/12
.
Now add block #4. Place blocks #13 on top of #4 so that CM
123
is at the right edge of block #4. (Block #4 takes the place of the
table for blocks #13.) How far to the left of CM
123
is the
CM
1234
of the 4 blocks combined? This is like starting with a
point mass 3m (blocks #1, 2, 3) at CM
123
and adding a point
mass m (block #4) a distance L/2 to the left of CM
123
. CM
1234
is
3m(0) + m(L/2)
3m + m
= L/8 to the left of CM
123
, and this point can
as far out as the edge of the table. So block #1 overhangs the
table by L/2 + L/4 + L/6 + L/8 = 25L/24
.
(c) As shown in part (b), 4
blocks are needed to give an overhang of 25L/24 which is > L.
[CHALLENGE: How many blocks are needed in order for 2 blocks to completely overhang the
edge of the table?]
L/2
1
2
+L/4
CM
1
CM
12
1
2
3
+L/6
CM
123
CM
12
1
2
3
4
+L/8
CM
123
CM
123
4
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1039
[Block on String]
(a) Yes, angular momentum of the block is conserved, because there are no forces that can exert a
torque on the block.
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 Fall '07
 LECLAIR,A
 Physics, mechanics

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