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HW__12_S06_Solutions_corrected

# HW__12_S06_Solutions_corrected - Physics 112 HW#12...

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- 1 - Physics 112 - HW #12 Solutions Spring 2006 11-74 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 point mass 2m (blocks #1 & 2) at CM 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 #1-3 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 #1-3.) 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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- 2 - 10-39 [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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