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First Home work Solution Set

First Home work Solution Set - CHAPTER 1 1.1 A has units of...

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C HAPTER 1 1.1 A  has units of L 2 , while h has L as its dimension.  L 2  x L = L 3 , the proper units of volume.  1.3 Substituting  in dimensions, we have 2 2 L T   T T L T = = = Thus, the  dimensions are consistent . 1.5 ( 29 ( 29 2 2 2 kg kg m = s m G , so cross-multiplying  gives the units of  G  as  3 2 m kg s . 1.7  (a) 78.9 0.2 ±  has  3 significant figures . (b) 9 3.788 10 ×   has  4 significant figures . (c) 6 2.46 10 - ×  has  3 significant figures . (d) 3 0.0032 3.2 10 - = ×  has  2 significant figures . 1.10 8 2.997 924 574 10   m s c = × (a) Rounded  to 3 significant figures:  c  =  8   3.00 10 m s × (b) Rounded  to 5 significant figures:  c  =  8   2.997 9 10 m s × (c) Rounded  to 7 significant figures:  c  =  8   2.997 926 10 m s × 1.21 8 3 m 3600 s 1 km 1 mi 3.00 10   s 1 h 10  m 1.609 km c       = × =             8 6.71 10   mi h × 1
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C H A P T E R   1 1.22 ( 29 ( 29 ( 29 2 3 3 2.832 10  m Volume of house 50.0 ft 26 ft 8.0 ft 1 ft - × = 2 3 2.9 10  m ×  =  ( 29 3 2 3 100 cm 2.9 10  m 1 m ×  =  8 3 2.9 10  cm × 1.23 ( 29 3 2 43 560 ft 1 m Volume 25.0 acre ft 1 acre 3.281 ft = =   4 3 3.08 10  m × 1.25 3 Volume of cube 1 quart L = =  (Where  L  = length of one side of the cube.) Thus,  ( 29 3 3 3 1 gallon 3.786 liter 1000 cm 1 quart  946 cm 4 quarts 1 gallon 1 liter L     = =     , and L = 9.82 cm . 1.32 A blade of grass is  ~1 4  inch wide, so we might expect each blade of grass to require at  least  2 4 2 1 16 in 4.3 10  ft - = × . Since  2 1 acre 43 560 ft = , the number  of blades of grass to be  expected  on a quarter-acre plot of land  is about ( 29 ( 29 2 -4 2 0.25 acre 43 560 ft acre total area area per blade 4.3 10  ft blade n = = × 7 2.5 10  blades,  or   = × 7  ~10  blades . 2
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C H A P T E R   1 1.33 Consider a room that is 12 ft square with an 8.0 ft high ceiling. The volume  of this room  is ( 29 ( 29 ( 29 3 3 1 m 12 ft 12 ft 8.0 ft 33 m 3.281 ft room V = = . A ping pong ball has a radius  of about 2.0 cm, so its volume  is ( 29 3 3 2 5 3 4 4 2.0 10  m 3.4 10  m 3 3 ball V r π π - - = = × = × . The number  of balls that would  easily fit into the room is therefore 3 5 -5 3 33 m 9.7 10 3.4 10  m room ball V n V = = = × ×  or  6 ~10 1.34 Assume  an average of 1 can per person each week and  a population  of 250 million. ( 29 ( 29 number cans person number cans year population weeks year week = = ( 29 ( 29 × 8 can person 2.5 10  people 52  weeks yr week × 10 1.3 10  cans yr  , or    10 ~10  cans yr ( 29 ( 29 number of tons weight can number cans year =   ×     10 oz 1 lb 1 ton can = 0.5  1.3 10   can 16 oz 2000 lb yr = × 5 2 10   ton yr ,  or     5
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