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UNITS, PHYSICAL QUANTITIES AND VECTORS

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1.1.

IDENTIFY: Convert units from mi to km and from km to ft. SET UP: 1 in. = 2.54 cm , 1 km = 1000 m , 12 in. = 1 ft , 1 mi = 5280 ft . ⎛ 5280 ft ⎞⎛ 12 in. ⎞⎛ 2.54 cm ⎞⎛ 1 m ⎞⎛ 1 km ⎞ EXECUTE: (a) 1.00 mi = (1.00 mi) ⎜ ⎟⎜ ⎟⎜ ⎟⎜ 2 ⎟⎜ 3 ⎟ = 1.61 km ⎝ 1 mi ⎠⎝ 1 ft ⎠⎝ 1 in. ⎠⎝ 10 cm ⎠⎝ 10 m ⎠

1.2.

⎛ 103 m ⎞⎛ 102 cm ⎞ ⎛ 1 in. ⎞⎛ 1 ft ⎞ 3 (b) 1.00 km = (1.00 km) ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ = 3.28 × 10 ft 1 km ⎠⎝ 1 m ⎠ ⎝ 2.54 cm ⎠⎝ 12 in. ⎠ ⎝ EVALUATE: A mile is a greater distance than a kilometer. There are 5280 ft in a mile but only 3280 ft in a km. IDENTIFY: Convert volume units from L to in.3 . SET UP: 1 L = 1000 cm3 . 1 in. = 2.54 cm
⎛ 1000 cm3 ⎞ ⎛ 1 in. ⎞ 3 0.473 L × ⎜ ⎟×⎜ ⎟ = 28.9 in. . ⎝ 1 L ⎠ ⎝ 2.54 cm ⎠ EVALUATE: 1 in.3 is greater than 1 cm3 , so the volume in in.3 is a smaller number than the volume in cm3 , which is 473 cm3 . IDENTIFY: We know the speed of light in m/s. t = d / v . Convert 1.00 ft to m and t from s to ns. SET UP: The speed of light is v = 3.00 × 108 m/s . 1 ft = 0.3048 m . 1 s = 109 ns . 0.3048 m EXECUTE: t = = 1.02 × 10−9 s = 1.02 ns 3.00 × 108 m/s EVALUATE: In 1.00 s light travels 3.00 × 108 m = 3.00 × 105 km = 1.86 × 105 mi . IDENTIFY: Convert the units from g to kg and from cm3 to m3 . SET UP: 1 kg = 1000 g . 1 m = 1000 cm .
EXECUTE: EXECUTE:
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1.3.

1.4.

g ⎛ 1 kg ⎞ ⎛ 100 cm ⎞ 4 kg × 11.3 ⎟×⎜ ⎟ = 1.13 × 10 3 ⎜ cm ⎝ 1000 g ⎠ ⎝ 1 m ⎠ m3

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1.5.

EVALUATE: The ratio that converts cm to m is cubed, because we need to convert cm3 to m3 . IDENTIFY: Convert volume units from in.3 to L. SET UP: 1 L = 1000 cm3 . 1 in. = 2.54 cm . EXECUTE:

( 327 in. ) × ( 2.54 cm in.) × (1 L 1000 cm ) = 5.36 L
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1.6.

EVALUATE: The volume is 5360 cm3 . 1 cm3 is less than 1 in.3 , so the volume in cm3 is a larger number than the volume in in.3 . IDENTIFY: Convert ft 2 to m 2 and then to hectares. SET UP: 1.00 hectare = 1.00 × 104 m 2 . 1 ft = 0.3048 m . EXECUTE:

⎛ 43,600 ft 2 ⎞ ⎛ 0.3048 m ⎞