01_InstructorSolutions

01_InstructorSolutions - UNITS, PHYSICAL QUANTITIES AND...

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1-1 U NITS , P HYSICAL Q UANTITIES AND V ECTORS 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 . EXECUTE: (a) 23 5280 ft 12 in. 2.54 cm 1 m 1 km 1.00 mi (1.00 mi) 1.61 km 1 mi 1 ft 1 in. 10 cm 10 m ⎛⎞ == ⎜⎟ ⎝⎠ (b) 32 3 1 in. 1 ft 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. 1.2. IDENTIFY: Convert volume units from L to 3 in. . SET UP: 3 1 L 1000 cm = . 1 in. 2.54 cm = EXECUTE: 3 3 3 1000 cm 1 in. 0.473 L 28.9 in. . 1 L 2.54 cm ××= EVALUATE: 3 1 in. is greater than 3 1 cm , so the volume in 3 in. is a smaller number than the volume in 3 cm , which is 3 473 cm . 1.3. IDENTIFY: We know the speed of light in m/s. / tdv = . Convert 1.00 ft to m and t from s to ns. SET UP: The speed of light is 8 3.00 10 m/s v . 1 ft 0.3048 m = . 9 1 s 10 ns = . EXECUTE: 9 8 0.3048 m 1.02 10 s 1.02 ns t × = × EVALUATE: In 1.00 s light travels 85 5 3.00 10 m 3.00 10 km 1.86 10 mi ×= × = × . 1.4. IDENTIFY: Convert the units from g to kg and from 3 cm to 3 m . SET UP: 1 kg 1000 g = . 1 m 1000 cm = . EXECUTE: 3 4 33 g 1 kg 100 cm kg 11.3 1.13 10 cm 1000 g 1 m m ×× = × EVALUATE: The ratio that converts cm to m is cubed, because we need to convert 3 cm to 3 m. 1.5. IDENTIFY: Convert volume units from 3 in. to L. SET UP: 3 1 L 1000 cm = . 1 in. 2.54 cm = . EXECUTE: ( ) () ( ) 3 327 in. 2.54 cm in. 1 L 1000 cm 5.36 L = EVALUATE: The volume is 3 5360 cm . 3 1 cm is less than 3 1 in. , so the volume in 3 cm is a larger number than the volume in 3 in. . 1.6. IDENTIFY: Convert 2 ft to 2 m and then to hectares. SET UP: 42 1.00 hectare 1.00 10 m . 1 ft 0.3048 m = . EXECUTE: The area is 2 2 43,600 ft 0.3048 m 1.00 hectare (12.0 acres) 4.86 hectares 1 acre 1.00 ft 1.00 10 m = × . EVALUATE: Since 1 ft 0.3048 m = , 22 2 1 ft (0.3048) m = . 1.7. IDENTIFY: Convert seconds to years. SET UP: 9 1 billion seconds 1 10 s . 1 day 24 h = . 1 h 3600 s = . EXECUTE: 9 1 h 1 day 1 y 1.00 billion seconds 1.00 10 s 31.7 y 3600 s 24 h 365 days = . 1
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1-2 Chapter 1 EVALUATE: The conversion 7 1 y 3.156 10 s assumes 1 y 365.24 d = , which is the average for one extra day every four years, in leap years. The problem says instead to assume a 365-day year. 1.8. IDENTIFY: Apply the given conversion factors. SET UP: 1 furlong 0.1250 mi and 1 fortnight 14 days. == 1 day 24 h. = EXECUTE: () 0.125 mi 1 fortnight 1 day 180,000 furlongs fortnight 67 mi/h 1 furlong 14 days 24 h ⎛⎞ = ⎜⎟ ⎝⎠ EVALUATE: A furlong is less than a mile and a fortnight is many hours, so the speed limit in mph is a much smaller number. 1.9. IDENTIFY: Convert miles/gallon to km/L. SET UP: 1 mi 1.609 km = . 1 gallon 3.788 L. = EXECUTE: (a) 1.609 km 1 gallon 55.0 miles/gallon (55.0 miles/gallon) 23.4 km/L 1 mi 3.788 L . (b) The volume of gas required is 1500 km 64.1 L 23.4 km/L = . 64.1 L 1.4 tanks 45 L/tank = . EVALUATE: 1 mi/gal 0.425 km/L = . A km is very roughly half a mile and there are roughly 4 liters in a gallon, so 2 4 1 mi/gal km/L , which is roughly our result.
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01_InstructorSolutions - UNITS, PHYSICAL QUANTITIES AND...

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