01_InstSolManual_PDF-1

01_InstSolManual_PDF-1 - MODELS MEASUREMENTS AND VECTORS 1...

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1-1 M ODELS ,M EASUREMENTS , AND V ECTORS 1 Answers to Multiple-Choice Problems 1. B 2. A 3. C 4. A 5. B 6. A 7. B 8. D 9. C 10. C 11. B 12. B 13. D Solutions to Problems 1.1. Set Up: We know the following equalities: and Solve: In each case multiply the quantity to be converted by unity, expressed in different units. Construct an expression for unity so that the units to be changed cancel and we are left with the new desired units. (a) (b) (c) (d) (e) Reflect: In each case, the number representing the quantity is larger when expressed in the smaller unit. For example, it takes more milligrams to express a mass than to express the mass in grams. 1.2. Set Up: From the meaning of the metric prefixes we know: and Solve: (a) (b) (c) (d) (e) 1 2 femtometer 2 1 10 2 15 meter 1 femtometer 2 5 2 3 10 2 15 meter 1 700 nm 2 1 10 2 9 meter 1 nm 2 5 7.00 3 10 2 7 meter 1 400 nm 2 1 10 2 9 meter 1 nm 2 5 4.00 3 10 2 7 meter; 1 3.00 3 10 8 m / s 2 1 1 gigameter 10 9 m 2 5 0.300 gigameter / s 1 5 picofarads 2 1 10 2 12 farad 1 picofarad 2 5 5 3 10 2 12 picofarad 1 7.85 megohms 2 1 10 6 ohms 1 megaohm 2 5 7.85 3 10 6 ohms 10 2 15 m. 1 femtometer 5 1 fm 5 1 nanometer 5 1 nm 5 10 2 9 m; 1 gigameter 5 1 Gm 5 10 9 m; 1 pf 5 10 2 12 farad; 1 picofarad 5 1 megaohm 5 1 M V5 10 6 ohms; 1 0.020 amp 2 5 1 1 milliamp 10 2 3 amp 2 5 20 milliamps 1 1500 ohms 2 1 1 kilohm 10 3 ohms 2 5 1.50 kilohms 1 500 mg / day 2 1 10 2 3 g 1 mg 2 5 0.500 g / day 1 120 m g / day 2 1 10 2 6 g 1 m g 2 5 1.20 3 10 2 4 g / day 1 2400 mg / day 2 1 10 2 3 g 1 mg 2 5 2.40 g / day 1 milliamp 5 10 2 3 amp. 1 kilohms 5 1000 ohms; 1 m g 5 10 2 6 g; 1 mg 5 10 2 3 g;
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1.3. Set Up: We know the equalities: and Solve: (a) (b) (c) The mass of each tablet is The number of tablets required each day is the number of grams recommended per day divided by the number of grams per tablet: Take 2 tablets each day. (d) 1.4. Set Up: In part (a), we need to solve an equation of the form where x is a series of conversion equalities and y is the unknown number of kilometers. For part (b), we must prove using the equalities and Part (c) requires the application of the equality Solve: (a) (b) (c) 1.5. Set Up: We need to apply the following conversion equalities: and Solve: (a) (b) (c) Reflect: We could express the density of water as 1.6. Set Up: We know that and that mph means miles per hour. Solve: (a) (b) 1 65 mph 2 1 1 km 0.6214 mi 2 5 105 km / h 1 150 km / h 2 1 0.6214 mi 1 km 2 5 93 mi / h 5 93 mph 1 km 5 0.6214 mi 1.00 kg / L. 1 1.00 kg 2 1 2.205 lb 1.00 kg 2 5 2.20 lb 1 1.00 L 2 1 1000 cm 3 1.00 L 21 1.00 g 1.00 cm 3 1.00 kg 1000 g 2 5 1.00 kg; 1 1050 kg / m 3 2 1 1000 g 1.00 kg 1.00 m 1000 cm 2 3 5 1.05 g / cm 3 1 1.00 g / cm 3 2 1 1.00 kg 1000 g 100 cm 1.00 m 2 3 5 1000 kg / m 3 1.00 L 5 1000 cm 3 . 100 cm 5 1.00 m, 1000 g 5 1.00 kg, 1 1.00 L 2 1 10 3 mL 1.00 L 1.00 cm 3 1.00 mL 2 5 1000 cm 3 1 1.00 mL 2 1 1.00 L 10 3 mL 1000 cm 3 1.00 L 2 5 1.00 cm 3 y 5 1.61 km S1 2.54 cm 1.00 in. 12.0 in. 1.00 ft 5280 ft 1.00 mi 2T 1 1.00 mi 2 1.00 m 100 cm 1.00 km 10 3 m 5 y ; 1 mL 5 1 cm 3 . 10 3 mL 5 1 L. 1 L 5 1000 cm 3 1.00 cm 3 1 1.00 mL 2 x 5 1 2.54 cm 1.00 in. 2 x 1 1.0 mi 2 5 y , 1 0.000070 g / day 2 1 1 mg 10 2 3 g 2 5 0.070 mg / day 0.0030 g / day 2.0 3 10 2 3 g / tablet 5 1.5 tablet / day.
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01_InstSolManual_PDF-1 - MODELS MEASUREMENTS AND VECTORS 1...

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