21Problems1.3Converting UnitsPROBLEMS1.Performthefollowingconversions:NOTESb.0.8hourstosecondsa.27minutesto seconds1.Conversion factors may bec.2h3min 47 sto sd.35 horsepower to wattsfound on the inside of thee.1827Wtohpf.23 revolutions to degreesfront cover or in thetables of2.Performthefollowingconversions:Chapter 1.a.27feetto metersb.2.3ydto cm2.Difficult problems have theirquestion number printed inc.36°F to degreesCd. 18 (US) gallons to litersred.f. 124 sq. in. to m?e. 100 sq.ft to m23.Answers to odd-numberedg.47-pound force to newtonsproblems are in Appendix D.3.Setup conversionfactors,computethefollowing,andexpresstheanswerinthe units indicated.a.The area of a plate1.2mby70cm in m2b.The areaof a triangle with base25cm,height 0.5m in mc.Thevolumeofabox10cmby25cmby80cminm.d.Thevolume of a spherewith10 in.radius in m4.An electric fan rotates at 300 revolutionsper minute.How many degrees isthis per second?5.If the surface mount robotmachine of Figure1-3places 15parts every12 s,what is its placement rateperhour?6. If your laser printer can print 8 pages per minute, how manypages can itprint in one tenth of an hour?7. A car gets 27 miles per US gallon. What is this in kilometers per liter?8.The equatorial radius of the earth is 3963 miles.What is the earth's circum-ferenceinkilometersattheequator?9.A wheel rotates 18°in 0.02 s.How manyrevolutions per minute is this?10. The height of horses is sometimes measured in “hands," where 1 hand = 4inches.Howmanymeters tall is a16-hand horse?Howmany centimeters?11.Suppose s =vt is given,wheres is distance travelled, vis velocity,and t istime.If you travel at =60 mph for 500 seconds,you get upon unthinkingsubstitution s = vt = (60)(500) = 30,000 miles.What is wrong with thiscalculation? What is the correct answer?12.How longdoes it takeforapizza cutter traveling at 0.12m/stocut diago-nally across a 15-in.pizza?13.JoeS.was asked to convert2000yd/h to meters per second.Hereis Joe'swork:velocity=2000×0.9144X60/60=1828.8m/s.Determineconver-sion factors, write units into the conversion, and find the corect answer.14. The mean distance from the earth to the moon is 238 857 miles.Radio signals travel at 299 792 458 m/s.How long does it take a radio signal to reachthe moon?
1.3 Converting Units 1. Perform the following conversions: a. 27 minutes to seconds b. 0.8 hours to seconds c. 2 h 3 min 47 s to s d. 35 horsepower to watts e. 1827 W to hp f. 23 revolutions to degrees 2. Perform the following conversions: a. 27 feet to meters b. 2.3 yd to cm c. 36°F to degrees C d. 18 (US) gallons to liters e. 100 sq. ft to m2 f. 124 sq. in. to m2 g. 47-pound force to newtons 3. Set up conversion factors, compute the following, and express the answer in the units indicated. a. The area of a plate 1.2 m by 70 cm in m2 . b. The area of a triangle with base 25 cm, height 0.5 m in m2 . c. The volume of a box 10 cm by 25 cm by 80 cm in m3 . d. The volume of a sphere with 10 in. radius in m3 . 4. An electric fan rotates at 300 revolutions per minute. How many degrees is this per second? 5. If the surface mount robot machine of Figure 1–3 places 15 parts every 12 s, what is its placement rate per hour? 6. If your laser printer can print 8 pages per minute, how many pages can it print in one tenth of an hour? 7. A car gets 27 miles per US gallon. What is this in kilometers per liter? 8. The equatorial radius of the earth is 3963 miles. What is the earth’s circumference in kilometers at the equator? 9. A wheel rotates 18° in 0.02 s. How many revolutions per minute is this? 10. The height of horses is sometimes measured in “hands,” where 1 hand 4 inches. How many meters tall is a 16-hand horse? How many centimeters? 11. Suppose s vt is given, where s is distance travelled, v is velocity, and t is time. If you travel at v 60 mph for 500 seconds, you get upon unthinking substitution s vt (60)(500) 30,000 miles. What is wrong with this calculation? What is the correct answer? 12. How long does it take for a pizza cutter traveling at 0.12 m/s to cut diagonally across a 15-in. pizza? 13. Joe S. was asked to convert 2000 yd/h to meters per second. Here is Joe’s work: velocity 2000 0.9144 60/60 1828.8 m/s. Determine conversion factors, write units into the conversion, and find the correct answer. 14. The mean distance from the earth to the moon is 238 857 miles. Radio signals travel at 299 792 458 m/s. How long does it take a radio signal to reach the moon? Problems 21 1. Conversion factors may be found on the inside of the front cover or in the tables of Chapter 1. 2. Difficult problems have their question number printed in red. 3. Answers to odd-numbered problems are in Appendix D. NOTES. PROBLEMS
22Chapter1Introduction15.Your plantmanager asks you to investigatetwomachines.The cost of elec-tricityforoperatingmachine#1is43cents/minute,whilethatformachine#2is $200.00per8-hour shift.Thepurchasepriceand production capacityfor both machines are identical. Based on this information, which machineshould you purchase and why?16.Given that 1 hp=550ft-Ib/s,1ft=0.3048m,1lb=4.448N,1J=1N-m,and1W=1J/s,showthat1hp=746W.1.4PowerofTenNotation17.Expresseachofthefollowing inpoweroftennotationwithonenonzerodigit to the left of the decimal point:b.0.008 72a. 8675d. 37.2 × 10-2C.12.4×102f.0.000215×10-3e. 0.003 48 × 10sg.14.7× 10018.Express the answerfor each of the following in power of ten notation withonenonzerodigittotheleftofthedecimal pointa. (17.6)(100)b.(1400)(27×X10-3)c.(0.15×10°)(14×10-4)d. 1 × 10-7 × 10-4× 10.65e.(12.5)(1000)(0.01)f. (18.4× 10°)(100)(1.5 × 10-5)(0.001)19.Repeat the directions in Question 18 for each of the following.1258×104b.a.1000(0.001)3 × 104(16 × 10-7)(21.8 × 10%)dc.(1.5 × 10%)(14.2)(12 ×10-5)20.Determine answers for the followingb. 72.3 ×10-2 + 1 × 10-3a. 123.7 + 0.05 + 1259 × 10-3c. 86.95 × 10° 383d. 452 × 10-2 + (697)(0.01)21.Convert the following to power of 10 notation and, without using your cal-culator, determine the answers.a.(4×10)(0.05)2b: (4 × 10)(-0.05)2(3 ×2× 10)2C.(2 ×5×10-)(30 +20)(2.5 × 10°)(6000)d.(1×10)(2×10-1)2(-0.027)1/3(-0.2)2e.(23 + 1)° × 10-3
15. Your plant manager asks you to investigate two machines. The cost of electricity for operating machine #1 is 43 cents/minute, while that for machine #2 is $200.00 per 8-hour shift. The purchase price and production capacity for both machines are identical. Based on this information, which machine should you purchase and why? 16. Given that 1 hp 550 ft-lb/s, 1 ft 0.3048 m, 1 lb 4.448 N, 1 J 1 Nm, and 1 W 1 J/s, show that 1 hp 746 W. 1.4 Power of Ten Notation 17. Express each of the following in power of ten notation with one nonzero digit to the left of the decimal point: a. 8675 b. 0.008 72 c. 12.4 102 d. 37.2 102 e. 0.003 48 105 f. 0.000 215 103 g. 14.7 100 18. Express the answer for each of the following in power of ten notation with one nonzero digit to the left of the decimal point. a. (17.6)(100) b. (1400)(27 103 ) c. (0.15 106 )(14 104 ) d. 1 107 104 10.65 e. (12.5)(1000)(0.01) f. (18.4 100 )(100)(1.5 105 )(0.001) 19. Repeat the directions in Question 18 for each of the following. a. 1 1 0 2 0 5 0 b. 8 (0 .00 1 1 0 ) 4 c. (1 3 .5 1 1 0 0 4 6 ) d. 20. Determine answers for the following a. 123.7 0.05 1259 103 b. 72.3 102 1 103 c. 86.95 102 383 d. 452 102 (697)(0.01) 21. Convert the following to power of 10 notation and, without using your calculator, determine the answers. a. (4 103 )(0.05)2 b. (4 103 )(0.05)2 c. d. e. ( ( 23 0. 027 1 ) ) 1 0 /3 ( 1 0 0 .2 ) 3 2 (30 20)2 (2.5 106 )(6000) (1 103 )(2 101 ) 2 (3 2 10) 2 (2 5 101 ) (16 107 )(21.8 106 ) (14.2)(12 105 ) 22 Chapter 1 ■ Introduction
23Problems22.Foreachof thefollowing,convertthenumberstopoweroftennotation,then perform the indicated computations.Round youranswer to fourdigits:a.(452)(6.73 ×10")b.(0.00985)(4700)d.12.40-236×10-2c. (0.0892)/(0.000 067 3)f. (-643 × 10-3)3e. (1.27)3 + 47.9/(0.8)2g.[(0.0025)"[1.6 × 10′]h. [(-0.027)]/3]/[1.5 × 10-"](3.5×10)-×(0.0045)×(729))3i[(0.008 72) × (47)] - 35623. For the following,a.convertnumberstopowerof ten notation,thenperformtheindicatedcomputation,b.perform theoperation directly on your calculator without conversion.What is your conclusion?0.0352i.842×0.0014ii0.0079124.Express each of the following in conventional notation:a.34.9 × 104b.15.1×100c. 234.6 × 10-4d. 6.97 × 10-2e.45786.97×10-1f. 6.97 × 10~525.Onecoulomb (Chapter 2)is theamount of chargerepresented by6240000000000000000electrons.Expressthisquantity inpoweroftennotation.26:Themass of an electron is 0.0000000000000000000000000000008999kg.Express as apower of 10 with one non-zero digit to theleft of the dec-imal point.27.If 6.24 ×1018 electrons pass through a wire in 1 s, how many pass throughitduring a time interval of2 hr, 47min and 10 s?28. Compute the distance traveled in meters by light in a vacuum in 1.2 × 10-8second.29.How long does it take light to travel 3.47 × 10°km in a vacuum?30.How far in km does light travel in one light-year?31.While investigating a site for a hydroelectric project, you determine that theflow of water is 3.73 × 10°m°/s. How much is this in liters/hour?32. The graviational force beween wo bodies is F=6.6726 × 10-mrN, where masses m, and mz are in kilograms and the distance rbetweengravitational centers is in meters.If body1is a sphere of radius 5000 milesand density of 25kg/m,and body2 is a sphere of diameter20000km anddensityof 12kg/m,and the distancebetween centersis100000miles,what is the gravitational force between them?1.5Prefixes33.What is the appropriate prefix and its abbreviation for each of the followingmultipliers ?b.1 000 000a.1000c. 109d. 0.000 001e. 10-3f. 10-12
22. For each of the following, convert the numbers to power of ten notation, then perform the indicated computations. Round your answer to four digits: a. (452)(6.73 104 ) b. (0.009 85)(4700) c. (0.0892)/(0.000 067 3) d. 12.40 236 102 e. (1.27)3 47.9/(0.8)2 f. (643 103 ) 3 g. [(0.0025)1/2][1.6 104 ] h. [(0.027)1/3]/[1.5 104 ] i. 23. For the following, a. convert numbers to power of ten notation, then perform the indicated computation, b. perform the operation directly on your calculator without conversion. What is your conclusion? i. 842 0.0014 ii. 0 0 .0 .0 0 3 7 5 9 2 1 24. Express each of the following in conventional notation: a. 34.9 104 b. 15.1 100 c. 234.6 104 d. 6.97 102 e. 45 786.97 101 f. 6.97 105 25. One coulomb (Chapter 2) is the amount of charge represented by 6 240 000 000 000 000 000 electrons. Express this quantity in power of ten notation. 26. The mass of an electron is 0.000 000 000 000 000 000 000 000 000 000 899 9 kg. Express as a power of 10 with one non-zero digit to the left of the decimal point. 27. If 6.24 1018 electrons pass through a wire in 1 s, how many pass through it during a time interval of 2 hr, 47 min and 10 s? 28. Compute the distance traveled in meters by light in a vacuum in 1.2 108 second. 29. How long does it take light to travel 3.47 105 km in a vacuum? 30. How far in km does light travel in one light-year? 31. While investigating a site for a hydroelectric project, you determine that the flow of water is 3.73 104 m3 /s. How much is this in liters/hour? 32. The gravitational force between two bodies is F 6.6726 1011 m r 1m 2 2 N, where masses m1 and m2 are in kilograms and the distance r between gravitational centers is in meters. If body 1 is a sphere of radius 5000 miles and density of 25 kg/m3 , and body 2 is a sphere of diameter 20 000 km and density of 12 kg/m3 , and the distance between centers is 100 000 miles, what is the gravitational force between them? 1.5 Prefixes 33. What is the appropriate prefix and its abbreviation for each of the following multipliers ? a. 1000 b. 1 000 000 c. 109 d. 0.000 001 e. 103 f. 1012 (3.5 104 ) 2 (0.0045)2 (729) 1/3 [(0.008 72) (47)3 ] 356 Problems 23
24Chapter1Introduction34.Express thefollowing in terms of their abbreviations,e.g.,microwatts asμW. Pay particular attention to capitalization (e.g.. V, not v,for volts).a.milliamperesb. kilovoltsd.microsecondsc. megawattsf. millisecondse. micrometersg.nanoamps35.Express thefollowing in the most sensible engineering notation (e.g. 1270μs = 1.27 ms).b.0.000 027sa.0.0015sc.0.00035ms36.Convert the following:a.156mVtovoltsb.0.15 mVtomicrovoltsc.47kWtowattsd.0.057MW tokilowattse. 3.5 X 10* volts to kilovoltsf. 0.000 035 7 amps to microamps37.Determine the values to be inserted in the blanks.a.150kV=_×10V=—×10vb.330μW=×10-3W=—×10-sW38.Perform the indicated operations and express the answers in the units indi-cated.a.700μA-0.4mA=—μA=mAb.600MW+300×10*W=_MW39. Perform the indicated operations and express the answers in the units indi-cated.a.330V+0.15kV+0.2×103V=Vb.60W+100W+2700mW=—W40.The voltage of a high voltage transmission line is 1.15X105V.What is itsvoltage in kV?41.You purchase a 1500 W electricheatertoheatyour room.HowmanykW isthis?42.While repairing an antiqueradio,you come across a faulty capacitor desig-nated 39 mmfd.After a bit of research,you find thatmmfd"is an obsoleteunit meaning "micromicrofarads".You need a replacement capacitor ofequal value.Consulting Table 1-6, what would 39“micromicrofarads" beequivalent to?43.:Aradiosignal travelsat 299792.458km/s and atelephone signal at150m/μs. If they originate at the same point, which arrives first at a destination5000kmaway?Byhowmuch?44.a.If0.045coulomb of charge (Question 25)passes through a wire in15ms, how many electrons is this?b.Attherateof9.36×10i9electrons per second,howmany coulombspass a point in a wire in 20 μs?
34. Express the following in terms of their abbreviations, e.g., microwatts as mW. Pay particular attention to capitalization (e.g., V, not v, for volts). a. milliamperes b. kilovolts c. megawatts d. microseconds e. micrometers f. milliseconds g. nanoamps 35. Express the following in the most sensible engineering notation (e.g., 1270 ms 1.27 ms). a. 0.0015 s b. 0.000 027 s c. 0.000 35 ms 36. Convert the following: a. 156 mV to volts b. 0.15 mV to microvolts c. 47 kW to watts d. 0.057 MW to kilowatts e. 3.5 104 volts to kilovolts f. 0.000 035 7 amps to microamps 37. Determine the values to be inserted in the blanks. a. 150 kV 103 V 106 V b. 330 mW 103 W 105 W 38. Perform the indicated operations and express the answers in the units indicated. a. 700 mA 0.4 mA mA mA b. 600 MW 300 104 W MW 39. Perform the indicated operations and express the answers in the units indicated. a. 330 V 0.15 kV 0.2 103 V V b. 60 W 100 W 2700 mW W 40. The voltage of a high voltage transmission line is 1.15 105 V. What is its voltage in kV? 41. You purchase a 1500 W electric heater to heat your room. How many kW is this? 42. While repairing an antique radio, you come across a faulty capacitor designated 39 mmfd. After a bit of research, you find that “mmfd” is an obsolete unit meaning “micromicrofarads”. You need a replacement capacitor of equal value. Consulting Table 1–6, what would 39 “micromicrofarads” be equivalent to? 43. A radio signal travels at 299 792.458 km/s and a telephone signal at 150 m/ms. If they originate at the same point, which arrives first at a destination 5000 km away? By how much? 44. a. If 0.045 coulomb of charge (Question 25) passes through a wire in 15 ms, how many electrons is this? b. At the rate of 9.36 1019 electrons per second, how many coulombs pass a point in a wire in 20 ms? 24 Chapter 1 ■ Introduction
25Problems6441AAAAAT6iiBE营号8024-0.8TYP--0.25± 0.10.45(b)(a)FIGURE1-101.6SignificantDigitsandNumericalAccuracyFor eachof thefollowing,assumethat thegiven digits are significant.45.Determine the answerto three significantdigits:2.351.47×10-646.Given V =IR.If I =2.54 and R =52.71, determine Vto the correct num-berof significantdigits47.IfA=4.05±0.01isdivided byB=2.80±0.01,a.Whatisthe smallest that theresult can be?b. What is the largest that the result can be?c.Basedon this,givetheresultA/Btothe correctnumberofsignificantdigits48.The largeblack plastic component soldered onto theprintedcircuitboardofFigure l-1O(a)is an electronic deviceknown as an integrated circuit. Asindicated in (b),the center-to-center spacing of its leads (commonly calledpins) is 0.8 ± 0.1 mm. Pin diameters can vary from 0.25 to 0.45 mm. Con-sideringtheseuncertainties,a.What is the minimumdistancebetween pins due to manufacturing toler-ances?b.What is themaximumdistance?1.7CircuitDiagrams49. Consider the pictorial diagram of Figure 1-11.Using the appropriate sym-bols from Table 1-7, draw this in schematic form. Hint: In later chapters,there aremany schematic circuits containing resistors,inductors,and capacitors.Usethese as aids
1.6 Significant Digits and Numerical Accuracy For each of the following, assume that the given digits are significant. 45. Determine the answer to three significant digits: 2.35 1.47 106 46. Given V IR. If I 2.54 and R 52.71, determine V to the correct number of significant digits. 47. If A 4.05 0.01 is divided by B 2.80 0.01, a. What is the smallest that the result can be? b. What is the largest that the result can be? c. Based on this, give the resultA/Bto the correct number of significant digits. 48. The large black plastic component soldered onto the printed circuit board of Figure 1–10(a) is an electronic device known as an integrated circuit. As indicated in (b), the center-to-center spacing of its leads (commonly called pins) is 0.8 0.1 mm. Pin diameters can vary from 0.25 to 0.45 mm. Considering these uncertainties, a. What is the minimum distance between pins due to manufacturing tolerances? b. What is the maximum distance? 1.7 Circuit Diagrams 49. Consider the pictorial diagram of Figure 1–11. Using the appropriate symbols from Table 1–7, draw this in schematic form. Hint: In later chapters, there are many schematic circuits containing resistors, inductors, and capacitors. Use these as aids. Problems 25 (a) 0.8 TYP 0.1 1 24 25 40 64 41 65 80 0.25 0.45 (b) FIGURE 1–10