Kosky, Wise, Balmer, Keat: Exploring Engineering, Second Edition

Transcription

1 Chapter 2: Key Elements of Engineering Analysis To help get you in the habit of ing these elements, in the following exercises the students should be graded on use of all of the elements we have discussed in this chapter. In these problems, where necessary, assume that on the surface of the earth, g = 9.81 m/s 2 = 32.2 ft/s 2 (i.e., each to three significant figures). Make sure the students are reporting the solution to the proper number of significant figures. While not taught until the next chapter, the solution set uses the need-know-how-tosolve method because the students should have covered the topic by the time their solution sets are handed back.

2 29 2-1) If a gallon has a volume of ft 3 and a human mouth has a volume of in 3 then how many mouthfuls of water are required to fill a 5.00 (US) gallon can? Need: 5.00 gallon can = mouthfuls Know: Conversions 1.00 ft = 12.0 inches & 1.00 gallon = ft 3. How: Units analysis. Solve: 5.00 gallon = [gallons][ft 3 /gallon] = ft 3 = [ft 3 ][in/ft] 3 = in 3 = /0.900 [in 3 ][mouthfuls/in 3 ] = = mouthfuls.

3 30 2-2) Identify whether you would perform the following unit conversions by definition, by conversion factors, by geometry, or by scientific law: a) How many square miles in a square kilometer? b) How many microfarads in a farad? c) What is the weight on Earth in N of an object with a mass of 10. kg? d) How many square miles on the surface of the earth? Need: For each part, conversion is (state whether definition, conversion factor, geometry, or scientific law) Know: Basic concepts of conversion factors, geometry and scientific laws. Also the diameter of the Earth 1 is 12,756 km How: For conversions use units method Solve: a) How many square miles in a square kilometer? Units conversion: mile = km; 1 square mile = [mile] 2 [km/mile] 2 = km 2. b) How many microfarads in a farad? Units conversion: 1 farad = 1 million microfarads = [F] [microf/f] = 10 6 microf. c) What is the weight on Earth in N of an object with a mass of 10.0 kg? Scientific law: W = mg = [kg][m/s 2 ] = 980. N. d) How many square miles on the surface of the earth? Geometry + units conversion: Geometry: Surface area of a sphere: πd 2. (Note: engineers prefer diameter to radius in many instances since it is easier to measure a diameter than to directly measure a radius) mile = km. A = π D 2 = ,756 2 / [km] 2 [mile/km] 2 = mile E.g.,

4 31 2-3) The height of horses to the shoulder is still measured in the old unit of hands and ocean depth in fathoms. There are 16 hands in a fathom, and 6.0 feet in a fathom. How many feet high is a horse that is 13 hands tall? Need: Height 13 hands = ft. Know: Conversion factors: 16 hands/fathom and 6.0 ft/fathom. How: Method of units. Solve: 13 hands = 13/16 [hands][fathoms/hand] = [fathoms] [ft/fathom] = 4.88 = 4.9 ft

5 32 2-4) An acre was originally defined as the amount of area that an oxen team could plow in a day. Suppose a team could plow 0.4 hectare per day, where a hectare is 10 4 m 2. There are 1609 meters in a mile. How many acres are there in a square mile? Need: Square mile = acres. Know: Conversion factors: 1609 m/mile, 10 4 m 2 /hectare. A team could plough 0.4 hectares/day = 1 acre/day. Thus 1.0 hectare = 2.5 acres. How: Method of units Solve: 1 square mile = [mile] 2 [m/mile] 2 = m 2 = /10 4 [m] 2 [hectares/m] 2 = [hectares] = [hectares][acres/hectare] = 647 = 600 acres (since the team plows 0.4 hectares, only known to one significant digit.)

6 33 2-5) There are 39 inches in a meter. What is the area in the SI system of the skin of a spherical orange that is 4.0 inches in diameter? Need: Area of orange skin = m 2. Know: Conversion factors: 39 inches/m; How: Method of units and a spherical orange whose surface area is πd 2 Solve: Skin area of orange = π [in] 2 = 50.3/39 2 [in] 2 [m/in] 2 = m 2

7 34 2-6) There are 39 inches in a meter. What is the volume in the Engineering English system of a spherical apple that is 10. cm. in diameter? Need: Volume of apple = in 3. Know: Conversion factors: 39 inches/m and 100 cm/m. How: Method of units and assume a spherical apple whose volume is πd 3 /6. Solve: Volume of orange = π /6 [cm] 3 = 524/100 3 [cm] 3 [m/cm] 3 = [m 3 ][in/m] 3 = 31. in 3

8 35 2-7) If the pressure in the tire on your car is 32.0 lbf/in 2 (or psi), what is its pressure in SI units? Need: Tire pressure in SI units (N/m 2 Know: Use convert.exe 2 for unit conversions lbf/in 2 = 6895 N/m 2. How: Method of units Solve: 32.0 lbf/in 2 = [lbf/in 2 ][N/m 2 / lbf/in 2 ] = 2.21 N/m

9 36 2-8) Suppose the mass in Example 2.1 was 50.0 slugs. What would its weight be in lbf (pounds force)? Need: Wt of 50.0 slugs in lbf Know: 1.00 slug is defined as F/g with F in lbf and g in ft/s 2 How: Use eqn 2.3 of text Solve: W = mg = = 1610 [slug][ft/s 2 ] = 1610 lbf.

10 37 2-9) What would the 5.00 slug mass in Example 2.1 weigh on the Moon where the acceleration of gravity is only 1/6 of that on Earth? Need: Mass of 5.0 slug on the Moon Know - How: Mass is a property Solve: m = 5.00 slugs anywhere in the Universe.

11 ) What would the force on the body in Example 2.2 be if its mass were 856 grams? Need: Force on a body of mass 856 g (= kg) accelerated at 9.81 m/s 2 Know: Newton s Law of Motion, F = ma How: F in N, m in kg and a in m/s 2. Solve: F = ma = [kg] [m/s 2 ] = = 8.40 N

12 ) What would the weight of the body in Example 2.3 on the Moon where the acceleration of gravity is just g moon = 1.64 m/s 2? Need: Wt of body on the Moon Know: Mass = kg, acceleration = 1.64 m/s 2 How: Newton s Law of Motion, F = ma or W = mg moon Solve: W = mg moon = [kg][m/s 2 ] = 1.67 N

13 ) What force would be necessary in Example 2.4 if the mass were 735 lbm? Need: Force to accelerate 735 lbm by 15.0 m/s 2 Know: Need proportionality constant, g c = 32.2 lbm ft/lbf s 2 How: Newton s Law of Motion, F = ma/g c Solve: F = ma = /32.2 [lbm][ft/s 2 ][lbf s 2 ][lbm ft] = 342 lbf

14 ) What is the value and units of g c in the Engineering English system on the Moon? Need: Value and units of g c in the Engineering English system on the Moon Know How: g c is a proportionality constant to convert units. Solve: g c is a fixed value (including the Moon) g c = 32.2 lbm ft/lbf s 2

15 ) Acceleration is sometimes measured in g s, where 1g = 9.8 m/s 2. How many g s correspond to the steady acceleration of a car doing zero-to-sixty 3 in 10.0 seconds. Need: Acceleration of car = g s. Know: 1.0g = 9.8 m/s 2 and acceleration is the rate of change of speed with time. How: Method of units and conversion factor of 60. mph = 88 ft/s (i.e., 60/ [miles/hr][hours/s][ft/mile]. Also that 1 ft = m. Solve: Acceleration of car = change of speed/time interval = 60. (88/60)/10.0 [miles/hr][ft/s] [hr/miles][1/s] = 8.8 ft/s 2. Acceleration = [ft/s 2 ][m/ft] = 2.68 m/s 2 = 2.68/9.8 [m/s 2 ][s 2 /m] = 0.27 [0] i.e., g s. 3. In the language of the car enthusiast, the standard test to accelerate a car from a standing start to 60 mph is called zero-to-sixty.

16 ) What is your mass in kilograms divided by your weight in pounds? Do you have to step onto a scale to answer this question? How did you answer the question? Need: Ratio of body mass in kg/weight in pounds = kg/lbf. Know: assume your mass in M kg. Conversion factor = 2.20 lbm/kg. Also weight is a force that, in the English Engineering system, is mg/g c where m is your body mass in lbm. How: Method of units and weight is a force that, in the English Engineering system, is W = mg/g c where m is your body mass in lbm. Solve: Ratio of M kg/w lbf where W = mg/g c and m = M/2.20 [kg]/[lbm]. W = M/ /32.2 [kg]/[lbm] [ft/s 2 ][lbf s 2 /lbm ft] = M/2.20 [kg]/[lbf]. M/W = 1/2.20 = 0.45[kg]/[lbf] The answer (to two significant digits) is 0.45[kg]/[lbf]. This is just a conversion factor that does not depend on your particular weight!

17 ) If power (measured in W, or watts) is defined as work (measured in J, or joules) performed per unit time (measured in s), and work is defined as force (measured in N or newtons) distance (measured in m) and speed is defined as distance per unit time (measured in m/s), what is the power being exerted by a force of 1000 N on a car traveling at 30. m/s. (Assume force and speed are in the same direction, and treat all numbers as positive). Need: Power of car = W. Know: Power of 1W = 1 J/s and 1 J = 1 N 1 m, speed in m/s. How: Method of units and 1 watt of power = 1 (N m)/s = 1 (N m/s) Solve: Power = 1, [N][m/s] = W

18 ) A rocket sled exerts N of thrust and has a mass of kg. What does it do zero-to-sixty in? How many g s (see problem 14) does it achieve? Need: Time to 60.0 mph (26.8 m/s) and # of g s on a rocket sled. Know: Newton s law, a = F/m; g = 9.81 m/s 2. Also t = v/a (v is speed) since a = v/t. How: Method of units and inverted Newton s law expressed in # g s = a/g = (F/m)g = F/mg. Solve: g s on a rocket sled = F/mg = /( ) [N][1/kg][s 2 /m] = 1.53 [0], i.e., g s. Time = v/a = v/g g/a (notice multiplying and simultaneously dividing by g): t = 26.8/9.81 1/1.53 [m/s][s 2 /m] [0] = 1.79 s.

19 ) A person pushes a crate on a frictionless surface with a force of 100. lbf. The crate accelerates at a rate of 3.0 feet per second 2. What is the mass of the crate in lbm? Need: Mass of crate = lbm. Know: F = 100. lbf, a = 3.0 ft/s 2. Also g = 32.2 ft/s 2 and g c = 32.2 lbm s 2 /lbf ft How: Newton s law, F = ma/g c ; Solve: Mass of crate = Fg c /a = /3.0 [lbf][lbm s 2 /lbf ft][ft/s 2 ] = 1073 = lbm.

20 ) The force of gravity on the moon is one-sixth (i.e., 1/6.0) as strong as the force of gravity on earth. An apple weighs 1.0 N on earth. What is a) the mass of the apple on the moon, in lbm? b) the weight of the apple on the moon, in lbf? (Conversion factor: 1.00 kg = 2.20 lbm) Need: a) Mass of moon apple = lbm and b) weight of moon apple = lbf Know: g c = 32.2 lbm ft/lbf s 2 and on the moon, g = 32.2/6.0 ft/s 2, g = 9.81 m/s 2 on Earth kg = 2.20 lbm. How: Newton s law, F = ma/g c, English units and F = ma SI units. Solve: a) Mass is the same on Moon as it is on Earth; on Earth, the apple weighs 1.0 N. Its mass is thus m = W/g = 1.0/9.81 [N][s 2 /m] = kg = [kg][lbm/kg] = 0.22 lbm. b) Moon apple s weight is W = ma/g c = 0.22 (32.2/6.0)/32.2 [lbm][ft/s 2 ][lbf s 2 /lbm ft] = lbf.

21 ) How many lbf does it take for a lbm car to achieve zero-to-sixty in 10. seconds. Need: Force = lbf to accelerate lbm car to 60. mph in 10. s. Know: g c = 32.2 lbm ft/lbf s 2, v = 60. mph = 88 ft/s, a = v/t How: Newton s law, F = ma/g c, English units. Solve: a = 88/10. [ft/s][1/s] = 8.8 ft/s 2. F = ma/g c = /32.2 [lbm][ft/s 2 ][ lbf s 2 /lbm ft] = 1093 = lbf.

22 ) Suppose a planet exerted a gravitational force at its surface that was 0.6 the gravitational force exerted by Earth. What is g c on that planet? Need: Value of g c in on another planet. Know - How: g c always and everywhere equals 32.2 lbm ft/lbf s 2. Solve: g c = 32.2 lbm ft/lbf s 2

23 ) Suppose you were going to accelerate a kg car by the Rube Goldberg contraption shown in this picture. The fan (A) blows apples (C) off the tree (B) into the funnel and thus into the bag (D). The bag is pulled downward by the force of gravity (equal to the weight of the apples in the bag), and that force is transmitted via the pulley (E) to accelerate the car (F). About how many apples each weighing 1.00 N would have to fall into the bag in order to achieve 0 to 60.0 mph in 7.00 seconds? Assume the filled bag applies a constant force to the car, equal to the weight of the apples in the bag. (A: apples.) Need: # of 1.00 N apples = to accelerate 2,000 kg car to 60. mph in 7.00 s. Know: v = 88 ft/s, 1 ft = m and a = v/t. How: Newton s law, F = ma Solve: Need force in N and each Newton is the weight of one apple. To get F need a from /7.00 [ft/s][m/ft][1/s] = 3.83 m/s 2. F = 2, [kg][m/s 2 ] = N; hence we need apples.

24 ) Calculate with the correct significant figures: (a) 100/( ), (b) / (A: 0.5, 0.50) Need: Round-off calculations. Know - How: Three rules for round-off. Solve: a) 100/( ) = 0.5 (Rule 2 because 100 has just one significant figure) b) / = 0.50 (Rule 2 because both numerator and denominator each have two significant figures)

25 ) Calculate a) 10/6, b) 10.0/6, c) 10/6.0, d) 10./6.0, and e) 10.0/6.00 Need: Round-off calculations. Know - How: Three rules for round-off. Solve: a) 10/6 = 2 (Rule 2 since both 6 and 10 have just one significant figure and rule 3 for round up) b) 10.0/6 = 2 (Rule 2 since 6 has just one significant figure and rule 3 for round up) c) 10/6.0 = 2 (Rule 2 since 10 has just one significant figure and rule 3 for round up) d) 10./6.0 = 1.7 (Rule 2 since both 6 and 10 have two significant figures and rule 3 for round up) e) 10.0/6.00 = 1.67 (Rule 2 since both 6 and 10 have three significant figures and rule 3 for round up)

26 ) What is minus ? Need: Round-off calculations. Know - How: Three rules for round-off. Solve: = (Rule 1 the smaller number is less than the least significant of the larger one)

27 ) A machinist has a sophisticated micrometer that can measure the diameter of a drill bit to 1/10,000 of an inch. What is the maximum number of significant figures that should be reported if the approximate diameter of the drill bit is: a) inches b) 0.1 inches c) 1 inch Need: Round-off calculations. Know How - Solve: Definition of significant figures. a) : 1 significant figure (i.e., , , ) b) 0.1 inches: 4 significant figures (i.e., , , ) c) 1 inch: 5 significant figures (i.e., , , )

28 ) Round off to 3 significant places: a) 1.53, b) , c) 16.67, d) , e) and f) Need: Round off of a series of numbers. Know How: Rule 3: Round down if discarded part is 0, 1, 2, 3, or 4 and up if 5, 6, 7, 8, or 9. Solve: a) 1.53 = 1.53 b) = 15.3 c) 16.67= 16.7 d) = 102 e) = -125 (Note that it s the unsigned numerical part of the number you have to round either up or down and not its position on the real number line.) f) =

29 ) Suppose you were going to design a front door and doorway to fit snugly enough to keep out the drafts, yet easy to open. (You are not showing off precision carpentry here, but merely designing a convenient ordinary door by standard methods). The dimensions are to be given in inches. To how many significant figures would you specify the length and width of the door and doorway 4. Assume a standard door is 30.0 by Need: = number of significant digits Know - How - Solve: At most you would need 3 significant figures (you don t need more because doors seal off doorways by latching to the doorway and hitting a jamb (a sort of lip on the doorway), not by fitting snugly together! So you can, and typically do, have a gap of about 1/10 inch between the door and the doorway. The door s dimensions would need to be between 30.0 ± 0.1 by 81.0 ± 0.1. So any precision greater than 0.1 of an inch for example, a measurement of inches (4 significant figures), instead of 81.1 inches would be a waste of effort. The door frame size would have to be at least 30.1 by 81.1, realistically < to the same tolerance (ignoring the finite thickness of the door to swing on its hinges and assuming these dimensions were stable, something not guaranteed in a wooden door or wooden frame). This problem illustrates a related subject of tolerancing, sometimes called gauge repeatability and reproducibility or Gauge R & R analysis. 4. The subject of tolerancing is important in mass manufacturing to ensure a proper fit with one part and another since each part will not be exact their combined tolerance will determine how well, if at all, they fit together. It is the subject of significant statistical analysis. Applying the methods rigorously allowed the Japanese automotive industry to eclipse those of the rest of the world in terms of quality.

30 ) You are browsing the Internet and find some units conversion software that may be useful in this course. Do you download the software on your PC at school and use it in this course? a) Check with the Internet site to make sure this software is freeware for your use in this course. b) Just download the software and use it, no one will know. c) Download the software at home and bring it to school. d) Never use software found on the Internet. Suggested method: Apply the Fundamental Canons and fill in an Engineering Ethics Matrix: Apply the Fundamental Canons: Engineers, in the fulfillment of their professional duties, shall: 1) Hold paramount the safety, health and welfare of the public 2) Perform services only in areas of their competence- 3) Issue public statements only in an objective and truthful manner 4) Act for each employer or client as faithful agents or trustees Although in reality, the university is a vendor to the student, in the classroom situation, for educational purposes, the student plays the role of employee and the teacher plays the role of employer or client. Assuming the teacher is playing the role of employer or client, use of proprietary software can be harmful to that employer or client (the teacher, or the teacher s employer, the university, could be sued by the software owner.) 5) Avoid deceptive acts. This weighs against c), which would be a deception aimed at circumventing the law. 6) Conduct themselves honorably, responsibly, ethically, and lawfully so as to enhance the honor, reputation, and usefulness of the profession This weighs against options b) and c) and obliges you to check to see that the software is freeware; ignorance of the law is no excuse. Put these in an Engineering Ethics Matrix form: Options Canons Hold paramount the safety, health and welfare of the public. a. Check for freeware b. Just download c. Download at home d. Never use internet software

31 58 Perform services only in the area of your competence Issue public statements only in an objective and truthful manner Act for each employer or client as faithful agents or trustees Avoid deceptive acts Conduct themselves honorably Yes Yes No-Student is acting as client to school and must obey the law on school s behalf No- ignoring the law is deceiving yourself that this is OK No-Student is acting as client to school and must obey the law on school s behalf, even at home No- this is a deception aimed at avoiding the law Yes No No Yes Would be ethical but would defeat educational purpose Would be ethical but would defeat educational purpose Solution: The applicable canons point in the same direction do a) or d). Both are ethically acceptable. However d) represents an over-reaction in practical terms. You would be depriving yourself of a valuable tool. As seen, the above considerations are more easily expressed in the engineering ethics matrix:

32 ) On December 11, 1998 the Mars Climate Orbiter was launched on a 760 million mile journey to the red planet. On September 23, 1999 a final rocket firing was to put the spacecraft into orbit, but it disappeared. An investigation board concluded that NASA engineers failed to convert the rocket s thrust from pounds force to newtons (the unit used in the guidance software), causing the spacecraft to miss its intended km altitude above Mars during orbit insertion, instead entering the Martian atmosphere at about 57 km. The spacecraft was then destroyed by atmospheric stresses and friction at this low altitude. As chief NASA engineer on this mission, how do you react to the national outcry for such a foolish mistake? a) Take all the blame yourself and resign. b) Find the person responsible, and fire, demote, or penalize that person c) Make sure it doesn t happen again by conduct a software audit for specification compliance on all data transferred between working groups. d) Verify the consistent use of units throughout the spacecraft design and operations. Fundamental Canons: Engineers, in the fulfillment of their professional duties, shall: 1) Hold paramount the safety, health and welfare of the public. This would argue for solutions c) and d). Resigning and firing would only help the public if there was assurance that the replacements would do better. 2) Perform services only in areas of their competence. An error of that magnitude suggests incompetence, and therefore violation of this standard. This suggests a) and b) are the options that should be considered. 3) Issue public statements only in an objective and truthful manner. unless the people involved deliberately generated data they knew to be false. 4) Act for each employer or client as faithful agents or trustees. Again, unless there was some ulterior motive for the error, this does not. 5) Avoid deceptive acts. Unless deliberate deception was practiced, this does not 6) Conduct themselves honorably, responsibly, ethically, and lawfully so as to enhance the honor, reputation, and usefulness of the profession. You and your subordinates brought dishonor on the profession and should resign. Do a) and b). Again, it s easier in Engineering Ethics Matrix format. Options Canons Hold paramount the safety, health and welfare of the public. a. Take blame and resign b. Fire responsible person c. Conduct audit d.verify consistent units approach

33 60 Perform services only in the area of your competence Issue public statements only in an objective and truthful manner Act for each employer or client as faithful agents or trustees Avoid deceptive acts Conduct themselves honorably No-unless you determine you actually are unfit for the post No-would be deceptive if you were not really the source of the problem Yes No- unless the error is part of a consistent pattern indicating unfitness of person for job Probably nofinding a scapegoat probably doesn t really address issue Probably not for reasons discussed above Yes Yes Yes Yes Yes Yes Solution: The canons are complementary, not in tension. So all four should be done. The engineers involved should be replaced, and their successors should make every effort to prevent a repetition.