Preface to the Instructor

Transcription

1 Preface to the Instructor With the exception of soe open-ended probles, this Instructor s Solutions Manual contains a solution to each of the nuerical probles in the textbook An Introduction to Mechanical Engineering (second edition). The description and style of these solutions (writing a brief approach, keeping track of units, aking sketches, staying organized and so forth) are intended to guide students with respect to the foratting and presentation of their own work. In addition, the copact disk accopanying this anual includes electronic versions of all photographs and figures in the textbook, and an electronic version of this anual. My intention is that these resources will be useful to instructors in two ways. First, instructors are able to easily iport photographs, drawings, and other art fro the textbook into their own handouts and lectures without the burden of having to photocopy or scan fro the textbook itself. Second, since any courses today have copanion web sites, instructors can use the copact disk to post electronic versions of solutions to their own proble sets. I hope that you will find this Instructor s Solutions Manual to be a useful resource for your own teaching of echanical engineering courses at the freshan and sophoore levels. As always, if you should have any coents on the textbook or anual, I would certainly appreciate hearing fro you. Jonathan Wickert Departent of Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 1513 wickert@cu.edu

2 Proble.1: Express your weight in the units lb and N, and your ass in the units slug and kg. Let w and represent weight and ass. w = 180 lb Convert to SI using the factor fro Table.6: N w = 448 lb ( 180 lb) 4. w = 801 N Calculate ass using gravitational acceleration in USCS: w 180 lb = = g 3. ft / s = slugs Convert to SI using the factor fro Table.6: kg = ( 5.59 slugs) slug = kg - 1 -

3 Proble.: Express your height in the units in, ft, and. Let h represent height. h = 6 ft in h = ( 6 ft) 1 ft h = 7 in Convert to SI using the factor fro Table.6: h = 3048 ( 6 ft) 0. ft h =

4 Proble.3: The solar power transitted to the ground is 0.6 kw/. Convert this quantity to the diensions of hp/ft. Convert to USCS using the factors fro Table.6. kw ft hp kw = hp ft hp ft - 3 -

5 Proble.4: One U.S. gallon is equivalent to ft 3, one foot is equivalent to , and 00 liters is equivalent to 1 3. By using those definitions, deterine the conversion factor between gallons and liters. Use the definitions of derived units and the conversion factors listed in Tables.,.5, and.6: 1 gal = ft 3 1 ft = L = 1 3 Convert gal to L using those factors: 1gal = 1 gal = ( 3) L ft ft 3 L - 4 -

6 Proble.5: A passenger autoobile is advertised as having a fuel econoy rating of 9 i/gal for highway driving. Express the rating in the units of k/l. Convert using factors fro Table.6: 9 i gal 0.64 gal k k = 1.33 L i L k 1.33 L - 5 -

7 Proble.6: (a) How any horsepower does a 0 W household light bulb consue? (b) How any kw does a 5-hp lawn ower engine produce? a) Convert W to kw using the prefix definition in Table.3. Convert fro kw to hp using the factor fro Table.6: kw hp hp W kw ( W ) = hp b) Convert fro hp to kw using factor fro Table.6: kw kw hp ( hp) = 3.79 kw - 6 -

8 Proble.7: A robotic wheeled vehicle that contains science instruents is used to study the geology of Mars. The rover weighs 408 lb on Earth. (a) In the USCS diensions of slugs and lb, what is the rover s ass? (b) What is the weight of the rover as it rolls off the lander s platfor (the lander is the protective shell that houses the rover during landing)? The gravitational acceleration on the surface of Mars is 1.3 ft/s. a) The rover s ass is the sae on Earth and Mars. On Earth, it weighs 408 lb, and the gravitational acceleration is 3. ft/s. By using = w/g 408 lb lb s = = ft s ft Fro Table.5, the diension is equivalent to the derived unit of slug. = slugs By definition, an object that weighs one pound has a ass of one pound-ass, so = 408 lb We double check by using the definition in Table.5 slugs = 67 lb ( 408 lb) 3.81 = 1. slugs b) Since the gravitational acceleration on Mars is only 1.3 ft/s, the weight becoes w = ( 1.67 slugs) ft slug ft 1.3 = s s The diension is the diensionally consistent group that is the sae as lb. w = lb It would not be correct to calculate weight as the product of 408 lb and 1.3 ft/s, since the units would not be diensionally consistent

9 Proble.8: Calculate various fuel quantities for Flight 143. The plane already had 7,68 L of fuel on board prior to the flight, and the tanks were to be filled so that a total of,300 kg were present at take-off. (a) Using the incorrect conversion factor of 1.77 kg/l, calculate in units of kg the aount of fuel that was added to the plane. (b) Using the correct factor of 1.77 lb/l, calculate in units of kg the aount of fuel that should have been added. (c) By what percent would the plane have been under-fueled for its journey? Be sure to distinguish between weight and ass quantities in your calculations. a) Aount of fuel that was added (kg): kg,300 kg ( 7,68 L) = 8,70.9 kg L 8,703 kg b) Aount of fuel that should have been added (kg): lb 1 kg,300 kg 59 L 3. ft / s slug 16,139 kg ( 7,68 L) = 16,139 kg c) Percent that the plane was under-fueled: 16,139 kg 8,703 kg ( 0% )= 46.07% 16,139 kg 46.1% - 8 -

10 Proble.9: Printed on the side of a tire on an all-wheel-drive sport utility wagon is the warning Do not inflate above 44 psi, where psi is the abbreviation for the pressure unit lb/in. Express the tire s axiu pressure rating in (a) the USCS unit of lb/ft (psf), and (b) the SI unit of kpa. a) Convert the area easure fro in to ft: lb in 44 1 = in ft 6,336 lb ft 6,336 psf where the abbreviation psf stands for pounds-per-square-foot. b) Use a conversion factor fro Table.6 and the SI prefix fro Table.3: lb 44 6,895 in kpa Pa psi = Pa = kpa - 9 -

11 Proble.: The aount of power transitted by sunlight depends on latitude and the surface area of the solar collector. On a clear day at a certain northern latitude, 0.6 kw/ of solar power strikes the ground. Express that value in the alternative USCS unit of (ft lb/s)/ft. Use conversion factors fro Table.6: kw 0.6 1,000 W kw ft lb / s = W ft ft lb/ s 41.1 ft ft lb/ s 41.1 ft - -

12 Proble.11: The property of a fluid called viscosity is related to its internal friction and resistance to being defored. The viscosity of water, for instance, is less than that of olasses and honey, just as the viscosity of a light otor oil is less than that of a grease. A unit used in echanical engineering to describe viscosity is called the poise, naed after the physiologist Jean Louis Poiseuille who perfored early experients in fluid echanics. The unit is defined by 1 poise = 0.1 (N s)/. Show that 1 poise is also equivalent to 1 g/(c s). Expand the derived unit N in ters of the SI base units: N s kg s kg 0.1 = 0.1 = 0. 1 s s Apply SI prefixes fro Table.3: kg g = s kg c 1 g c s 1 g c s

13 Proble.1: Referring to the description in Proble.11, and given that the viscosity of a certain engine oil is 0.5 kg/( s), deterine the value in the units (a) poise, and (b) slug/(ft s). a) Express viscosity in ters of the derived unit (N s)/ : kg kg 0.5 = 0.5 = 0.5 s s ( kg / s ) Use the definition of poise P fro Proble.11: N s 0.5 ( N.5 P P =.5 P s) / s N s = 0.5 b) Use conversion factors fro Table.6: kg slug slug = s kg ft ft s slug ft s - 1 -

14 Proble.13: Referring to the description in Proble.11, if the viscosity of water is 0.01 poise, deterine the value in ters of the units (a) slug/(ft s) and (b) kg/( s). Express 0.01 P in ters of SI base units: ( 0.01P ) kg s ( N s) / = P Use conversion factors fro Table.6: N s = kg s kg slug = s kg ft slug ft s slug ft s

15 Proble.14: The fuel efficiency of an aircraft s jet engines is described by the thrust-specific fuel consuption, or TSFC. The TSFC easures the rate of fuel consuption (ass of fuel burned per unit tie) relative to the thrust (force) that the engine produces. In that anner, just because an engine ight consue ore fuel per unit tie than a second engine, it would not necessarily be ore inefficient if it also produced ore thrust to power the plane. The TSFC for an early hydrogen-fueled jet engine was 0.08 (kg/h)/n. Express that value in the USCS units of (slug/s)/lb. Use SI to USCS conversion factors fro Table.6: kg / hr slug N kg hr s N lb = slug / s lb slug / s lb

16 Proble.15: An autoobile engine is advertised as producing a peak power of 118 hp (at an engine speed of 4000 rp), and a peak torque of 186 ft lb (at 500 rp). Express those perforance ratings in the SI units of kw and N. For the power, apply the hp to kw conversion factor fro Table.6: kw kw hp ( hp) = kw For the torque, apply USCS to SI conversion factors fro Table.6: N N lb ft ( ft lb) = 5 N

17 Proble.16: For the exercise of Exaple.6, express the sideways deflection of the tip in the units of ils (defined in Table.5) when the various quantities are instead known in the USCS. Use the values F = 75 lb, L = 3 in, d = 3/16 in, and E = 30 x 6 psi. Evaluate the deflection equation using nuerical values that are diensionally consistent: 64( 75lb)( 3in. ) 3 ( 30 6 lb / in. )( in. ) 64FL 3 x = = = 0.371in. 3π Ed 4 3π 4 Apply the definition of il fro Table.5: 1 il = 0.001in. 371 ils

18 Proble.17: Heat Q, which has the SI unit of joule (J), is the quantity in echanical engineering that describes the transit of energy fro one location to another. The equation for the flow of heat during the tie interval t through an insulated wall is A t Q = κ L ( ) T h T l where κ is the theral conductivity of the aterial fro which the wall is ade, A and L are the wall s area and thickness, andth Tl is the difference (in degrees Celsius) between the high- and low-teperature sides of the wall. By using the principle of diensional consistency, what is the correct diension for theral conductivity in the SI? The lowercase Greek character kappa (κ) is a conventional atheatical sybol used for theral conductivity. Appendix A suarizes the naes and sybols of Greek letters. Let [κ] denote the SI units for theral conductivity. Apply the principle of diensional consistency and the definition of watt in Table.: [ ] s o C J = κ [κ ] = J s 1 o C = W o C W o C

19 Proble.18: Convection is the process by which war air rises and cooler air falls. The Prandtl nuber, Pr, is used when echanical engineers analyze certain heat transfer and convection processes. It is defined by the equation µ c p Pr = κ where c p is a property of the fluid called the specific heat having the SI unit kj /( kg o C ) ; µ is the viscosity as discussed in Proble.11; and κ is the theral conductivity as discussed in Proble.17. Show that Pr is a diensionless nuber. The lowercase Greek characters u (µ) and kappa (κ) are conventional atheatical sybols used for viscosity and theral conductivity. Appendix A suarizes the naes and sybols of Greek letters. Let [Pr] denote the units for Prandtl nuber. In the SI, a unit for viscosity is N s/, and fro the solution to Proble.11, the units for theral conductivity are W/( o C). Apply the principle of diensional consistency and the definition of watt fro Table.: [ Pr ] = ( kj /( kg o C) ) [ W /( ( N s / ) kj N s o C = o C)] W kg o C kj N s = kg s kj 1 = s W ( N ) 1 = N kw W which has no units but does contain a diensionless factor of 00 because of the kilo prefix

20 Proble.19: Referring to Proble.18 and Table.5, if the units for c p and µ are Btu/(slug o F) and slug/(ft h), respectively, what ust be the USCS units of theral conductivity in the definition of Pr? Apply the principle of diensional consistency and deterine the units for theral conductivity so that the Prandtl nuber is diensionless. Let [κ] denote the USCS units for theral conductivity: c p µ Pr = κ [ κ ] Btu = slug o F slug ft hr = Btu / hr ft o F Btu / hr ft o F

21 Proble.0: Soe scientists believe that the collision of one or ore large asteroids with the Earth was responsible for the extinction of the dinosaurs. The unit of kiloton is used to describe the energy released during large explosions. It was originally defined as the explosive capability of 00 tons of trinitrotoluene (TNT) high explosive. Because that expression can be iprecise depending on the explosive s exact cheical coposition, the kiloton has been subsequently redefined as the equivalent of x 1 J. In the units of kiloton, calculate the kinetic energy of an asteroid that has the size (box-shaped, 13 x 13 x 33 k) and coposition (density,.4 g/c 3 ) of our solar syste s asteroid Eros. Kinetic energy is defined by 1 U = v where is the object s ass and v is its speed. Objects passing through the inner solar syste generally have speeds in the range of 0 k/s. Volue: Mass: (13k) (13k) (33k) = k 3 ( c 3) = ( k 3) = c 3 g g c 3 = = kg 3 5 c k Speed: k 0 00 = 4 s k s Kinetic energy: 1 ( kg) kiloton kg 4 4 =.68 s s =.68 4 N =.68 4 J ( 4 1 =.68 J ) = kiloton kiloton J - 0 -

22 Proble.1: A structure known as a cantilever bea is claped at one end but free at the other, analogous to a diving board that supports a swier standing on it. Using the following procedure, conduct an experient to easure how the cantilever bea bends. In your answer, report only those significant digits that you know reliably. (a) Make a sall table top test stand to easure the deflection of a plastic drinking straw (your cantilever bea) that bends as a force F is applied to the free end. Push one end of the straw over the end of a pencil, and then clap the pencil to a desk or table. You can also use a ruler, chopstick, or a siilar coponent as the cantilever bea itself. Sketch and describe your apparatus and easure the length L. (b) Apply weights to the end of the cantilever bea, and easure the tip s deflection y using a ruler. Repeat the easureent with at least a half-dozen different weights to fully describe the bea s force-deflection relationship. Penny coins can be used as weights; one penny weighs approxiately 30 N. Make a table to present your data. (c) Next draw a graph of the data. Show tip deflection on the abscissa and weight on the ordinate, and be sure to label the axes with the units for those variables. (d) Draw a best-fit line through the data points on your graph. In principle, the deflection of the tip should be proportional to the applied force. Do you find this to be the case? The slope of the line is called the stiffness. Express the stiffness of the cantilever bea either in the units lb/in or N/. A 1.6 diaeter steel rod was used as the cantilever bea, and it was claped in a vise as shown in Figure 1. Sall weights were held in a plastic bag attached to the bea s free end. The distance between the bea s tip and the surface of the table was easured for each weight, and the data were recorded in Table 1. Beas of three different lengths were tested. Figure shows a graph of force versus tip deflection, H-h, for the 0 c bea length. The deflection is proportional to the force. The slope of the line is.3 N/, or.3 N/. Figure 1: Test stand

23 Proble.1, continued Table 1: Measured tip deflection. Figure : Graph of force versus deflection for the 0 c bea. - -

24 Proble.: Perfor easureents as described in Proble.1 for cantilever beas of several different lengths. Can you show experientally that for a give force F, the deflection of the cantilever s tip is proportional to the cube of its length? As in Proble.1, present your results in a table and a graph, and report only those significant digits that you know reliably. A 1.6 diaeter steel rod was used as the cantilever bea, and it was claped in a vise as shown in Figure 1. Sall weights were held in a plastic bag attached to the bea s free end. The distance between the bea s tip and the surface of the table was easured for each weight, and the data were recorded in Table 1. Beas of three different lengths were tested. Figure shows a graph of tip deflection, H-h, versus bea length for tip forces of 196 N and 39 N. The curve fit indicates that the deflection is proportional to the cube of the length in each case. Figure 1: Test stand. Table 1: Measured tip deflection

25 Proble., continued Figure : Graph of deflection versus bea length for two different applied forces