EVERYDAY EXAMPLES OF ENGINEERING CONCEPTS

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1 EVERYDAY EXAMPLES OF ENGINEERING CONCEPTS D3: Work & Ener Copriht 03 This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a cop of this license, visit or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 9404, USA. Everda Eamples from of6

2 This is an etract from 'Real Life Eamples in Dnamics: Lesson plans and solutions' edited b Eann A. Patterson, first published in 006 (ISBN: ) which can be obtained online at and contains suested eemplars within lesson plans for Sophomore Solids Courses. Prepared as part of the NSF-supported project (#043756) entitled: Enhancin Diversit in the Underraduate Mechanical Enineerin Population throuh Curriculum Chane". INTRODUCTION (from 'Real Life Eamples in Dnamics: Lesson plans and solutions') These notes are desined to enhance the teachin of a junior level course in dnamics, increase the accessibilit of the principles, and raise the appeal of the subject to students from diverse backrounds. The notes have been prepared as skeletal lesson plans usin the principle of the 5Es: Enae, Eplore, Eplain, Elaborate and Evaluate. The 5E outline is not oriinal and was developed b the Bioloical Sciences Curriculum Stud in the 980s from work b Atkin and Karplus in 96. Toda this approach is considered to form part of the constructivist learnin theor and a number of websites provide eas-to-follow eplanations of them 3. These notes are intended to be used b instructors and are written in a stle that addresses the instructor, however this is not intended to eclude students who should find the notes and eamples interestin, stimulatin and hopefull illuminatin, particularl when their instructor is not utilizin them. In the interest of brevit and clarit of presentation, standard derivations and definitions are not included since these are readil available in tetbooks which these notes are not intended to replace but rather to supplement and enhance. Similarl, it is anticipated that these lessons plans can be used to enerate lectures/lessons that supplement those coverin the fundamentals of each topic. It is assumed that students have acquired a knowlede and understandin of topics usuall found in a Sophomore level course in Statics, includin free-bod diarams and efficienc. This is the second in a series of such notes. The first in the series entitled Real Life Eamples in Mechanics of Solids edited b Eann Patterson (ISBN: ) was produced in 006 and is available on-line at Acknowledements Man of these eamples have arisen throuh livel discussion in the consortium supported b the NSF rant (#043756) on Enhancin Diversit in the Underraduate Mechanical Enineerin Population throuh Curriculum Chane and the input of these colleaues is cheerfull acknowleded as is the support of National Science Foundation. Eann A. Patterson A.A. Griffith Chair of Structural Materials and Mechanics School of Enineerin, Universit of Liverpool, Liverpool, UK & Roal Societ Wolfson Research Merit Award Recipient Enleman, Laura (ed.), The BSCS Stor: A Histor of the Bioloical Sciences Curriculum Stud. Colorado Sprins: BSCS, 00. Atkin, J. M. and Karplus, R. (96). Discover or invention? Science Teacher 9(5): e.. Trowbride, L.W., Bbee, R.W., Becomin a secondar school science teacher. Merrill Pub. Co. Inc., 990. Everda Eamples from of6

3 KINETICS OF PARTICLES 3. Topic: Work & Ener Enae: Brin a slinshot and a handful of rubber balls into class, pull the elastic band back and release a few rubber balls into the class. Eplore: Remind students about the basic meanin of conservation of ener. Ask students to work in pairs and to identif the conservation of ener durin the loadin, firin and trajector of the balls. Invite some pairs to talk throuh to the class their understandin of the ener conversions. Discuss how strain ener stored in the slin material is transferred as work to the ball and becomes kinetic ener. Ask them in their pairs to reconsider conservation of ener durin loadin, firin and fliht of projectile. Eplain: Applin the principle of work and ener to the rubber ball durin firin: KE U KE where KE and KE are the initial and final kinetic eneries of the ball respectivel and U - is the work done b all the eternal and internal forces actin on the ball between the initial and final state. B definition, kinetic ener, KE mv, and KE = 0 (because v =0). The work done on the ball durin firin is the strain ener released from the slin shot which was stored in the material as it was stretched, U uv where u is the specific strain ener at ield and V is the volume of material and assumin the slin shot is stretched to the limit of its elastic behavior. Durin fliht potential ener mabe ained or lost with heiht but this is neliible compared to the kinetic ener at launch. Some kinetic ener will be lost due to dra but aain it is small so that the ball will arrive at its taret with a substantial portion of the launch kinetic ener. Everda Eamples from 3 of6

4 Elaborate The strain ener stored at ield in an elastic band is u = 3.6 MJ/m 3 ; if it is of lenth, 50mm with a cross-section of 6mm and volume, V of 400mm 3, then the ener stored when it is pulled to ield is (see chapter 6 in Real Life Eamples in Mechanics of Solids): U uv so for a ellow dot squash ball of mass 4 with initial kinetic ener KE =0: U 8.6 KE U KE mv and v 7 ms - 3 m 40 If the ball is launched parallel to the round from a heiht of.5m, then its rane can be calculated usin kinematics (nelectin dra) since in the vertical direction: s =.5m, v =0 = 0, and a = = 9.8m/s, J so v v 0 a s and v a s m/s and v v v at so t 0. 8 s a 9.8 In the horizontal direction (nelectin dra): s v t a t so the slinshot has a rane of almost 7.5m. (Note: potential ener ained in fliht is (mh = = ) 0.35J or 4% of the kinetic ener at launch). m Evaluate Ask students to do the followin eamples: Eample 3. A two-slice toaster is switched on b depressin a slider which causes the slices of bread to be drawn downwards into the toaster between the heatin elements and also etends a sprin at each end of the toaster. When the toast is read a pair of triers releases both sprins simultaneousl which in turn provide an impulse to the toast so that it pops up. A tpical slice of bread is 5mm 5mm and has a mass of 40, and in the off position a slice sits with two-thirds of its lenth inside the toaster. (a) Calculate the force which must be applied to the slider so that toast pops up but just does not come out of the toaster when it is read, nelectin the weiht of the mechanism and assumin there are no losses in it. (b) If the toaster is redesined with each slot rotated outwards so that the plane of the slice is at 60 to the horizontal table top and two additional identical sprins are fitted; then how far awa from their respective slots will the slices land if the effect of the shape of slice is nelected. Everda Eamples from 4 of6

5 Solution (a) Toast must not jump hiher than minimum depth of slot lenth of a slice of bread At top of jump, vertical velocit, v = v = 0 thus usin v a s ms - v a v Hence the kinetic ener received b each slice from the sprins at launch is: KE mv J To store this much ener in a sprin the work done (W) on the sprins is KE W Fd where F is the force applied and moved throuh a distance d. Since in the restin position the bread is two-thirds within the toaster the available travel for the slider, d m. W So F. 8N d For the two-slice toaster the force that needs to be applied is.35n (=.8 ) 3 s (b) With the additional sprins the ener stored will be doubled, i.e. the kinetic ener delivered to each slice will be 0.098J (= ). KE Thus, the eit velocit will be v. ms - from m 0.04 The vertical component will be v vsin 60.sin ms - KE mv and the horizontal component, v vcos60.cos ms - For time to top of fliht:.9 v v at and v = 0 so t 0. 9s 9.8 The time for the rise and fall to the top of the fliht is 0.39 seconds (=0.9), and distance travelled horizontall is v t at i.e. each slice will land 430mm awa from the toaster. s m Everda Eamples from 5 of6

6 Eample 3. Estimate the rane of a lonbow of the tpe used in medieval Enland (e.. b Robin Hood). Such bows are about m lon, made of ew with a draw of about 0.76m and were used with arrows havin a mass of about 50. The draw force has been estimated to be about 65N. To see a lonbow in action just tpe lonbow in ( Solution: The incremental work done, W b the archer as the bow is pull back (drawn) over a incremental distance, d is iven b W Fd, so interatin this over the total draw ives the total work done, W Fd J assumin the draw force is linearl related to the draw, i.e. the bow has a constant stiffness. This work is stored as strain ener in the bow and, when the arrow is released, it is transferred to the arrow as kinetic ener, i.e. U 0 KE U KE mv and v ms - m If the arrow is launched at an anle, to the round then the vertical component of velocit is v 0 vsin and horizontal component is v 0 vcos. The time of fliht can be calculated as the twice the time required to reach its maimum heiht when its vertical velocit, v = 0, i.e. v v 0 a t and v t a 0 vsin The distance travelled horizontall durin time, t will be s v t at thus v s vcos t cos sin ds v For maimum rane 0 cos sin d v 63.6 Hence substitutin in s cos sin 4 m 9.8 sin i.e. and =45 cos Replica lonbows have been shown to have a rane of about 300m so this estimate is a little lon which is unsurprisin since dra and ener losses were nelected. Everda Eamples from 6 of6