EVERYDAY EXAMPLES OF ENGINEERING CONCEPTS

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1 EVERYDY EXMPLES OF ENINEERIN CONCEPTS D4: Ipulse & oentu Copyright 04 This work is licensed under the Creatie Coons ttribution-noncoercial-noderis 3.0 Unported License. To iew a copy of this license, isit or send a letter to Creatie Coons, 444 Castro Street, Suite 900, Mountain View, California, 9404, US. Eeryday Exaples fro of 5

2 This is an extract fro 'Real Life Exaples in Dynaics: Lesson plans and solutions' edited by Eann. Patterson, first published in 006 (ISN: ) which can be obtained online at and contains suggested exeplars within lesson plans for Sophoore Solids Courses. Prepared as part of the NSF-supported project (#043756) entitled: Enhancing Diersity in the Undergraduate Mechanical Engineering Population through Curriculu Change". INTRODUCTION (fro 'Real Life Exaples in Dynaics: Lesson plans and solutions') These notes are designed to enhance the teaching of a junior leel course in dynaics, increase the accessibility of the principles, and raise the appeal of the subject to students fro dierse backgrounds. The notes hae been prepared as skeletal lesson plans using the principle of the 5Es: Engage, Explore, Explain, Elaborate and Ealuate. The 5E outline is not original and was deeloped by the iological Sciences Curriculu Study in the 980s fro work by tkin and Karplus in 96. Today this approach is considered to for part of the constructiist learning theory and a nuber of websites proide easy-to-follow explanations of the 3. These notes are intended to be used by instructors and are written in a style that addresses the instructor, howeer this is not intended to exclude students who should find the notes and exaples interesting, stiulating and hopefully illuinating, particularly when their instructor is not utilizing the. In the interest of breity and clarity of presentation, standard deriations and definitions are not included since these are readily aailable in textbooks which these notes are not intended to replace but rather to suppleent and enhance. Siilarly, it is anticipated that these lessons plans can be used to generate lectures/lessons that suppleent those coering the fundaentals of each topic. It is assued that students hae acquired a knowledge and understanding of topics usually found in a Sophoore leel course in Statics, including free-body diagras and efficiency. This is the second in a series of such notes. The first in the series entitled Real Life Exaples in Mechanics of Solids edited by Eann Patterson (ISN: ) was produced in 006 and is aailable on-line at cknowledgeents Many of these exaples hae arisen through liely discussion in the consortiu supported by the NSF grant (#043756) on Enhancing Diersity in the Undergraduate Mechanical Engineering Population through Curriculu Change and the input of these colleagues is cheerfully acknowledged as is the support of National Science Foundation. Eann. Patterson.. riffith Chair of Structural Materials and Mechanics School of Engineering, Uniersity of Lierpool, Lierpool, UK & Royal Society Wolfson Research Merit ward Recipient Englean, Laura (ed.), The SCS Story: History of the iological Sciences Curriculu Study. Colorado Springs: SCS, 00. tkin, J. M. and Karplus, R. (96). Discoery or inention? Science Teacher 9(5): e.g. Trowbridge, L.W., ybee, R.W., ecoing a secondary school science teacher. Merrill Pub. Co. Inc., 990. Eeryday Exaples fro of 5

3 KINETICS OF PRTICLES 4. Topic: Ipulse & oentu Engage part I: ring a tennis racket and a ball (or two) into class plus a eter rule. Drop a tennis ball on the floor and let it bounce freely. Do this a nuber of ties and ask the class to count the nuber of bounces the ball rolls across the floor. Explore part I: sk the class why the ball does not bounce back to the sae height, i.e. why the height of rebound decays. Explain that the ball loses a fraction of its echanical energy with each ipact with the floor. Since the conseration of energy ust apply, ask the class to identify what happens to the lost energy. Explain that it is dissipated in acoustical energy (they can hear the bounce) and heat. Those that hae played squash will know that the ball wars up sufficiently during a gae to feel the teperature difference. Note that the sound of the bounce changes with successie bounces, with the ipact surface and with the height of the initial drop. Use the eter rule to drop it fro different heights in order to illustrate this effect. Explain part I: ball of ass, on released fro a height, h has a potential energy, PE = gh; hitting the floor it bounces to height, d where it has a potential energy, PE = gd. The coefficient of restitution, e = (d/h) and is equal to the fraction of echanical energy lost. This fraction is the sae for successie bounces, i.e. e d h d d d 3 d d where d, d, d 3, d 4 are the heights of successie bounces. 4 d 3 The coefficient of restitution of a tennis ball bouncing on a concrete floor is about 0.7 so if the ball is dropped fro the height of successie bounces will be d = e h = 0.7 = 0.5 and d = 0.5, d 3 = 0.3, d 4 = 0.07 Engage part II: Place a second tennis ball on a bench and roll the first one into it with sufficient oentu to cause the both to oe the ipact. Eeryday Exaples fro 3 of 5

4 Explore part II: Explain how conseration of energy causes kinetic energy fro the oing ball, ipact to be conerted to strain energy of deforation for both balls whilst they are in contact and then restituted as kinetic energy in both balls ipact. The coefficient of restitution can also be defined in ters of elocities, so for two balls (particles), and : e Elaborate In a tennis achine (for an exaple goto and type in tennis achine 4 ) tennis ball rolls down a chute fro a ertical height of 0.5 and ipacts tennis ball at the botto of the chute, we can calculate the elocity at the instant ipact by conseration of energy. The kinetic energy of the ball, at the botto of the chute equals its potential energy at the top, i.e. gh so gh Now considering the coefficient of restitution in ters of elocities, assuing ball is stationary the ipact: e so Now applying the principle of conseration of oentu: and = so and or 0. 3 and In other words the stationary ball oes off at.9 and the ipacting ball at 0.3. Ealuate sk students to attept the following exaples: Exaple 4. 4 year-old boy weighing 5kg is sitting on the botto edge of a waterslide (with his legs dangling in the swiing pool) when his 7 year-old sister weighing kg coes down the slide 4 Eeryday Exaples fro 4 of 5

5 fro a height of 3. ssuing the end of the slide is horizontal and neglecting friction, calculate the elocity of the boy ipact if (a) his sister grabs hi and they oe off together and (b) if they separate contact with a coefficient of restitution of 0.8. Solution: (a) For the girl (subscript ), the kinetic energy ipact is equal to her potential energy at top of slide: So gh and gh So in case (a) applying conseration of oentu using subscript for the boy: with and i.e. they will shoot off the slide together at a elocity of 4.6 (0 ph) horizontally. (b) for a coefficient of restitution of e = 0.8 e 7. 67e and now applying conseration of oentu: thus and 7.7e so 7.7e i.e. the boy slides off the slide at 8 (8 ph) and the girl follows at (4 ph). Exaple 4. sk students to identify other eents with which they are failiar that can be analyzed in this way and then to select one and perfor a siilar analysis to the one aboe Eeryday Exaples fro 5 of 5