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1 Rotational Equilibrium: A Question of Balance Teacher In Service Program (TISP) Cape Town, South Africa Moshe Kam and Douglas Gorham IEEE Educational Activities 4 August 2006

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2 Who are we? l This weekends workshop is a joint activity of two organizational units of IEEE l The IEEE Educational Activities Board (EAB) l The IEEE South Africa Section (est. 1977) l IEEE is a transnational organization dedicated to engineering, technology and science l Established in 1963 by two associations l AIEE (est. 1884) and IRE (est. 1912)

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3 Attributes of IEEE l Largest engineering association in the world l 360,000 members in 150 countries l Major publisher and organizer of conferences l Major developers of standards l Provider of communication and networking opportunities for engineers, scientists, and technology practitioners l A public charity, dedicated to serving the public l Guided and lead by VOLUNTEERS

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4 What do you need to know about TISP? (1) l It is a program of IEEE l Specifically, IEEEs Educational Activities Board (EAB) l It is about using IEEE volunteers to help pre- university teachers l Teachers of technology, mathematics, and science

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5 What do you need to know about TISP? (2) l The basic idea: present teachers with lesson plans that they can use to enhance student understanding of Engineering and Engineering Design l The ultimate outcome is classroom activities with students about Engineering l We are concentrating, however, on interacting with the teachers l Success = teachers take our lesson plans to their classrooms l All TISP lesson plans need to be aligned with national curriculum standards

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6 What are we going to do today? l Simulate a TISP activity l Provide an opportunity for volunteers to experience first hand what we are trying to do with teachers l Motivate IEEE volunteers to conduct TISP sessions with educators throughout the pre-university educational system in South Africa

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7 Lesson content l We will build a Mobile to meet specifications l Including basic calculations of design parameters l In teams of 2 l We will develop specifications for a second Mobile and then build it

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8 How does this lesson align with Educational Standards in South Africa ?

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9 Alignment to National Curriculum Statements l Critical Outcomes l As a result of the activities, all learners should develop and demonstrate the ability to; l identify and solve problems and make decisions using critical and creative thinking; l work effectively with others as members of a team, group, organisation and community; l organise and manage themselves and their activities responsibly and effectively; l collect, analyse, organise and critically evaluate information; l communicate effectively using visual, symbolic and/or language skills in various modes; l use science and technology effectively and critically showing responsibility towards the environment and the health of others; and l demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.

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10 Learning Outcomes of Mathematics: Grade 10 l As a result of the activities, all learners should develop and demonstrate the ability to; l Generate as many graphs as necessary, initially by means of point- by-point plotting, supported by available technology, to make test conjectures and hence to generalise the effects of the parameters a and g on the graphs of the functions.(10.2.2) l Investigate, generalise and apply the effect of the following transformations of the point (x; y): l A translation of p units horizontally and q units vertically; l A reflection in the x-axis, the y-axis or the line y = x. (10.3.4) l Demonstrate an appreciation of the contribution to the history of the development and use of geometry and trigonometry by various cultures through a project. (10.3.7)

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11 Learning Outcomes of Physical Science: Grade 10 l As a result of the activities, all learners should develop and demonstrate the ability to; l plan and conduct a scientific investigation to collect data systematically with regard to accuracy, reliability and the need to control one variable. (10.1.1) l seek patterns and trends in information collection and link it to existing scientific knowledge to help draw conclusions. (10.1.2) l Communicate information and conclusions with clarity and precision (10.1.4) l Apply scientific knowledge in familiar, simple contexts. (10.2.2)

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12 Learning Outcomes of Mechanical Technology: Grade 10 l As a result of the activities, all learners should develop and demonstrate the ability to; l present assignments by means of a variety of communication media. (10.2.5) l describe the functions of appropriate basic tools and equipment (10.3.2) l explain the use of semi-permanent joining applications (10.3.5) l distinguish between different types of forces found in engineering components by graphically determining the nature of these forces (10.3.6)

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13 Learning Outcomes of Civil Technology Grade 10 l As a result of the activities, all learners should develop and demonstrate the ability to; l present assignments by means of a variety of communication media. (10.2.5) l describe the properties and the use of materials in the built environment. (10.3.2) l describe functions, use and care of basic tools and equipment. (10.3.3) l demonstrate an understanding of applicable terminology. (10.3.5) l distinguish between different types of forces found in load bearing structures. (10.3.6) l list different manufacturing process or construction methods. (10.3.7) l identify quantities of materials for small projects. (10.3.9) l explain the use of different joining applications. (methods) ( )

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14 Todays activity: Build a Mobile

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15 Focus and Objectives l Focus: demonstrate the concept of rotational equilibrium l Objectives l Learn about rotational equilibrium l Solve simple systems of algebraic equations l Apply graphing techniques to solve systems of algebraic equations l Learn to make predictions and draw conclusions l Learn about teamwork and working in groups

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16 Anticipated Learner Outcomes l As a result of this activity, students should develop an understanding of l Rotational equilibrium l Systems of algebraic equations l Solution techniques of algebraic equations l Making and testing predictions l Teamwork

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17 Concepts the teacher needs to introduce l Mass and Force l Linear and angular acceleration l Center of Mass l Center of Gravity l Torque l Equilibrium l Momentum and angular momentum l Vectors l Free body diagrams l Algebraic equations

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18 Theory required l Newtons first and second laws l Conditions for equilibrium F = 0 (Force Balance)Translational = 0 (Torque Balance)Rotational l Conditions for rotational equilibrium l Linear and angular accelerations are zero l Torque due to the weight of an object l Techniques for solving algebraic equations l Substitution, graphic techniques, Cramers Rule

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19 Mobile l A Mobile is a type of kinetic sculpture l Constructed to take advantage of the principle of equilibrium l Consists of a number of rods, from which weighted objects or further rods hang l The objects hanging from the rods balance each other, so that the rods remain more or less horizontal l Each rod hangs from only one string, which gives it freedom to rotate about the string 3 August 2006

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20 Historical Origins l Name was coined by Marcel Duchamp in 1931 to describe works by Alexander Calder l Duchamp l French-American artist, l Associated with Surrealism and Dada l Alexander Calder l American artist, l Inventor of the Mobile

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23 Lobster Tail and Fish Trap, 1939, mobile Hanging Apricot, 1951, standing mobile Standing Mobile, 1937 Mobile, 1941

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24 Alexander Calder on building a mobile "I used to begin with fairly complete drawings, but now I start by cutting out a lot of shapes.... Some I keep because they're pleasing or dynamic. Some are bits I just happen to find. Then I arrange them, like papier collé, on a table, and "paint" them -- that is, arrange them, with wires between the pieces if it's to be a mobile, for the overall pattern. Finally I cut some more of them with my shears, calculating for balance this time." Calder's Universe, 1976.

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25 Our Mobiles l Version 1 l A three-level Mobile with four weights l Tight specifications l Version 2 l An individual design under general constraints

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26 Version 1 l A three-level four-weight design Level 1 Level 2 Level 3

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27 Materials l Rods made of balsa wood sticks, 30cm long l Strings made of sewing thread or fishing string l 5-cent coins l 240 weight paper (cardboard) l Adhesive tape l Paper and pens/pencils

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28 Tools and Accessories l Scissors l Hole Punchers l Pens l Wine/water glasses l Binder clips l 30cm Ruler l Band Saw (optional) l Marking pen l Calculator (optional)

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29 Instructions and basic constraints l Weights are made of two 5 cent coins taped to a circular piece of cardboard l One coin on each side l If you wish to do it with only one coin it will be slightly harder to do l Each weight is tied to a string l The string is connected to a rod 5mm from the edge

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30 5 mm

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31 Level 1 Level 2 Level 3 5 mm Rods of level 3 and 2 are tied to rods of level 2 and 1 respectively, at a distance of 5mm from the edge of the lower level rod

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32 Designing the Mobile Level 3 l W x 1 = W y 1 l x 1 + y 1 = 290 Level 2 l 2W x 2 = W y 2 l x 2 + y 2 = 290 Write and solve the equations for x i And y i (i=1,2,3) 290 mm

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33 Level 1 3W x 3 = W y 3 x 3 + y 3 = 290

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34 Solve Equations for Level 1 3 W x 3 = W y 3 (1) x 3 + y 3 = 290(2) From (1): y 3 = 3x 3 (3) Substitute (3) in (2): 4x 3 = 290 or x 3 = 72.5mm (4) From (2) y 3 = 290 – x 3 or y 3 = 217.5mm(5) By substitution

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35 Solve Equations for Level 1 3 W x 3 = W y 3 (1) x 3 + y 3 = 290(2) From (1): y 3 = 3x 3 or 3x 3 -y 3 =0(3) From (1) and (2) using Cramers rule Using Cramers Rule

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36 Solve Equations for Level 1 Generate points for: Y 3 = 3X 3 Y 3 = X 3 Using Graphics

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37 Numerical values for graph x3y3y3x3y3y3

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38 The intersection is at x=72.5mm y=217.5mm x and y in mm

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39 Graphic solution from handout

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40 Activity 1: Build Version-1 Mobile l Record actual results l Compare expected values to actual values l Explain deviations from expected values

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41 Hints l Sewing strings much easier to work with than fishing string l Use at least 30cm strings to hang weights l Use at least 40cm strings to connect levels l If you are very close to balance, use adhesive tape to add small amount of weight to one of the sides

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42 Version 2 l Design a more complicated mobile l More levels (say 5) l Three weights on lowest rod, at least two on each one of the other rods l Different weights l First, provide a detailed design and diagram with all quantities l Show all calculations, specify all weights, lengths, etc. l Then, build, analyze and provide a short report

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43 Report l Description of the design, its objectives and main attributes l A free body diagram of the design l All forces and lengths should be marked l Key calculations should be shown and explained l A description of the final product l Where and in what areas did it deviate from the design l Any additional insights, comments, and suggestions

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44 Questions for Participants l What was the best attribute of your design? l What is one thing you would change about your design based on your experience? l What approximations did we make in calculating positions for strings? How did they affect our results? l How would the matching of design to reality change if we… l Used heavier weights l Used heavier strings l Used strings of different lengths connected to the weights l Used heavier rods l To educators: Can you implement this lesson plan in your classroom?

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45 Questions, comments, reflections

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