AIMS Education Foundation

TM Developed and Published by AIMS Education Foundation This book contains materials developed by the AIMS Education Foundation. AIMS (Activities Integrating Mathematics and Science) began in 1981 with a grant from the National Science Foundation. The non-profit AIMS Education Foundation publishes hands-on instructional materials that build conceptual understanding. The foundation also sponsors a national program of professional development through which educators may gain expertise in teaching math and science. Copyright 1993, 2007, 2013 by the AIMS Education Foundation All rights reserved. No part of this book or associated digital media may be reproduced or transmitted in any form or by any means except as noted below. A person purchasing this AIMS publication is hereby granted permission to make unlimited copies of any portion of it (or the files on the accompanying disc), provided these copies will be used only in his or her own classroom. Sharing the materials or making copies for additional classrooms or schools or for other individuals is a violation of AIMS copyright. For a workshop or conference session, presenters may make one copy of any portion of a purchased activity for each participant, with a limit of five activities or up to one-third of a book, whichever is less. All copies must bear the AIMS Education Foundation copyright information. Modifications to AIMS pages (e.g., separating page elements for use on an interactive white board) are permitted only for use within the classroom for which the pages were purchased, or by presenters at conferences or workshops. Interactive white board files may not be uploaded to any third-party website or otherwise distributed. AIMS artwork and content may not be used on non-aims materials. Digital distribution rights may be purchased for users who wish to place AIMS materials on secure servers for school- or district-wide use. Contact us or visit the AIMS website for complete details. AIMS Education Foundation 1595 S. Chestnut Ave., Fresno, CA 93702-4706 888.733.2467 aimsedu.org ISBN: 978-1-881431-85-5 Printed in the United States of America MACHINE SHOP ii 2007 AIMS Education Foundation

Table Of Contents Introduction Meet the Machine Shop s Neighbors... 1 Journal Entries... 3 Friction Journal Entries... 9 All Wound Up... 12 Slip and Slide... 21 Levers Journal Entries... 27 Penny Weight... 33 Clever Lever 1... 38 Sandbagging the Seesaw... 45 Clever Lever 2... 53 Clever Lever 3... 65 Push-a-Door... 76 Lever Assessment... 84 Catapults Journal Entries... 87 May the Force be With You... 90 The Great Catapult Caper... 100 Wheels and Gears Journal Entries... 106 One Good Turn Deserves Another... 110 Gearing Up... 118 Tooth to Tooth... 130 Designer Gears... 137 Pulleys Journal Entries... 155 Meet the Equalizer... 158 Block and Tackle... 165 Pulley Power... 173 Inclined Plane, Wedges, Screws, and Power Journal Entries... 184 Making the Grade... 187 The Plane Truth... 197 Wedge-Ease... 206 Nuts and Bolts... 216 Watt Power... 224 MACHINE SHOP iii 2007 AIMS Education Foundation

To the teacher... Machine Shop is organized with journal entries preceeding the activities that address various types of simple machines. The journal entries are not activities per se but are included to give a story line that contains content information and problem development for students. The story line contains the activities of a youngster who calls herself Fantastic Force. She and her friend, Mucky Mass, explore a machine shop belonging to a mechanical engineer by the name of Handy MacAnnic. Handy encourages Fantastic to discover the uses of various simple machines and the forces that affect them. The journal entries allow students to develop concepts dealing with simple machines, to see applications of the various simple machines, to clarify relevant definitions, and to employ formulae. The journal entries are written using a youngster s terminology and lingo. The activities in Machine Shop can be used without the journal entries as the content information for each lesson is found in the Background Information of the teachers pages.the decision of whether or not to use these journal entries lies with the teacher. Energy and Systems and Interactions are themes that permeate all the investigations in this book. In order to make some of the concepts understandable to students, some units of measurements have been simplified. The intent has been to develop activities that will allow students to get at the most basic concepts and not get lost in the abstract calculations and measurements. We trust our physicist friends will understand. The editors welcome any constructive comments on lesson content, sequencing of lessons, materials recommended, or any other relevant topic. Greedy Fiendish Mucky Fantastic Handy Gravity Friction Mass Force MacAnnic MACHINE SHOP v 2007 AIMS Education Foundation

Supply List This list may help you in assembling the supplies for the activities in this book. acetate film aluminum foil balances bathroom scale blocks of wood (scraps) block of wood 1" x 1" x 6" board 2" x 6" x 8' bolts with nuts 3" long, 1/2" diameter; 3" long, 3/8" diameter bricks broom handles or 1" doweling burlap sacks calculators clay colored pencils cooking spray corrugated cardboard cover stock craft knife design toys such as Spirograph doweling film canisters galvanized wire, 14 gauge gloves glue hammer hand lenses hexagonal pencils hole punch margarine tubs markers masking tape masses meter sticks sturdy, wooden metric tape measures monofilament fishing line nails paper clips paper cup paraffin wax pegboard pieces 1/4" holes, 10 cm x 25 cm pencils pennies (minted after 1982) plain paper plastic cups plastic playing cards pliers polyester thread pushpins ring stand rubber bands rulers marked in millimeters sand sandpaper scissors self-stick removable notes 3" x 3" soap bars spring scales steel washers string synthetic rope 50' x 1/4" diameter tagboard tape 10-speed bicycle thread, heavy duty thread spools large and small thumbtacks toy car vegetable oil washers 1/4" hole, 1 1/4" diameter watch with second hand waxed paper MACHINE SHOP vi 2007 AIMS Education Foundation

Conceptual Overview Machine Shop is written to provide hands-on experience in the mechanics of phys ics for students in grades 5-9. Students are intrigued by how machines work and are amazed how simple machines allow them to increase their force. This natural fascination draws them into the exploration and understanding of some basic concepts of physics. The underlying theme of every activity in this book is the conservation of energy. Ma chines do not create energy to get work done, they only alter the factors of work, the force used, and the distance through which that force moves (Law of the Conservation of Energy). Students progressing through the activities in this book come to realize that given the right machine, they could use their own limited strength to literally move mountains. This concept of energy is coupled with the understanding that every machine involves a trade off: If a ma chine alters a small force to a great force, it requires that small force to go a great distance to make the great force go a small distance. Following is a list of more specific concepts developed in this book and a visual or ga ni za tion of how they are related. General Concepts of Science Energy cannot be created or destroyed; it can be changed from one form to another. Energy comes in many forms. Energy is used to accomplish work. Machines only transfer and transform energy. They cannot create or destroy it. Friction is a force that resists motion. The types of materials in contact and the amount of lubrication between the surfaces affects how much friction occurs. General Concepts about Mechanics Work is done when something is moved. Power is a measure of how fast work is done. The amount of work done on an object is determined by how much force was used to move the object and the distance the object was moved. The amount of energy or work put into a machine will come out of the machine in some form. Mechanical advantage is a comparison of force produced by a machine compared to the force applied to the machine. Mechanical advantage is inversely related to the distance the produced force moves through to the distance the applied force moves through. Efficiency is the measure of how effectively a machine has transferred energy. It is the ratio of work output to total input; or the percentage of work put into a machine that is converted to useful work output. Friction is a major variable that reduces the efficiency of a machine. Friction is a cause for the difference between the expected (ideal) mechanical advantage and the measured (actual) mechanical advantage. Ideal mechanical advantage is the calculated value determined from theoretical understanding. It does not take into account the effect of forces such as friction. Actual mechanical advantage is the comparison of the actual generated force to the applied force. Specific Concepts about Machines A lever transforms energy by inversely changing applied and produced force. This change is made by ad just ing how torque is applied or produced by the lever. Torque is a rotational force generated around a pivot. It is the product of a force and the distance the force is applied from the pivot. Wheels and axles act as modified levers and transform energy, inversely changing applied and produced force. Wheels and axles act as separate lever-arms rotating around a common pivot. Gears are a form of wheel and axle. Pulleys transform energy by dividing the produced force over several support lines. Inclined planes transform energy by changing the required amount of applied force by adjusting the distance over which it must be applied. Screws and wedges are modified inclined planes. MACHINE SHOP vii 2007 AIMS Education Foundation

ENERGY Energy comes in many forms. Energy is used to accomplish work. MECHANICAL EN ER GY The energy due to the position or the movement of something Levers help to lift loads with less effort. The force needed for lifting changes as the dis tance of the effort arm changes. Wheels and axles are turning levers. Gears are toothed wheels. Gears can be used to transfer forces from one part of a ma chine to another. MACHINES A machine is a device for mul ti ply ing forces or changing the direction of forces. Inclined planes can be used to raise objects with less force than a straight lift. Inclined planes are flat, sloping surfaces over which objects can be pushed or pulled to move them to a higher level. A wedge is two inclined planes placed back to back. Pulleys can be used to increase force and/or change the di rec - tion of force. The effort needed to raise the resistance depends on the number of lines of support the pulley system contains. Energy cannot be created or de stroyed; it can be changed from one form to another. The amount of energy or work put into a machine will come out of the machine in some form. A screw is an inclined plane that is wrapped around a shaft. EFFICIENCY Efficiency is the measure of how effectively a machine has transferred energy. Efficiency is the ratio of work output to total input; work put into a machine that is con vert ed to useful work output. Machines lose ef fi cien cy because of friction WORK Work is done when something is moved. The amount of work done is determined by how much force was used to move the object and how far the object was moved. FRICTION POW ER Friction is a force that resists motion. Friction can be reduced. MECHANICAL ADVANTAGE Mechanical advantage is a comparison of force produced by a machine compared to the force applied to the machine. Ideal mechanical advantage is the calculated value determined from theoretical understanding. It does not take into account the effects of forces such as friction. Actual mechanical advantage is the comparison of the actual generated force to applied force. Power is the rate at which work is done. MACHINE SHOP viii 2007 AIMS Education Foundation

Conceptual Assessment The following questions are presented as the type students should be able to an swer after completing the investigations in this book. They do not provide an exhaustive list, but present a model of how questioning might be used to as sess student un der stand ing. The questions should be used with a picture or sam ple of a simple machine. What simple machine is this? Where is work put into (applied to) this machine? Where does work come out of this machine? How does this machine alter the force that is put into it (applied)? Explain how you know if this machine will increase or decrease the force put into it. How can you determine how much this machine will alter the force put into it? Explain how you know if the distance the applied force moves will be greater or less than the distance the output force moves. How does the distance and force applied to this machine relate to the distance and force generated by this machine? How could you test to see if you were correct on your predictions about force and dis tance on this machine? Explain what might cause the actual outcome to be different from your pre dic tion. How will friction affect this machine? How could you make this machine more efficient? What are some examples of other uses for this machine? What could you change about this machine to alter the applied force? Why would you choose to use this machine rather than to do the job without it? What drawbacks would exist for using this machine? MACHINE SHOP ix 2007 AIMS Education Foundation

Science Pro cess ing Skills Observing Classifying Measuring Comparing Collecting and recording data Interpreting data Predicting/inferring Identifying and controlling variables Making and testing hypotheses Applying/generalizing/concluding All Wound Up X X X X X X X Slip and Slide X X X X X Penny Weight X X X X X X Clever Lever 1 X X X X X X Sandbagging the Seesaw X X X X X X X Clever Lever 2 X X X X X Clever Lever 3 X X X X X X Push-a-Door X X X X X X X May the Force be With You X X X X X X X X The Great Catapult Caper X X X X X X X X One Good Turn Deserves Another X X X X X X X Gearing Up X X X X X X X Tooth to Tooth X X X X X Designer Gears X X X X X Meet the Equalizer X X X X X Block and Tackle X X X X X X X Pulley Power X X X X X Making the Grade X X X X X X X The Plane Truth X X X X X X X Wedge-Ease X X X X X Nuts and Bolts X X X X X Watt Power! X X X X X X MACHINE SHOP x 2007 AIMS Education Foundation

Math Content Using computation Using rational numbers Estimating Measuring Graphing Averaging Identifying/analyzing patterns Using geometry and spatial sense Using/applying formulae Using calculators Using positive and negative integers All Wound Up X X X X Slip and Slide X X X X X Penny Weight X X Clever Lever 1 X X X X Sandbagging the Seesaw X X X X Clever Lever 2 X X X X X Clever Lever 3 X X X X X Push-a-Door X X X May the Force be With You X X X X X X The Great Catapult Caper X X X X X X One Good Turn Deserves Another X X X Gearing Up X X X Tooth to Tooth X X Designer Gears X X Meet the Equalizer X X X X Block and Tackle X X X Pulley Power X X X X X Making the Grade X X X X X The Plane Truth X X X Wedge-Ease X X X X X Nuts and Bolts X X X X Watt Power! X X X X X MACHINE SHOP xi 2007 AIMS Education Foundation

Topic Inclined planes, forces Key Question What type of surface is best for making a slide? Learning Goals Students will: measure the degree of slope required to overcome friction on different surfaces, and apply a lubricant to the surfaces to test its effect. Guiding Documents Project 2061 Benchmarks In the absence of retarding forces such as friction, an object will keep its direction of motion and its speed. Whenever an object is seen to speed up, slow down, or change direction, it can be assumed that an unbalanced force is acting on it. Find the mean and median of a set of data. NRC Standards The motion of an object can be described by its position, direction of motion, and speed. That motion can be measured and represented on a graph. Use appropriate tools and techniques to gather, analyze, and interpret data. NCTM Standards 2000* Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision Represent data using tables and graphs such as line plots, bar graphs, and line graphs Math Measurement angles Averaging Graphing Science Physical science simple machines Integrated Processes Observing Collecting and recording data Interpreting data Drawing conclusions Applying Materials For each group: scissors glue tape flat 30 cm ruler plastic 35 mm film canister 10 pennies vegetable oil 2.5 cm x 10 cm strips of each of the following: plain paper overhead acetate film aluminum foil fine sandpaper hand lenses, optional Background Information Friction is the force that acts to resist motion when surfaces are in contact with each other. It is caused by the irregularities in the surfaces of materials. Every surface has bumps and hollows so that when two surfaces are rubbed together, the bumps and hollows catch and stick to resist the movement of the surfaces over each other. Friction makes it hard to push one material across another. The amount of friction between two objects is de pen dent upon the types of surfaces involved. Smooth sur fac es produce less friction than rough surfaces. More force is needed to start an object sliding than to keep it sliding because starting friction is greater than sliding friction. And likewise, less force is needed to roll objects than to slide them because rolling friction is less than sliding friction. In rolling friction, the roller or wheel has less surface area in contact with another surface to catch in the bumps and hollows. Making the surfaces smoother by leveling out the bumps and hollows reduces the friction between them. Slippery ma te ri als called lu bri cants (in this activity, veg e ta ble oil) reduce friction. The lubricant is placed between the two surfaces, filling in and leveling out the bumps and hollows. MACHINE SHOP 21 2007 AIMS Education Foundation

As the slope of an incline is increased, the force of gravity acting down the incline increases. It is this part of the force of gravity on the object that will cause it to move down the incline. Without any friction, even the tiniest slope angle will cause the object to move down the incline. But when friction is present, no motion will take place unless the force of gravity acting down the incline becomes larger than the force of friction. In this activity, the amount of friction between two surfaces will be determined to be large or small. If the angle of inclination is large when motion occurs, it means more force was needed to overcome friction, hence friction is greater. Management 1. This activity is best done in groups of four: one student to raise the ruler, one to measure the angle, the third to change the surfaces, and the last to record the results. 2. Allow one class period (45 minutes) for this activity. 3. If possible, copy the protractor and stand page onto cover stock. This stronger weight paper will stand up better to student use. 4. Smooth plastic is a relatively slippery surface. Film canisters are used to take advantage of this char ac ter is tic. By placing the ten pennies inside, the can is ter will provide enough weight to achieve adequate re sults. If film canisters cannot be found, other objects may be substituted, but the teacher should try out the sub sti tu tion before class to judge its effectiveness. 5. A thick coat of vegetable oil is needed to act as a lubricant. As this tends to be quite messy, it is ad vis able to protect the desk or table surface with several layers of newspaper. Procedure 1. Discuss the Key Question. 2. Distribute materials and instruct students to cut out, fold, and glue the protractor and stand as explained on the student page. 3. Have students tape the stand to the table so the pro trac tor is in a vertical position. 4. Using tape as a hinge, have students tape the ruler to the mark on the protractor stand. The smoothest side of the ruler should be face up. 5. If you are using the optional hand lenses, invite stu dents to observe the various surface textures of the paper, acetate film, aluminum foil, and sand paper. 6. Have students tape the paper strip to the top side of the ruler. 7. Direct students to place the bottom of the film can is ter, which is filled with the ten pennies, on top of the strip of paper. 8. Instruct one student to slowly raise the free end of the ruler until the canister begins to move. 9. Invite another student to measure and record the angle at which the canister starts to slide. 10. Have students place the ruler flat on the table with the film canister in its original position and repeat steps eight through 10 two more times, recording the results for each trial. 11. Tell students to complete the chart. 12. Have them repeat the procedure for the over head acetate film, the aluminum foil, and the sandpaper. 13. Ask students to heavily lubricate each strip of material and the bot tom of the canister with the vegetable oil. 14. Have them repeat the procedure with the lu bri cant and record the measurements on the second chart. 15. Have students make a bar graph of their data. Connecting Learning 1. What material allowed the canister to slip at the lowest angle? [Answers may vary. Plastics tend to be slippery so the acetate is usually the lowest. Sandpaper is very rough and tends to be the highest] 2. What material caused the least friction? How did you determine this? 3. How did the lubricant affect friction on each of the four materials? What problems were created when ap ply ing the lubricant? Could these problems be over come? Explain. [Paper tends to absorb oil and often becomes tacky. If enough lubricant is used, the object will float on the lubricant. The sandpaper is so rough that the lubricant has little effect.] 4. How does the graph display this information? 5. If you wanted to make the best slide, how would you make it? Extensions 1. Discuss other variables that might affect friction. [weight of object, other contact surfaces, other lu bri cants] Have students devise their own ex per i ments and test these variables. 2. Have students study the soles of shoes for dif fer enc es in construction and materials and how the con struc tion and materials affect the amount of friction they provide. Dis cuss why the soles are dif fer ent for such sports as basketball and bowling. Have stu dents de vise a test to rank shoes by amount of friction. 3. Discuss with students the positive and negative as pects of friction. Have them find as many ex am ples of each as they can. Major Conceptual Components Energy is used to accomplish work. Work is done when something is moved. Friction is a force that resists mo tion. Friction can be reduced. * Reprinted with permission from Principles and Standards for School Mathematics, 2000 by the National Council of Teachers of Mathematics. All rights reserved. MACHINE SHOP 22 2007 AIMS Education Foundation

Key Question What type of surface is best for making a slide? Learning Goals measure the degree of slope required to overcome friction on different surfaces, and apply a lubricant to the surfaces to test its effect. MACHINE SHOP 23 2007 AIMS Education Foundation

85 80 75 70 65 60 55 50 45 40 Attach mark for brace 35 30 25 20 15 Attach mark for brace 90 0 Fold forward along line above so protractor is vertical and this part is face up on table. After making the protractor unit and taping it to the table, attach ruler with tape so it hinges on the line to the left and covers this writing. Fold back along line above so that this side faces the table and serves as the base. 10 5 Cut out the rectangle to the left along the exterior bold line, then follow the instructions. Fold back along the line above so that this side makes a diagonal brace to hold the protractor in a vertical position. Fold back along the line above and use this as a tab to attach the brace to the protractor. Make sure the protractor will stand vertically before attaching. MACHINE SHOP 24 2007 AIMS Education Foundation

Trial 1 Trial 2 Trial 3 Total Average Trial 1 Trial 2 Trial 3 Total Average Paper Plastic Degrees of Incline Aluminum Foil Paper Plastic Degrees of Incline Aluminum Foil 50 45 40 35 30 25 20 Degrees of Incline Without Lubricant With Lubricant What surface makes the best slide? Average Degrees of Incline for Different Surfaces With and Without Lubricant With Lubricant Without Lubricant With Lubricant Without Lubricant With Lubricant Without Lubricant With Lubricant Without Lubricant 15 10 5 0 Paper Plastic Aluminum Foil Sandpaper Sandpaper Sandpaper MACHINE SHOP 25 2007 AIMS Education Foundation

Connecting Learning 1. What material allowed the canister to slip at the lowest angle? 2. What material caused the least friction? How did you determine this? 3. How did the lubricant affect friction on each of the four materials? What problems were created when ap ply ing the lubricant? Could these problems be over come? Explain. 4. How does the graph display this information? 5. If you wanted to make the best slide, how would you make it? MACHINE SHOP 26 2007 AIMS Education Foundation