Work and Energy Simple

™ Real Investigations in Science and Engineering Overview Chart for Investigations–Simple Machines Investigation Key Question Summary Learning Goals Vocabulary A1 Ropes and Pulleys How can ropes and Students define , identify • Develop an understanding of force force Pages 1–8 pulleys be used to input and output in a and how it can be measured. gravity 50 minutes lift large weights simple , and discover • Identify input and output force on a input force with small forces? how a rope-and- machine . newton can multiply force. • Discover how a simple machine can output force be used to multiply force. rope-and-pulley system simple machine weight A2 What Is Work? How can a Students measure the length • Discover the relationship between friction Pages 9–16 simple machine of string that they must pull in the number of pulleys utilized in a input distance 50 minutes multiply forces? order to lift the bottom block a simple machine and the distance input work certain height when using one the string is pulled to lift the load. joule or more pulleys. Students learn • Define work as force (newtons) output distance the scientific definition of work, multiplied by distance (meters). output work calculate input and output work • Calculate and compare input work in their rope-and-pulley system, and output work in a rope-and- work and discover that output work pulley machine. cannot exceed input work. • Explain why output work can never exceed input work. A3 The How does a Students work together to • Describe how a lever works. fulcrum Pages 17–24 lever work? balance using various • Identify the relationship between input arm 50 minutes combinations of weights placed input force, output force, input arm, lever at different distances from the and output arm on a lever. output arm fulcrum. Through this process, • Learn the difference between speed they discover the relationship and acceleration. between the input arm, input force, output arm, and output force.

A4 Levers and the How does the Students explore how the human • Define mechanical advantage. mechanical Human Body human arm work? arm acts as a lever. They learn • Explain the relationship between advantage Pages 25–32 how to find the mechanical lever arm length and mechanical 50 minutes advantage of a lever, and advantage. discover that the lever system in • Show how the arm acts as a lever the human arm has a mechanical with a mechanical advantage of advantage of less than 1. less than 1. A5 How do gears This investigation introduces • Discover the relationship between Pages 33–38 work? students to gears and gear ratios. number of teeth on a pair of gears gear ratio 50 minutes Students work with pairs of gears and the number of turns each gear input gear and determine the rule that will make. output gear relates the number of turns of one • Express gear ratios in different gear to the number of turns of forms. another. xvi Overview Chart for Investigations–Simple Machines Investigation Key Question Summary Learning Goals Vocabulary A6 Gear Machines How can you build Students discover that placing • Build compound gear machines. compound gear Pages 39–44 machines with a third gear between a pair • Calculate gear ratios for compound machine 50 minutes higher gear ratios? of gears does not change the machines. original gear ratio. Next, students experiment with stacking two gears on a single axle, creating an inner pair of gears and an outer pair of gears. Finally, they build their own complex gear machine and find its gear ratio.

A7 Designing Gear How can you Students begin with a simple • Use number theory to determine criteria Machines design machines number theory exercise to which gear ratios are possible using constraints Pages 45-52 with different gear determine which gear ratios are CPO gears. engineering cycle ratios? possible using the CPO gears. 100-150 minutes • Design and test a compound gear prototype Next, they design their own gear machine. machines using mathematical • Use the engineering cycle to design principles. Finally, they build and a ping pong ball launcher using CPO test their own gear machine that gears. will launch a ping pong ball.

B1 Forces in Machines How do simple Students build a simple machine • Identify input and output forces on input force Pages 53–60 machines work? using rope and pulleys. They a simple machine. mechanical 50 minutes measure the input force required • Measure input and output forces on advantage to lift a weight as the number a rope-and-pulley machine. output force of pulleys over which the string • Calculate the mechanical advantage rope-and-pulley passes is increased. Students of the rope-and-pulley system system develop a mathematical rule with different arrangements of the simple machine based on their observations. string. Finally, students learn to calculate the mechanical advantage of their simple machine for each arrangement of the string.

B2 Work and Energy What happens Students will measure input and • Calculate the amount of work done energy Pages 61–68 when you multiply output distance as well as input by simple machines. friction 50 minutes forces in a and output force for various • Analyze the effect of changing force input distance machine? arrangements of the rope-and- or distance in a simple machine. input work pulley system. They use their data • Describe the relationship between joule to calculate input and output work work and energy. for the machine. kinetic energy output distance output work potential energy work

Getting Started with Simple Machines xvii Overview Chart for Investigations–Simple Machines Investigation Key Question Summary Learning Goals Vocabulary B3 Levers, Torque, How do levers Students learn to calculate • Build and test three types of levers. first-class lever and Mechanical work? torque for levers with multiple • Define and calculate torque for each fulcrum Advantage forces on the input and/or output arm of a lever. input arm side. Next, they learn how to Pages 69–78 • Develop a rule relating input force, lever apply the concept of mechanical 100 minutes output force, input length, and output arm advantage to the lever, and output length. distinguish between theoretical second-class lever • Define and calculate theoretical and and actual mechanical third-class lever actual mechanical advantage for advantage. They learn about each class of lever. torque the three classes of levers and construct a model of each one. B4 Gears and Rotating How do simple gear Students are introduced to • Practice using rotations, degrees, angle Motion machines work? simple gear machines. They and radians to measure rotational degree Pages 79–84 learn to measure input and motion. gear output rotation using degrees 50 minutes • Demonstrate the law of gearing. law of gearing and radians. They build gear machines with input and output radian gears of various sizes. As they rotation measure and record input and output gear rotation, students discover the relationship between number of teeth and number of turns of the gears. This relationship is known as the law of gearing. B5 Compound Gear How can you Students learn to evaluate the • Explain how mechanical advantage criteria Machines evaluate the performance of a gear machine and gear ratios are used to evaluate compound Pages 85–94 performance of a by calculating the mechanical gear machines. gear machine 150 minutes gear machine? advantage and the gear ratio. • Design and test a compound gear constraints They build compound gear machine. engineering cycle machines and calculate the gear • Use the engineering cycle to design gear ratio ratios. Next, they design and test a Rube Goldberg-type device using prototype their own gear machines. a minimum of three different simple machines.

B6 Machines with How does a bicycle In this investigation, students • Build complex machines with gears crankset Gears and Levers work? explore combinations of and levers. freewheel Pages 95–100 gears and levers to help them • State the rule that relates force, 50 minutes understand how a bicycle works. distance, and number of teeth on a They build machines using gear for their machines. two gears and two levers, and • Explain the value of multiple gears develop a mathematical rule for on a bicycle. making the two levers balance.

xviii Overview Chart for Investigations–Simple Machines Investigation Key Question Summary Learning Goals Vocabulary C1 Simple and How can different Students review the three classes • Construct and test various types of actual mechanical Complex Pulley types of pulley of levers and compare them with pulley systems. advantage Systems systems be used to three types of pulley systems. • Calculate the ideal and actual ideal mechanical Pages 101–110 move objects? They build each type of pulley mechanical advantage of various advantage of a 100 minutes system and calculate its ideal and types of pulley systems. lever actual mechanical advantage. • Evaluate the types of tasks that ideal mechanical They learn to use a pulley system each type of pulley system can advantage of a in an unconventional manner to accomplish. rope-and-pulley increase output distance without system increasing input distance. C2 Rotational Motion How is the speed Students use a timer and • Measure angular speed and express angular speed Pages 111–118 of a rotating object photogates to measure the the speed in rotations, degrees, and linear speed 50 minutes measured? angular speed of a rotating gear. radians per unit time. pitch circumference They practice expressing angular • Calculate linear speed of a point on speed in rotations, degrees, and a rotating object. radians per unit time. Next, they • Describe the relationship between find the formula for linear speed angular and linear speed of a of a rotating object and calculate rotating object. the linear speed of two different points on the gear. C3 Center of Gravity How can the Students use their understanding • Find a lever’s center of gravity. center of gravity and Equilibrium weight of a lever be of rotational equilibrium to • Set up a lever so that rotational equilibrium Pages 119–126 determined using solve a problem. They identify equilibrium is achieved. rotational 50 minutes the principle of forces contributing to clockwise • Access prior knowledge about equilibrium and counterclockwise torque in rotational calculating torque to find the torque equilibrium? the lever. Next, they write an weight of a lever. equation relating clockwise and • Compare the calculated weight counterclockwise torque that with the lever’s weight found will allow them to solve for the experimentally. weight of the lever.

Getting Started with Simple Machines xix Next Generation Science Standards Correlation CPO Science Link investigations are designed for successful implementation of the Next Generation Science Standards. The following chart shows the NGSS Performance Expectations and dimensions that align to the investigations in this title.

NGSS Performance Expectations Simple Machines Investigations

MS-PS3-2. Develop a model to describe that when the arrangement of objects interacting at a distance A1, A3, A4 changes, different amounts of potential energy are stored in the system.

MS-PS3-5. Construct, use, and present arguments to support the claim that when the motion energy A2, C2 of an object changes, energy is transferred to or from the object.

MS-ETS1-2. Evaluate competing design solutions using a systematic process to determine how well A5, A6, A7, C1 they meet the criteria and constraints of the problem.

HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one form of B1, B2, B3, B4, B5, B6 energy into another form of energy.

HS-PS2-4. U se mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to C3 describe and predict the gravitational and electrostatic forces between objects.

NGSS Simple Machines NGSS Simple Machines Science and NGSS Crosscutting Simple Machines Investigations Disciplinary Core Ideas Investigations Engineering Practices Concepts Investigations

Constructing B1, B2, B3, B4, B5, ETS1.A: Defining B1, B2, B3, B4, Explanations and B6, C1 and Delimiting an B5, B6 Systems and A1, A3, A4, A5, A6, Designing Solutions Engineering Problem System Models A7

Developing and A1, A3, A4 ETS1.B: Developing A5, A6, A7 Energy and Matter A2, B1, B2, B3, B4, Using Models Possible Solutions B5, B6, C1, C2

Engaging in Argument A2, A5, A6, A7, C2 ETS1.C: Optimizing the C1 Patterns C3 from Evidence Design Solution

Using Mathematics and C3 PS2.B: Types of C3 Computational Thinking Interactions PS3.A: Definitions A1, A3, A4, B1, of Energy B2, B3, B4, B5, B6

PS3.B: Conservation A2, C2 of Energy and Energy Transfer

PS3.C: Relationship A1, A3, A4 Between Energy and Forces

* Next Generation Science Standards is a registered trademark of Achieve. Neither Achieve nor the lead states and partners that developed the Next Generation Science Standards was involved in the production of, and does not endorse, this product. xx Common Core State Standards Correlation CCSS-Mathematics Simple Machines Investigations MP.2 Reason abstractly and quantitatively. A2, A5, A6, A7, C3 MP.4 Model with mathematics. B1, B2, B3, B4, B5, B6, C1, C2, C3

RP.A.2 Recognize and represent proportional relationships between quantities. A2, A3, A4, A5, A6, A7

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational A5, A6, A7 numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; B1, B2, B3, B4, B5, B6, C1, C2, C3 choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. B1, B2, B3, B4, B5, B6

HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. B1, B2, B3, B4, B5, B6, C3

HSA.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. C1, C2, C3

HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the C3 quantity represented by the expression.

CCSS-English Language Arts & Literacy Simple Machines Investigations SL.8.5 Integrate multimedia and visual displays into presentations to clarify information, strengthen A1, A3, A4 claims and evidence, and add interest. RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the A2, A5, A6, A7 precise details of explanations or descriptions. WHST.6-8.1 Write arguments focused on discipline content. A2

WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), A5, A6, A7 drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration.

WHST.6-8.9 Draw evidence from informational texts to support analysis, reflection, and research. A5, A6, A7

WHST.9-12.7 Conduct short as well as more sustained research projects to answer a question (including a B1, B2, B3, B4, B5, B6 self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.

Getting Started with Simple Machines xxi