I. PHYSICS OF ROLLER COASTERS:

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1 I. PHYSICS OF ROLLER COASTERS: They love to ride them, now they ll love to build them! Students explore potential and kinetic energy and Conservation of Energy while building their own marble roller coasters. Grade Levels: 4-8 Educational Outcomes: 1) Students will design a roller coaster and demonstrate their knowledge of Potential and Kinetic Energy. 2) Students will gain an understanding of the concepts of friction, velocity and acceleration. Optional 7 th & 8 th outcomes: 3) Students will determine the average velocity a given marble travels on their roller coaster. 4) Students will apply their knowledge of various measurement systems by converting the average velocity from cm per second to miles per hour. Estimated Time: 2 hrs, 15 minutes Introductory Design Challenge: Jumping Marbles - 45 minutes Building 15 minutes Demonstration and Reflection 15 minutes Science Discussion: 15 minutes Design Challenge: Design a Roller Coaster (Part I) 45 minutes Building 15 minutes Demonstration and Reflection 15 minutes Science Mini Lessons: Converting Energy 15 minutes Design Challenge: Design a Roller Coaster (Part II) 45 minutes Building 20 minutes Demonstration and Reflection 20 minutes Clean-up 5 minutes Optional Activity: Determine average velocity of Roller coaster 45 minutes National Science Education Standards Connections: Grades 5-8 Content Standard B (Physical Science) 2: Motions and Forces 1. 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. 2. An object that is not being subjected to a force will continue to move at a constant speed and in a straight line. 3. If more than one force acts on an object along a straight line, then the forces will reinforce or cancel one another, depending on their direction and magnitude. Unbalanced forces will cause changes in the speed or direction of an object's motion. 3. Transfer of Energy 1. Energy is a property of many substances and is associated with heat, light, electricity, mechanical motion, sound, nuclei, and the nature of a chemical. Energy is transferred in many ways. Page 1

2 Grades 5-8 Content Standard E (Science and Technology) 1. Abilities of technological design 1. Design a solution or product. 2. Implement a proposed design. 3. Communicate the process of technological design. 2. Understandings about science and technology National Council of Teachers of Mathematics Standards Connections: Grades 6-8 Measurement 1. Understand measurable attributes of objects and the units, systems, and processes of measurement 2. understand relationships among units and convert from one unit to another within the same system; 2. Apply appropriate techniques, tools, and formulas to determine measurements. 2. select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision; 6. Solve simple problems involving rates and derived measurements for such attributes as velocity and density. California Math/Science Standards Connections: Grade 6 - Mathematics (Statistics, Data Analysis, and Probability): 1. Students compute and analyze statistical measurements for data sets. 2. Students determine theoretical and experimental probabilities and use these to make predictions about events. Grade 6 - Physical Science: 3a. Students know energy can be carried from one place to another by heat flow or by waves, including water, light and sound waves, or by moving objects. Grade 7 Mathematics (Measurement & Geometry): Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems. Grade 8- Physical Science: 1. The velocity of an object is the rate of change of its position. 1 e. Students know changes in velocity may be due to changes in speed, direction, or both. 2. Unbalanced forces cause changes in velocity. 2 a. Students know a force has both direction and magnitude. 2 b. Students know when an object is subject to two or more forces at once, the result is the cumulative effect of all the forces. 2 c. Students know when the forces on an object are balanced, the motion of the object does not change. 2 d. Students know how to identify separately the two or more forces that are acting on a single static object, including gravity, elastic forces due to tension or compression in matter, and friction. Page 2

3 2 e. Students know that when the forces on an object are unbalanced, the object will change its velocity (that is, it will speed up, slow down, or change direction). All Grades: Investigation and Experimentation: Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other three strands, students should develop their own questions and perform investigations. Tech Gallery Connections: Innovation: Virtual Design Design a Bike, Design & Ride a Rollercoaster; Life Tech: Beyond our Limits Human-Powered Vehicles; Big Ball Machine energy and motion, transfer of energy; Imagination Playground II. PHYSICS OF ROLLER COASTERS: ADVANCED PREP & SET-UP Introductory Design Challenge: Jumping Marbles Each team of three to four will have: One glass marble Masking tape 1 Plastic cup 1 half piece of foam pipe insulation cut lengthwise (3/8" wall x 6'; semi-slit, Polyethylene foam, Fits 1" Copper Or 3/4" Steel Pipe) Design Review Question page (see appendix) Tinker toys (optional) Design Challenge: Design a Roller Coaster (Part I) Each team of three to four will have: One glass marble Masking tape 1-2 half pieces of foam pipe insulation cut lengthwise (3/8" wall x 6'; semi-slit, Polyethylene foam, Fits 1" Copper Or 3/4" Steel Pipe) Design Review Question page (see appendix) Tinker toys (optional) Student research station Images of roller coasters Key words with definitions Plastic roller coaster/ race car track to manipulate Science Mini Lessons Computer connected to Internet (for How Stuff Works demo) Pipe insulation and marble (for demo) Design Challenge: Design a Roller Coaster (Part II) Page 3

4 Each team of three to four will have: Masking tape, glass marble 2-3 half pieces of foam pipe insulation cut lengthwise (3/8" wall x 6'; semi-slit, Polyethylene foam, Fits 3/4" Copper Or 1/2" Steel Pipe) Twist ties or pipe cleaners Paper & pencil Design Review Question page (see appendix) Tinker toys (optional) Velocity Worksheets (optional, see appendix) Stop watch & Metric Measuring Tape (7 th & 8 th grade option) Calculator (7 th & 8 th grade option) : Page 4

5 III. PHYSICS OF ROLLER COASTERS: LESSON PLAN Introduction: This class is about the thrill of velocity, acceleration, and unbalanced forces we re talking about Roller Coasters! In this class we are going to create a roller coaster that is the fastest and most exciting ride you can build! Question for students: What makes a roller coaster fun and exciting? Gather all responses from students to discuss later. Share that you will be exploring these responses as you embark upon your study of roller coasters. A. Introductory Design Challenge: Jumping Marbles Time: (10-15 minutes) Challenge: Design a ramp for a marble to travel on that will allow the marble to jump the greatest distance possible to land in a cup. Constraints: Your marble must complete the ramp before jumping off. You may not use human force to get your marble started on the ramp. The distance of the jump is measured when the marble leaves the ramp (from the end of the ramp to the cup). Notes to teachers: We suggest using 3 separate days (based on your teaching schedule) to teach this lesson. Day 1: Introductory design and discuss findings Day 2: Complete the first roller coaster challenge, demonstrate designs, and receive direct instruction Day 3: Design second roller coaster and review the information learned. Optional Day: Complete velocity investigation and share out designs and findings. B. Student Demonstration and Reflection: Time: (10-15 minutes) Have students demonstrate their ramp designs to one other team and explain their design strategy and challenges that they experienced with the various approaches that they took. (See appendix for Design Review Question page). C. Science Discussion Time: (10-15 minutes) Teaching Points (Conservation of Energy content): Potential Energy (PE) is stored Energy that, in this challenge, Page 5

6 can be either gravitational (gravity) or elastic (rubber bands, springs...). Kinetic Energy (KE) is Energy in motion. Questions to encourage teaching points: - What makes your marble move on your ramp? Is there anything pulling your marble? (Gravity) - How did you make your marble jump further? (Greater length, slope or combination of the two) - Do you know what stored energy is called? (Potential Energy is stored energy of position or condition) - Do you know what energy in motion is called? (Kinetic Energy is energy in motion.) - Do you know what type of Potential Energy is being demonstrated by your design? (Gravitational PE) - Why do roller coasters begin with a really high hill and then continue with smaller hills, loops and turns? (Potential Energy is greatest at the start of the ride). D. Design Challenge: Design a Roller Coaster (Part I) Time: (15-20 minutes) Scenario: Great America has enlisted your help to create an old fashioned roller coaster that relies solely on the force of gravity to move the cars. Challenge: Design a roller coaster for a marble to travel on (without falling off), which has at least one complete vertical loop. Constraints: Your marble must complete the course while staying on the track. You may not use human force to get your marble started on the track. You need to have one complete vertical loop. Each group member must participate in the design, construction, and operation of the roller coaster. KEY WORDS: Kinetic Energy: Energy of Motion. Includes heat, sound, and light (motion of molecules). Potential Energy: Energy of position; energy that is stored and held in readiness. Includes chemical energy, such as fossil fuels, electric batteries, and the food we eat. Elastic Potential Energy: Potential energy due to tension -- either stretch (rubber bands, etc.) or compression (springs, etc.). Gravitational Potential Energy: Potential energy stored in an object as a result of its vertical position (i.e., height). Inertia: The tendency of matter to remain at rest if at rest, or, if moving, to keep moving in the same direction, unless affected by an outside (or unbalanced) force. : Page 6

7 E. Student Demonstration and Reflection: Time: (10-15 minutes) Have students demonstrate their roller coaster designs to one other team and explain their design strategy and challenges that they experienced with the various approaches that they took. (See appendix for Design Review Question page). F. Science Mini Lessons Time: (15-20 minutes) Note to Teacher: The following are several different mini lessons of concepts that can be covered with designing roller coasters. The concepts range in levels and should be chosen according to the level of your students and the concepts most appropriate to your curriculum. Research shows that covering one or two key concepts in depth will result in deeper learning and longer retention on the part of students, so it is our intention that only one or two of these concepts would be discussed with students. 1. Converting Energy (Potential and Kinetic Energy) How Stuff Works Roller Coaster demo: Questions to ask students before showing the demo: Note to Teacher: Ask the students the questions and gather their predictions without answering the questions. After they see the simulation, ask the questions again and answer as a class. Where will you find the greatest amount of Potential Energy? (at the top of the 1 st initial hill) Where will you find the greatest amount of Kinetic Energy? (at the bottom of the 1 st hill) Will the roller coaster store anymore potential energy during the ride? If so, where? (Yes, on the smaller hill and on the loop as it goes up) Will the roller coaster run out of energy? (Yes and no, the stored energy reservoir will be depleted by transforming into kinetic energy and the KE will have been lost to friction or transformed into heat. But the amount of energy still remains constant; it has simply transformed.) Notes to teachers: 1. Newton s Laws of Motion should be posted in classroom to be referred to during this part of the mini lesson/ inquiry. 2. To determine the velocity in a conventional form (distance traveled over time), students will need to measure their tracks in cm (using a metric tape measure) and time the run of their marbles in seconds (using a stop watch). They will then need to divide the actual length by the amount of time it took the marble to complete the track. This allows students to find out how many cm per second the marble travels. Actual length = X cm per sec Actual time Students should complete at least 3 trials and then find the average of those 3 trials to get a more accurate result. Note: 7 th & 8 th grade students can complete the more advanced worksheet (Velocity Investigation Worksheet 2) to determine MPH. *Worksheets are provided at the end of the lesson, but we encourage you to make your own with your class! : Page 7

8 What type of Potential Energy is being stored by this design? (Gravitational Potential Energy) Show the demo and check the results with your students 2. Conservation of Energy, Inertia and Velocity (Demonstration and Review): Roller Coaster Demonstration Create a simple roller coaster out of the same pipe insulation to investigate the science underlying how roller coasters work. Introduce Newton s 1 st Law (Law of Inertia): Place a marble on the pipe insulation in a horizontal position. Ask students: Why isn t the marble moving? An object at rest tends to stay at rest until a force acts upon it. Angle the track down so that the marble begins to move. Ask students: Why does the marble start to accelerate or go faster? Gravity is pulling on it or acting upon it. Place the marble at the top of the track, allow it to travel down and then place your hand in the path of the marble to stop it Ask students: Why did the marble stop moving? Hand acted upon marble. KEY WORDS: Acceleration: The rate at which an object changes its velocity. An object is accelerating if it is changing its speed or direction. Velocity: The rate at which an object changes its position. The distance traveled over time. Force: A push or pull. The force applied to a machine is called work input or effort force. Mass: The amount of matter that is contained by an object. Momentum: The quantity of motion of a moving object, equal to the product of its mass and its velocity. Once again, place the marble at the top of the track but this time let it stop on it s own. Ask students: Why did the marble stop moving? Friction, transfer of energy An object in motion (at a constant speed and in a straight line) will stay that way until a force acts upon it. A good example is when you are driving in a car and all of a sudden your Mom or Dad hits the brakes your body continues to move forward, but is kept in your seat by the force of your seatbelt (which is why we wear seatbelts!). : Page 8

9 3. Velocity Investigation Note to Teacher: The following discussion guides students in developing their own conceptual understanding of the rate X time = distance formula helping them to retain this concept and how it is derived rather than just memorizing the formula. This also helps them develop problem-solving skills. Ask students: How can you find out how fast your roller coaster is (what the velocity of the ball is)? They will likely suggest using a stopwatch to time it. Ask students: How can you compare your velocity with that of other roller coasters? You need to compare the speed (velocity) over the same distance. Ask students: How can you do this? You can measure your track and then time how long it takes to go that distance. Ask students: Since we want to compare, we need to agree on what units of measurement to use. What measurement unit shall we use to measure the track and to measure time? Centimeters or inches are both appropriate for measuring the track length. Centimeters are preferred to emphasize the metric system. Seconds are best for measuring the length of time, since other units of time are too long or too short. Notes to teachers: With math it s very powerful to encourage students to discover formulas as much as possible, rather than simply giving them the formula and telling them what to do. This allows students to create a deeper understanding of the concept behind the formula and hopefully the ability to reconstruct it again without memorizing it. Using this particular approach, some good measurement math standards can also be covered, since students are supposed to be able to select appropriate units of measurement. Ask students: What if someone has a longer track than someone else? How can we compare the speeds? You ll need to divide the length of the track by the time so that you get the number of seconds per cm. Ask students: Is one timing of your roller coaster a fair test of your its speed? Why? It s important to do several trials and average the results to correct for the errors or changes that can happen in a trial. (Starting the ball at a slightly different spot; using some force; slight changes in the shape of the roller coaster, etc.) : Page 9

10 Have Students complete the Velocity Investigation Worksheet to calculate the velocity of their roller coaster. If you want to have students also convert their velocity from cm/sec to miles/hour, you can use the Velocity Investigation Worksheet #2. Again, ask students to think through how they would make this conversion, rather than giving them the steps. G. Design Challenge: Design a Roller Coaster (Part II) Time: (15-20 minutes) Challenge: Great America was very pleased with the performance of your previous design, so much so that they are asking for more! They would like you to continue to work with your roller coaster, but they ve decided that they would like you to add more loops to it (the more the better!). Constraints: Your marble must complete the full length of the track without falling off. You may not decrease the length of the track, but you can add to it. You may not use human force to get your marble started. Your track needs to have at least 3 vertical loops. You can visit the research station at any time to get ideas for your design. Each group member must participate in the design, construction, and operation of the roller coaster. H. Demonstration and Reflection: Time: (20 minutes or more) Demonstration: Have students demonstrate their roller coaster designs with the class (optional: If students conducted the optional velocity investigation, have them share their results). Reflection: Each group of students will explain their design strategy and how their marble uses energy, forces, and motion to complete the roller coaster. Instructor should ask leading questions to get at the science behind the designs. : Page 10

11 Questions to elicit student thinking & understanding: - How did you change your original design? What affect did this/these change(s) have upon the performance of your roller coaster? - How does your marble transform potential energy (gravitational) to kinetic energy? - Did you do any research to inform your design? How did it help you? - If you had more time what would you add, change, or do differently? - Optional: What is the average velocity at which your marble travels? Did you do anything specific to your roller coaster design to increase the velocity? Final Point: What makes a roller coaster really fun is the changes of velocity due to the twists, turns and forces acting upon it! I. Clean up: Reduce! Re-use! Recycle! Time: (5 minutes or more) Only throw away items that cannot be re-used. All items should be returned to the appropriate place. J. Post Activities: Have students redesign their roller coasters for a marble with more mass (use a steel marble) or greater diameter (use a shooter marble). Determine various categories to judge the performance of the marbles (e.g. smoothness of ride, safety ). Have students work together to create a classroom roller coaster. Challenge them to create as many loops as possible. Our record is 8 loops What s yours?! : Page 11

12 IV. PHYSICS OF ROLLER COASTERS: TEACHER NOTES Roller coasters Historical Perspective: The roller coaster is believed to have begun in 15 th century Russia as an ice slide. Built in St. Petersburg, this early slide was made from a wooden frame 70 feet (21m) high that was packed with snow and watered down. Riders rode down these hills on blocks of ice that were slightly hollowed out to fit their bodies. Glossary & Concepts: Physics Terms Acceleration: The rate at which an object changes its velocity. An object is accelerating if it is changing its velocity, both speeding up or slowing down. Centripetal force requirement: an inward force acting upon an object that is moving in a circle, in order to cause its inward acceleration. Elastic Potential Energy: Potential energy due to tension -- either stretch (rubber bands, etc.) or compression (springs, etc.). Energy: Nature s way of keeping score. Measured in joules. Appears in many forms, most of which are ultimately derived from the sun or from radioactivity. Force: A push or pull. The force applied to a machine is called work input or effort force. Gravitational Potential Energy: Potential energy due to elevated position. Gravitation potential energy = weight x height. Note this only depends on vertical displacement and not the path taken to get it there. This value is always relative to some reference level. Inertia: The tendency of matter to remain at rest if at rest, or, if moving, to keep moving in the same direction, unless affected by an outside (or unbalanced) force. Kinetic Energy (KE): Energy of motion. KE= ½ mass x velocity 2 = ½ mv 2 Note that small changes in speed can result in large changes of KE (it s speed squared!). Net force x distance = KE. Includes heat, sound, and light (motion of molecules). KE is a scalar quantity; it cannot be canceled. Mass: the amount of matter that is contained by an object. Mechanical Energy: Energy possessed by an object due to its motion or its stored energy of position. Mechanical energy can be either kinetic : Page 12

13 energy (energy of motion) or potential energy (stored energy of position). Momentum: The quantity of motion of a moving object, equal to the product of its mass and its velocity. Potential Energy (PE): Energy of position; energy that is stored and held in readiness. Includes chemical energy, such as fossil fuels, electric batteries, and the food we eat. Velocity (speed): How fast an object is moving. The distance traveled over time. Newton s Law of Conservation of Energy: Energy cannot be created or destroyed; it may be transformed from one form into another, or transferred from one place to another, but the total amount of energy never changes. Newton s Laws of Motion: 1 st Law (Law of Inertia): An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. 2 nd Law: When an unbalanced force acts on a body, it is accelerated in the direction of the force; the magnitude of the acceleration is directly proportional to the force and inversely proportional to the mass of the body F=ma : Page 13

14 Resources: Conceptual Physics for Parents and Teachers: Mechanics by Paul Hewitt. Focus Publishing/ R. Pullins Company, Newburyport, MA Exploring Energy with Toys by Beverley A. P. Taylor. Terrific Science Press, Middletown, OH, Physics Tricks: Fun Experiments with Everyday Materials by Terry Cash. Sterling Publishing, New York, New York The Inventa Book of Mechanisms by Dave Catlin. Valiant Technology Ltd., London, England, U.K., Rutgers University Physics Education Resource website: The Physics Classroom tutorial website: Amusement Park Physics Roller Coasters: Roller Coasters Inventing the Scream Engine: How Stuff Works Roller Coasters: Converting Energy : Page 14

15 Appendix : Page 15

16 Design Review Questions Questions for the team that is sharing their design: 1. Can you tell us about your design process (the thinking behind the design)? Did your first design work? Why or why not? Did you make any modifications? How did that affect your design? 2. Can you describe for us how your design works? If it s not finished, what were you planning to do how did you hope it would work? What would you do if you had some more time? What materials might you like to have had? 3. What was the hardest part about your design process? How did you solve that problem (or plan to solve it)? Questions for the students that are reviewing the design: 1.What do you think are the advantages of this solution? 2. What do you think are the disadvantages of this solution? 3. What is one idea that you can offer the team to help improve their design? : Page 16

17 Velocity Investigation Worksheet Velocity = Distance traveled/ Time To determine the velocity you will first need to measure your roller coaster track in centimeters using a metric tape measure. Length of track= cm Next, you will need to time how fast a marble completes your roller coaster, using a stopwatch. Run Time= seconds Then you will simply divide your Length of Track by your Run Time to find out how many cm per second your marble travels! cm seconds = Length of track Run Time cm per second To find your average velocity, measure the run time 3 times and determine the average: Trial # 1: cm seconds = Length of track Run Time cm per second Trial # 2: cm seconds = Length of track Run Time cm per second Trial # 3: cm seconds = Length of track Run Time cm per second * Add the 3 scores and divide by 3 to find average Average Velocity : Page 17

18 Velocity Investigation Worksheet 2 Velocity = Distance traveled/ Time To determine the velocity you will first need to measure your roller coaster track in centimeters using a metric tape measure, then find out how fast a marble completes your roller coaster, using a stopwatch. Length of track= cm Run Time= seconds Then you will simply divide your Length of Track by your Run Time to find out how many cm per second your marble travels! cm seconds = Length of track Run Time cm per second To find a more accurate average velocity, measure the run time 3 times and calculate the average: Trial # 1: cm seconds = Length of track Run Time cm per second Trial # 2: cm seconds = Length of track Run Time cm per second Trial # 3: cm seconds = Length of track Run Time cm per second * Add the 3 scores and divide by 3 to find average Average Velocity To Convert Centimeters Per Second to Miles Per Hour: centimeters per second 100,000 = kilometers per second kilometers per second x 60 = kilometers per minute kilometers per minute x 60 = kilometers per hour kilometers per hour x 0.62 = miles per hour : Page 18

19 Record of Roller Coaster Changes Team: Please remember to only change only one variable at a time and record the outcome. Change to Roller Coaster Predicted Outcome Actual Outcome Run Time : Page 19