Table of Contents

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Table of Contents

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Standards Addressed by Activity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Science Lessons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Do You Have Lightning Reflexes? . . . . . . . . . . . . . . . . . . . . . . Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Can You Find Mu of the Shoe? . . . . . . . . . . . . . . . . . . . . . . . . Center of Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . You Lift Me Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .



*Times are estimates and will vary with class size.

90 minutes* 45 minutes* 45 minutes* 45 minutes* 45 minutes*

Math Lessons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Making Sense of Physics Formulas . . . . . . . . . . . . . . . . . . . . . . What Does All This Data Mean? . . . . . . . . . . . . . . . . . . . . . . . When Things Get Graphic . . . . . . . . . . . . . . . . . . . . . . . . . . . Shape Up or Surface Area Out . . . . . . . . . . . . . . . . . . . . . . . .



*Times are estimates and will vary with class size.

45 45 90 90

minutes* minutes* minutes* minutes*

Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Additional Resources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

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Center of Gravity

Teacher Instruction

Objectives Students determine the center of gravity for an object.

Concepts center of gravity – the balance point of an object; the location in an object where mass is concentrated mass – the amount of matter in an object

Standards Addressed NSTA 9-12 Standard A: Science as Inquiry Students develop the abilities necessary to do scientific inquiry. • Students use technology and mathematics to improve investigations and communications. Students develop understandings about scientific inquiry. • Students understand mathematics is essential in scientific inquiry and understand mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations, and communicating results.

Standard B: Physical Science Students understand motions and forces. • Students understand objects change their motion only when a net force is applied; understand laws of motion are used to calculate precisely the effects of forces on the motion of objects; understand the magnitude of the change in motion can be calculated using the relationship F = ma, which is independent of the nature of force; and understand whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object. • Students understand gravitation is a universal force that each mass exerts on any other mass and understand the strength of the gravitational attractive force between two masses is proportional to the masses and inversely proportional to the square of the distance between them. NCTM 9-12 Standard 3: Geometry Students analyze characteristics and properties of two- and three-dimensional shapes and develop mathematical arguments about geometric relationships. • Students analyze properties and determine attributes of two- and threedimensional objects. Students use visualization, spatial reasoning, and geometric modeling to solve problems. • Students use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.

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Center of Gravity Standard 4: Measurement Students understand measurable attributes of objects and the units, systems, and processes of measurement. • Students make decisions about units and scales that are appropriate for problem situations involving measurement. Students apply appropriate techniques, tools, and formulas to determine measurements. • Students analyze precision, accuracy, and approximate error in measurement situations. • Students understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders. Standard 10: Representation Students create and use representations to organize, record, and communicate mathematical ideas. • Students use representations to model and interpret physical, social, and mathematical phenomena. ITEA 9-12 Standard 11: Apply the Design Process Students develop the abilities to apply the design process. • Students learn to refine a design by using prototypes and modeling to ensure quality, efficiency, and productivity of the final product.

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Teacher Instruction Standard 12: Use and Maintain Technological Products and Systems Students develop the abilities to use and maintain technological products and systems. • Students learn to document processes and procedures and communicate them to different audiences using appropriate oral and written techniques. Standard 13: Assess the Impact of Products and Systems Students develop the abilities to assess the impact of products and systems. • Students learn to synthesize data, analyze trends, and draw conclusions regarding the effect of technology on the individual, society, and environment.

Time Requirement 45 minutes

Background The center of gravity is the point in an object where all of the mass can be considered to be concentrated. Mass is the amount of matter found in an object. The center of gravity also represents the point around which rotation will occur in the absence of other forces. For symmetrical objects, such as a sphere or a cube, the center of gravity is at the geometric center of the object. For irregular objects, the center of gravity can be away from the center of the object. A hammer, for example, has its center of gravity closer to the head.

Center of Gravity

Teacher Instruction The center of gravity may actually lie outside the geometric boundaries of the object. For example, the center of gravity of a glazed doughnut is in the middle of the hole!

Opening Activity Discuss the idea that an object’s mass can be concentrated in a single point. The balancing bird available at most dollar stores is a good illustration of center of gravity.

Materials

2

Tie a string through one of the holes and suspend the shape so that it can rotate freely.

• Plumb bob (can use a common nail or comparable object weighing approximately six grams and hanging on a string) • String • “Vehicles” handout • Scissors • Three-hole punch • Tape • Blank sheets of paper

Safety Materials should be used according to your guidelines.

Procedure

1

Cut out the vehicles from the “Vehicles” handout. Punch three holes around the edge of each shape.

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Center of Gravity

Teacher Instruction

Analysis and Conclusions 1. Tape your vehicles to a blank sheet of paper with the center of gravity indicated. 2. Which vehicle had the highest center of gravity? The lowest? 3. Which vehicle is the most likely to topple if it goes around a corner too fast?

3

Hang your plumb bob from the same attachment point and allow the string to stop moving. Trace a line on the shape that follows the string.

4

Repeat this process for each of the holes in the vehicle. The point where the lines intersect is the center of gravity.

Extension/ Enrichment Activities 1. Have students choose objects of their own and determine the center of gravity of each object. 2. Have students create sketches of items for determination.

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Determine the center of gravity for each vehicle by repeating Steps 2-4.

Shape Up or Surface Area Out

Student Instruction

Objectives Discuss how aerodynamics can make a car faster or slower. Explain why race cars look the way they do and what part acute, obtuse, and right angles play in the design of these cars.

A sleeker design will allow for more aerodynamic flow, lower drag, and the lowest amount of air displaced. Like a diver in a pool, the straighter the dive the smaller the splash in the water. We want to disturb only the smallest area of air to have the smallest impact in air movement.

Make concrete three-dimensional models using foam, cardboard, or paper. Use a wind tunnel and fog machine to examine air currents and see how aerodynamic these three-dimensional shapes are. Predict the best and the worst design for a race car. Examine why some shapes will move faster in the airflow and how surface area, volume, and area affect a car. Predict where downforce is important and why.

Background Surface area and frontal area are where most air resistance comes from in racing. The moving car must push aside the molecules of air, and the amount of air will be proportional to the frontal area of the car. That air mass, as it is moving around the car, will move off in some direction. If the surface area is larger, more air must be moved. For example, if you move a plate though the air, that will take large amounts of energy to displace a large quantity of air. Engineers have found that there is a lot of drag when the shape moves large amounts of air.

Materials • • • • • • •

Race car models Graph paper Fan or wind tunnel Foam Cardboard Scissors Tape

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Shape Up or Surface Area Out

Safety Materials should be used according to your instructor’s guidelines.

Procedure Part 1: Teacher Demonstration Your teacher will discuss what angles will be best for the front of a race car. You will be asked to draw and label these angles.

Student Instruction

Part 3: Student Activity

1 2 3

Pick which shape you believe is the best and worst for your car.

Use the formulas to determine the surface area of each of these shapes and the volume for each of the models.

After the data is collected, compare how surface area affects the ability for the car to cut the air effectively.

Part 2: Student Activity

1

Now, make the three angles (obtuse, acute, and right angle) three dimensional by making each of these angles out of the graph paper, cardboard, or foam.

2 3 4

Predict which of the 3-D models will have the least wind resistance and which will have the most.

Square

side2

Rectangle

length * width

Parallelogram

base * height

Triangle

base * height/2

Cube

(surface)

6 * side2

Sphere

(surface)

4 * pi * radius2

Volume Formula Decide which model will be more aerodynamic and explain why.

Make observations at each point and write why these things would help or hinder the race car.

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Area Formula

Cube

side3

Rectangular Prism

side 1 * side 2 * side 3

Sphere

(4/3) * pi * radius3

Cylinder

pi * radius2 * height

Cone

(1/3) * pi * radius2 * height

Pyramid

(1/3) * base area * height

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Student Instruction

Part 4: Student Activity

1 2 3 4 5 6 7

Next, separate into groups of three or four, obtain graph paper from the teacher, and bring it back to the group.

Shape Up or Surface Area Out

Analysis and Conclusions 1. Why is it important to look at types of angles and the shapes they produce?

Cut and tape the graph paper on the top of a model car you receive from your teacher.

Estimate the surface area and the volume of the car.

2. How does frontal area and surface area of a car affect the aerodynamics? 3. Does the length of a car play into the aerodynamics? 4. On F1 cars, the CO2 cartridge housing needs to be present in all cars. How can this be made as aerodynamic as possible? 5. Does the wing in the front and the back help or hurt aerodynamics?

Change the configuration and refigure the surface area and volume. This will act as a check for your first estimate.

Put your car in the wind tunnel and determine the drag coefficient force for the

car.

6. If you take all these things into consideration, how will you be able to change all of these variables to make your car perfect? 7. In conclusion, what do you see as the most important piece to keep in mind for aerodynamics, and what will be the hardest to change?

Compare your surface area and the drag forces to that of other student groups.

As a group, draw the best design for an F1 car using the information and the concepts you have learned.

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