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TE Activity: Don't Crack Humpty

Student groups are provided with a generic car base. The groups then design a device/enclosure that will protect an egg on or in the car as it is rolled down a ramp at increasing slopes. Students will be expected to perform basic mathematical calculations using their data.

Automotive manufacturers hire engineers to redesign cars in an effort to make them safer. This process always involves a trade-off between cost of manufacturing a new design and level of safety. After this activity students will be able to recognize this trade-off and understand the concept of cost to benefit ratio.

Pre-Req Knowledge
Learning Objectives
Materials
Introduction/Motivation
Procedure
Attachments
Safety Issues
Troubleshooting Tips
Assessment
Extensions
Activity Scaling

Grade Level: 7 (6-10)	Group Size: 4
Time Required: 3 hours This activity can be modified to go from 2 hours to 5 hours depending on the number of redesign steps the students are allowed and the number of standards you want to address. It is an indepth physics/science/technology activity.	Activity Dependency : None
Expendable Cost Per Group : US$ 3 Additional start-up cost is not included in this amount. A basic wooden ramp whose angle can be varied and cars for each group need to be made. These can be used several times and do not need to be remade for every class.
Keywords: Engineering design process, Inertia, Center of gravity, Material properties, Mass, Weight, Speed, Acceleration, Friction, Newton's laws, Gravity , Angles, Slopes, Ratio, Cost to benefit ratio

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Massachusetts Math
- 6.M.3 Solve problems involving proportional relationships and units of measurement, e.g., same system unit conversions, scale models, maps, and speed. (Grades 5 - 6) [2000]
- 6.P.6 Produce and interpret graphs that represent the relationship between two variables in everyday situations. (Grades 5 - 6) [2000]
- 6.N.1 Demonstrate an understanding of positive integer exponents, in particular, when used in powers of ten, e.g., 10², 105. (Grades 5 - 6) [2000]
- 6.N.4 Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on the number line. (Grades 5 - 6) [2000]
- 6.N.5 Identify and determine common equivalent fractions, mixed numbers, decimals, and percents. (Grades 5 - 6) [2000]
- 6.N.7 Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents. (Grades 5 - 6) [2000]
- 6.N.9 Select and use appropriate operations to solve problems involving addition, subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. (Grades 5 - 6) [2000]
- 6.N.11 Aply the Order of Operations for expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ÷). (Grades 5 - 6) [2000]
- 6.N.13 Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals. (Grades 5 - 6) [2000]
- 6.N.14 Accurately and efficiently add, subtract, multiply, and divide positive fractions and mixed numbers. Simplify fractions. (Grades 5 - 6) [2000]
- 6.N.16 Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates. (Grades 5 - 6) [2000]
- 8.N.3 Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change. (Grades 7 - 8) [2000]
- 8.N.10 Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1). (Grades 7 - 8) [2000]
- 8.N.11 Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. (Grades 7 - 8) [2000]
- 10.D.1 Select, create, and interpret an appropriate graphical representation (e.g., scatter-plot, table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. (Grades 9 - 10) [2000]
- 10.M.4 Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements. (Grades 9 - 10) [2000]
- 10.P.7 Solve everyday problems that can be modeled using linear, reciprocal, quadratic, or exponential functions. Apply appropriate tabular, graphical, or symbolic methods to the solution. Include compound interest, and direct and inverse variation problems. Use technology when appropriate. (Grades 9 - 10) [2000]
- 10.N.1 Identify and use the properties of operations on real numbers, including the associative, commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive real numbers for any positive integer n; and the inverse relationship between taking the nth root of and the nth power of a positive real number. (Grades 9 - 10) [2000]
- 10.N.2 Simplify numerical expressions, including those involving positive integer exponents or the absolute value, e.g., 3(2² - 1) = 45, 4|3 - 5| + 6 = 14; apply such simplifications in the solution of problems. (Grades 9 - 10) [2000]
- 10.N.4 Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers. (Grades 9 - 10) [2000]
Massachusetts Science
- 1.1 Given a design task, identify appropriate materials (e.g., wood, paper, plastic, aggregates, ceramics, metals, solvents, adhesives) based on specific properties and characteristics (e.g., weight, strength, hardness, and flexibility). (Grades 6 - 8) [2001]
- 2.1 Identify and explain the steps of the engineering design process, i.e., identify the need or problem, research the problem, develop possible solutions, select the best possible solution(s), construct a prototype, test and evaluate, communicate the solution(s), and redesign. (Grades 6 - 8) [2001]
- 2.2 Demonstrate methods of representing solutions to a design problem, e.g., sketches, orthographic projections, multiview drawings. (Grades 6 - 8) [2001]
- 6.2 Given a transportation problem, explain a possible solution using the universal systems model. (Grades 6 - 8) [2001]
- 2.3 Describe and explain the purpose of a given prototype. (Grades 6 - 8) [2001]
- 2.5 Explain how such design features as size, shape, weight, function, and cost limitations would affect the construction of a given prototype. (Grades 6 - 8) [2001]

One time cost:

Wooden ramp with adjustable incline (6 ft long, 7-8 inch wide track, elevation 0º to 90º) (1 per class - see attachment for details on how to build one)
5" x 8" wooden base (1 per group)
Screw eyes (4 per group)
Threaded rod to fit through screw eyes or wooden dowel (2 per group)
Wheels (Hobby or cut from a dowel) (4 per group)
E-clips or washers (4 per goup)
Stop watches
Meter stick
Protractor
Balance
String
Stapler
Scissors
Razor blade

Suggested materials

Eggs (Atleast one per group)
Wooden eggs for practice (optional)
Cardboard squares
Pipe cleaners
Small rubber bands
Large rubber bands
Cotton balls
Soda straws
Craft sticks
Masking tape
Scotch tape
Soda bottles
Super glue
Packaging peanuts
Cups (paper or plastic)
Bubble wrap
Binder clips
Staples

You and your team are members in the research and development department of a major car manufacturing company. You are in charge of testing a prototype safety harness on the latest line of cars. Your research team has provided you with instructions to create the device. Now it's your job to construct and test this prototype and determine how effective it is. In a real lab situation, the car would be accelerated into a wall. As you do not have the facilities to perform this test, you will be using a ramp to simulate acceleration. To do your test, run your prototype car down the ramp starting at the lowest angle and see how well it performs. If it passes one angle, increase the slope and run the experiment again. If it fails, record the angle and stop testing. Compare your results with those of the other tests in the class to determine the average angle at which the prototype's safety mechanism failed. Based upon your results, make a recommendation as to whether or not the safety mechanism is effective. The company standards require that the safety mechanism be able to withstand an impact at a 50º incline run.

Before the Activity

Introduce the challenge: To design a safety device that will hold an egg on the car and keep it from breaking as the car is rolled down the ramp at increasing slopes. The target is to have the egg roll down the ramp at a 50 degree angle without cracking. Extra credit can be given to groups that can acheive success at a greater angle.
Ensure that while the students are making the total cost calculations, they include only the cost of the materials used in the final device. They may have redesigned their device while construction and decided not to use some of the materials they chose initially. They should not be charged for materials that they did not end up using in their final product.
Explain the constraints (see attachment).
Conduct the activity.
After completion of the activity discuss the importance of having the "cost-to-performance" ratio and go over the principles of physics that can be observed in each device prototype. (see notes by a teacher attachment for more details)

With the students

Distribute student handouts (see attachments).
Work in their groups to discuss and draw possible solutions and choose the best ideas. (The brainstorming/sketch should be a graded component of the project). This is a possible breakpoint for a short activity.
The teacher verifies that the group has a unified drawing or idea, and the group is allowed to "purchase" materials.
Groups are given 30-60 minutes to construct their devices.
Calculate materials cost. This is another possible breakpoint.
One group presents its design, describing the construction, explaining why it is designed as it is, and announcing the construction cost to the class.
The teacher records the construction cost in the design database (which could be a chart on the wall or a spreadsheet projected for the class to see). He/she then revisits the design constraints and verifies that the device is in conformance.
Have each group take the mass of their device (record in data table).
The device is then tested at a low slope on the ramp.
Record the time it takes to move down the ramp and the incline number of the ramp in the data table.
The device is repeatedly tested until the highest slope is reached or the egg is broken (to any observable degree).
If a device needs minor repairs between runs, the design team can be given a set amount of time (perhaps 1-2 minutes) to make the minor repairs (record mass of newly designed device).
Each device is checked and tested in the same manner.
Determine angle measurements for each incline number. (optional).
Calculate weight, speed, and cost/performance ratio*. Use the Excel file (attached) to project the results on a screen/wall.

* Note: The fictional dollar cost from the "Cost Account" sheet is divided by the highest ramp level survived to create the cost/performance ratio.

If time and enthusiasm permit, have students re-design their solutions at home. The re-designs could be presented to the class at a later date.
Have students evaluate their own devices: What is good/bad about the design solution and why? How could it be improved?
Explore what formula might provide a fairer cost/performance ratio.
Explore how to mass-produce the best design(s). All of the standards related to manufacturing could be addressed through the production process.
Use weight of the device constructed as a design constraint.

Depending on the level of the class make use of the "possible breakpoints" indication in the procedure. If availability of materials is an issue stop at the point where the students draw a sketch of the device. Have them explain their design and discuss how it might be successful or not. Another possibility is to have students bring in their own materials for the cars - although this would make the car bases uneven across the class, the principles of physics can still be observed in the devices they build.

K-12 Outreach Office, Worcester Polytechnic Institute This project was developed as an IQP project by Scott Beaurivage, Justin Riley, and Ryan St. Gelais, undergraduate engineering students at, Worcester Polytechnic Institute, Funded in part by, Pratt & Whitney © 2005 by Worcester Polytechnic Institute including copyrighted works of other educational institutions; all rights reserved.

Last Modified: June 22, 2006