Early Phase of the Program

Roller Coaster

Title of the Lesson: Roller Coaster

NJ Core Curriculum Content Standards addressed in the lesson.

5.1.12.C.1 (Refinement of understandings, explanations, and models occurs as new evidence is incorporated): Reflect on and revise understandings as new evidence emerges.
5.1.12.D.1 (Science involves practicing productive social interactions with peers, such as partner talk, whole-group discussions, and small-group work): Engage in multiple forms of discussion in order to process, make sense of, and learn from others' ideas, observations, and experiences.
5.1.12.D.2 (Science involves using language, both oral and written, as a tool for making thinking public): Represent ideas using literal representations, such as graphs, tables, journals, concept maps, and diagrams.
5.2.C (Forms of Energy): Knowing the characteristics of familiar forms of energy, including potential and kinetic energy, is useful in coming to the understanding that, for the most part, the natural world can be explained and is predictable.
5.2.D (Energy Transfer and Conservation): The conservation of energy can be demonstrated by keeping track of familiar forms of energy as they are transferred from one object to another.
5.2.12.D.1 (The potential energy of an object on Earth's surface is increased when the object's position is changed from one closer to Earth's surface to one farther from Earth's surface.): Model the relationship between the height of an object and its potential energy.
5.2.E (Forces and Motion): It takes energy to change the motion of objects. The energy change is understood in terms of forces.
5.2.12.E.2 (Objects undergo different kinds of motion (translational, rotational, and vibrational).): Compare the translational and rotational motions of a thrown object and potential applications of this understanding.
5.2.12.E.3 (The motion of an object changes only when a net force is applied.): Create simple models to demonstrate the benefits of seat belts using Newton's first law of motion.
5.2.12.E.4 (The magnitude of acceleration of an object depends directly on the strength of the net force, and inversely on the mass of the object. This relationship (a=Fnet/m) is independent of the nature of the force.): Measure and describe the relationship between the force acting on an object and the resulting acceleration.

Identify Resources needed.
Teacher Use: Ruler/ meter stick
Student Use: Lesson handout, pen/pencil, bisected foam tubing, tape, toothpicks, marbles

Describe what students should know before they start the lesson.

Students should be able to work cooperatively in small groups. They should listen to and have respect for others' ideas.
Students should understand energy conservation and how it relates to the motion of the marble.
Students should understand how the potential energy of a system is related to the height of the system object (marble).

State the objectives of the lesson.

Students will increase their ability to work cooperatively to solve a problem.
Students will learn how to use a systematic approach to solving a problem.
Students will learn how to use the engineering design process to solve a problem.
Students will learn that engineering involves using their ideas and knowledge to solve real-world problems.
Students will learn to balance the cost of materials used with the benefits they provide.
Students will apply their knowledge of physics to solve a real world problem.

Identify important ideas in terms the subject area - describe in detail.

Conservation of energy: Gravitational potential energy stored in the marble when it begins is transferred into kinetic and rotational kinetic energy of the marble as it moves to lower height. The kinetic energies transfer back into gravitational potential energy as the marble travels up through a loop.
Friction: The marble will only roll (as opposed to slide) if there is enough friction to cause rotational motion via torque exerted by the track surface on the marble. Friction between the track and the marble will also cause some energy to be transferred into thermal energy and lost. The marble will not return to its original height because some of the original gravitational potential energy will be lost as thermal energy.
Torque: Torque = Force * radius * sin Θ. For the marble, sin Θ = 1 so the torque exerted on the marble by the track surface, which causes the marble's rotational motion, = friction force exerted by track on marble * radius of the marble.
Center of mass: The free-standing roller coaster will only be stable if there is support for the center of mass of the structure.
Uniform circular motion: The velocity necessary for the marble to stay in contact with the track at the top of the loop is such that the entirety of the force necessary to cause the marble to accelerate towards the center (stay in uniform circular motion) is supplied by the force exerted by Earth on the marble, thus m*g = mv2/r or v = (g*r)½ . The larger the loop radius, the faster the marble must be moving to “make it” around the loop.
The engineering problem-solving strategy (which mimics the ISLE cycle for experimentation) involves devising a series of possibilities that are tested and revised.
The eight steps of the engineering design process are: identify the need or problem, research the need or problem, develop possible solutions, select the best possible solution, draw a prototype, test & evaluate, communicate the solution, and redesign.

Describe potential difficulties students may experience with the content. Describe all formative assessments that you plan to use and how you will provide feedback.

Students may have difficulty working cooperatively. One group member may dominate, especially boys in mixed gender groups.
Students may have difficulty applying the engineering design process, rather than just employing a trial and error strategy. I will remind the students to plan ahead. Also, I can present the problem but not make the materials available for the first five minutes, which will force students to plan (steps 2-5) before building their prototype.
I will monitor the groups, and make sure to engage group members whose opinions don't appear to be being listened to. This will demonstrate to the dominating group members that the others' ideas are to be valued. This also will ensure that all group members are contributing equally, and that all group members understand the successes and failures of their prototypes.
I will ask groups what problems they are having, or what is standing in the way of their meeting their goals, to engage them in a discussion about the possible strategies they could employ to solve their problems, rather than just using trial and error. I will ask students what assumptions they made in their initial plan that turned out to not be valid, and how they have revised their assumptions.
If a group adopts a new approach, I will ask them to explain what they changed and the reason for the change. In addition, I will try to get them thinking about the physics explanation for the failure of their prior prototype.
I will ask students to draw energy bar charts for the marble-Earth system at various locations in their roller coaster. Students will need to account gravitational potential energy, rotational (for advanced students) and translational kinetic energy, and the change in internal/ thermal energy of the system.

Provide a description of the lesson including an agenda for the lesson.

See handout attached at end of lesson plan

Time Table – who is going to be doing what and when during the lesson to make sure that students are actively engaged.

Clock reading / Title of activity / Students doing / Me doing
0 - 5 min / Introduction / Listening / Presenting the activity including available materials, assigning groups
5 – 10 min / Planning / Working in groups to brainstorm ideas / Monitoring group work
10 – 35 min / Construction / Evaluating different ideas, constructing and testing prototypes / Monitoring group work
35 – 40 min / Final test / Testing final roller coaster prototypes / Testing final roller coaster prototypes, assigning asthetic scores
40 – 45 min / Reflection / Talking, sketching prototypes from other groups (necessary for homework assignment) / Listening, commenting

Describe the homework you will assign. What guidance will you provide the students?

The homework will be for students to assess the strengths and weaknesses of their own design, and also that of at least one other group.

Teacher's Guide

Make sure students are divided into effective groups. Group together students with differing strengths. Make sure all group members are actively participating.
Make sure students follow the engineering design process and plan before building.
Ensure that you are familiar with the materials and their benefits/ pitfalls.
The challenge (designing a free-standing roller coaster) provides an additional activity for students who complete the first activity quickly. It can be skipped/ omitted for time constraints.

Roller Coaster

Goal #1: Develop and construct a roller coaster with the smallest possible Ratio.

Here are the design criteria you must follow:

The marble must travel the entire length of the roller coaster without losing contact with the track surface.
You may include one or more loops in your design, The total number of inches of all loop diameters will be added to calculate the Total Loop Diameter.
Only material listed may be used.

Available materials and cost:

Material / Quantity Used / Cost per piece / Total (Quantity * Amount)
Foam tubing / $1.00
Tape (per foot) / $0.10
Toothpick / $0.10
TOTAL COST:

Total loop diameter in Inches: ______

Aesthetic Rating: ______(1 to 6, with 1 having the best look, assigned by teacher)

Calculation of Cost & Aesthetic Ratio:

(total cost divided by total loop diameter in inches added to the aesthetic rating divided by 10)

Total cost: Aesthetic Rating:

______+ ______= ______

Total loop 10

diameter:

Be sure to follow the Engineering Design Process and document your work:

Step Number / Comments and Observations
1: Identify the need or problem
2: Research the need or problem
3: Develop possible solutions
4: Select the best possible solution
5: Draw a prototype
6: Test and evaluate
7: Communicate the solution
8: Redesign

Roller Coaster

Goal #2: Develop and construct a free-standing roller coaster with the smallest possible Ratio.

Here are the design criteria you must follow:

The marble must travel the entire length of the roller coaster without losing contact with the track surface.
You may include one or more loops in your design, The total number of inches of all loop diameters will be added to calculate the Total Loop Diameter.
Only material listed may be used.
Your roller coaster must be free-standing which means you can pick it up and move it. The only object it may be in contact with is the floor, and it may be be attached to the floor in any way.

Available materials and cost:

Material / Quantity Used / Cost per piece / Total (Quantity * Amount)
Foam tubing / $1.00
Tape (per foot) / $0.10
Toothpick / $0.10
TOTAL COST:

Total loop diameter in Inches: ______

Aesthetic Rating: ______(1 to 6, with 1 having the best look, assigned by teacher)

Calculation of Cost & Aesthetic Ratio:

(total cost divided by total loop diameter in inches added to the aesthetic rating divided by 10)

Total cost: Aesthetic Rating:

______+ ______= ______

Total loop 10

diameter:

Be sure to follow the Engineering Design Process and document your work:

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