Grade level: Grade 12 (taking physics too)
Materials: Video, pencil, paper, calculator
Objectives: Students will observe how velocity and centrifugal forces work together and be able to answer questions, using formulas, about the two.
Mathematical Concepts: Velocity, centrifugal force, meters, seconds, initial velocity, rotation, circular motion, tangent, prportion, calculation.
NCTM Standards:
Standard 1: Mathematics as Communication
Standard 2: Mathematics Communication
Standard 3: Mathematics as Reasoning
Standard 4: Mathematical Connections
Standard 6: Number Systems and Number Theory
Standard 7: Computation and Estimation
Procedure: Show students a video of people riding the "Gravitron" (this will instruct students on exactly how it works). The "Gravitron" is a popular ride up in Orlando, Florida.
Instructions: This basically gives a brief description on how the "Gravitron" works. When the rotor reaches a certain speed, the floor drops out. But the riders do not fall ! A centrifugal force pushes a Rotor Rider against the wall, and the reaction force of the wall balances this force so he is at rest with respect to the rotating frame. To an outside observer, a rider standing away from the wall cannot maintain the circular motion and flies off tangentially up against the wall, where the reaction force supplies the centrifugal force needed for circular motion. The only force to balance the downward gravitional weight force is the upward frictional force between a rider and the wall.
Questions:
1. What keeps the people from falling?
2. Since the frictional force is proportional to the reaction force of the Rotor Wall on a person, what would happen if the Rotor speed was greater than the Critical speed?
3. What if the frictional force was to become greater, would the people move up the wall?
4. Calculate the Critical speed given the following data.
References: Today's Mathematical Physics (1993)
Mathematics and Science Office of Barry University
Contributors: Major: Shervon Monrose
Minor: Carol Marinas