roller coaster / Lesson Plan

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Objective

By the end of this lesson, the student will be able to apply mathematical concepts to analyze and understand the physics of roller coasters.

Materials and Prep

  • Paper and pencil
  • Calculator (optional)
  • Access to the internet (for research)
  • Basic knowledge of algebra and geometry

Activities

  1. Research and analyze the design of a roller coaster:

    • Choose a roller coaster that interests you and find information about its height, length, and speed.
    • Calculate the potential energy, kinetic energy, and total energy of the roller coaster at different points along its track.
    • Graph the energy changes on a coordinate plane.

  2. Create a scale model of a roller coaster:

    • Design a roller coaster using paper and pencil.
    • Label the different parts of the roller coaster, such as the highest point, the lowest point, and any loops or twists.
    • Calculate the slope and curvature of different sections of the roller coaster.

  3. Explore the forces acting on a roller coaster:

    • Identify and describe the forces acting on a roller coaster, such as gravity, normal force, friction, and air resistance.
    • Calculate the net force and acceleration of the roller coaster at different points along its track.
    • Discuss how these forces affect the motion of the roller coaster.

Talking Points

  • "Roller coasters are a thrilling combination of physics, engineering, and mathematics."
  • "When analyzing a roller coaster, it's important to consider the different types of energy involved."
  • "Potential energy is the energy an object possesses due to its position or height."
  • "Kinetic energy is the energy an object possesses due to its motion."
  • "Total energy is the sum of potential energy and kinetic energy."
  • "Creating a scale model of a roller coaster can help us understand its design and mathematical properties."
  • "The slope of a roller coaster represents its steepness or incline."
  • "Curvature refers to how sharply or smoothly the track bends."
  • "Forces play a crucial role in the motion of a roller coaster."
  • "Gravity is the force that pulls the roller coaster downwards."
  • "Normal force is the force exerted by a surface to support the weight of an object."
  • "Friction and air resistance can affect the speed and movement of a roller coaster."
  • "Net force is the vector sum of all forces acting on an object."
  • "Acceleration is the rate at which an object's velocity changes."

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