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Roller Coaster Energy Conservation

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About This MicroSim

This simulation demonstrates conservation of mechanical energy by showing a cart rolling along a roller coaster track. Watch as energy transforms between kinetic energy (speed) and potential energy (height) while the total mechanical energy remains constant.

Key Concepts

Conservation of mechanical energy:

\[KE_i + PE_i = KE_f + PE_f\]
\[\frac{1}{2}mv_i^2 + mgh_i = \frac{1}{2}mv_f^2 + mgh_f\]

At any point along the track: - Maximum PE, minimum KE: At the highest points (cart moves slowest) - Maximum KE, minimum PE: At the lowest points (cart moves fastest) - Total energy: Remains constant (green line stays flat)

Controls

  • Release Cart: Start the simulation from the top of the track
  • Pause/Resume: Pause or continue the simulation
  • Reset: Return cart to starting position
  • Track Shape: Choose between Simple Hill, Double Hill, or Loop-de-loop
  • Mass: Adjust cart mass (0.5-5 kg)
  • Height: Set initial drop height (5-15 m)
  • Friction: Add friction to see energy dissipation (0-0.3)

Visual Elements

  • Stacked Bar Chart: Shows current KE (blue) and PE (red) distribution
  • Energy vs Time Graph: Plots KE, PE, and total energy over time
  • Cart Color: Changes from blue (slow) to red (fast) based on speed
  • Height Markers: Reference scale on left side

Learning Objectives

  • Visualize energy transformation between kinetic and potential forms
  • Verify that total mechanical energy remains constant without friction
  • Understand how friction causes mechanical energy to decrease over time
  • Predict where the cart will move fastest and slowest