Explore the fundamental law of mechanical energy conservation with interactive roller coaster tracks. Sculpt custom terrain splines, test vertical loop-the-loop critical apex velocities (h_min = 2.5R), inspect real-time floating energy pie charts, and measure normal force G-meter loads.
Interactive Experiment Guide
Start with fundamental scientific principles, launch the simulation, and verify mathematical predictions against real-time outcomes.
Scientific Foundation
The Law of Conservation of Energy states that total energy in an isolated system remains strictly constant: E_total = E_p + E_k + E_th = constant. Gravitational potential energy Ep = mgy converts into kinetic energy Ek = ½mv² as the cart descends. In real systems with friction, non-conservative friction forces fk = μk·mg·cosθ perform negative work, transforming mechanical energy into internal thermal dissipation (Eth).
Interactive Simulation Flow
Launch the simulation workspace, adjust parameters in real time, and observe the immediate response in the telemetry and graphical indicator loops.
Frequently Asked Questions
At the top of the loop (apex), the cart requires a minimum centripetal acceleration ac = v²/R = g so that normal force FN ≥ 0 (critical velocity v_apex = √(gR)). Conserving mechanical energy from release height h to apex height 2R gives mgh = mg(2R) + ½m(gR) = 2.5mgR, proving h_min = 2.5R.