Conservation of mechanical energy
Frictionless roller-coaster loop: ½mv² + mgy = mgh; critical v_top = √(gR), minimum height h_min = 2.5R.
Work & mechanical energyWork, kinetic/potential energy, and conservation.
Start here
Conservation of mechanical energy
Energy conservation on a frictionless roller coaster loop. This “Conservation of mechanical energy” page is an MVP interactive sketch — formulas, controls, and live readouts in the browser; a fuller bench may follow.
Energy conservation on a frictionless roller coaster loop.
Key formulas
\tfrac12 mv^2+mgy=mghv_{\text{顶}}=\sqrt{gR}h_{\min}=2.5R
How to use
- Adjust parameters in the left panel.
- Use play / pause and speed controls.
- Match right-side readouts to the formulas.
- Reset to return to the initial state.
Applications
- Conservation of mechanical energy: Energy conservation on a frictionless roller coaster loop.
- Classroom focus: critical v_top = √(gR), minimum height h_min = 2.
FAQ
What does MVP mean on this page?
An interactive sketch with formulas and parameters. Polished Ready labs are the full bench experience.
What does the “Conservation of mechanical energy” lab practice?
Tune parameters and match readouts to the “Conservation of mechanical energy” relations — useful for prep and demos.
Self-study or classroom?
Both — tune alone, or project “what if…?” demos in class.
Readouts don’t match the formula?
Check units and ranges, then substitute step-by-step from the formula panel.