Core Formulas
Mechanical energy
Conservation of energy (no friction)
Speed at bottom from height h
Concept

Mechanical energy is the sum of kinetic energy (KE = ½mv²) and gravitational potential energy (PE = mgh). When friction is absent, total mechanical energy is conserved — it converts between KE and PE but never disappears.

Adding friction introduces thermal energy: total energy (KE + PE + thermal) is always conserved, but mechanical energy decreases. The skater slows down as energy transfers to heat.

Watch the energy bars: with zero friction the green Total bar stays constant at every instant — that's the proof of conservation.

How to Use

Place the skater on the ramp with the Start Height slider and press play. Watch the energy bars as the skater rises and falls. Enable friction to see energy converted to thermal energy. Try the presets — energy conservation holds on the Moon and Mars too.

Key Facts
Historical Context
Gottfried Leibniz coined "vis viva" (living force) in 1686 — the precursor to kinetic energy. The modern term "energy" wasn't standardized until Thomas Young in 1807.
Common Misconception
Heavier skaters don't go faster! Mass cancels out in energy conservation (mgh = ½mv²), so release height alone determines speed at the bottom.
AP Connection
AP Physics 1 Big Idea 5: The total energy of a closed system is conserved. This is tested in free-response questions about roller coasters, pendulums, and springs.
Why It Matters
Roller coasters are engineered using energy conservation — no engine needed after the first drop
Hydroelectric dams convert gravitational PE of water into electrical energy at ~90% efficiency
Planetary orbits, pendulum clocks, and bouncing balls all obey the same E = KE + PE law
Energy Panel
KE (Kinetic) 0.00 J
PE (Potential) 0.00 J
Thermal 0.00 J
Total (KE+PE+Th) 0.00 J
Height: 0.00 m
Speed: 0.00 m/s
Mass: 60 kg
Gravity: 9.80 m/s²
Quiz
1. A 60 kg skater starts from rest at a height of 5 m. What is their speed at the bottom of the ramp? (g = 9.8 m/s²)
2. With friction enabled, can the skater reach the same height on the other side of the ramp?
3. How does the skater's mass affect the maximum speed at the bottom of the ramp (no friction)?
Live Data
Time: 0.0 s
Position: 0.00 m
Velocity: 0.00 m/s
KE: 0.00 J
PE: 0.00 J
Thermal: 0.00 J
E_total: 0.00 J
Speed:
60 kg
4.0 m
9.80 m/s²
0.00
⌨ Space: play/pause · R: reset · 1–5: presets · , / . : slower / faster