Gravitational Potential Energy & the Roller Coaster
From the formula GPE = mgh to the physics of a real roller coaster — stored energy becoming motion.
GPE = Stored Energy Due to Height
Gravitational potential energy is the energy an object stores because of where it is — how high it sits above the ground. The object doesn't have to be moving. The energy is stored, waiting to become motion the moment the object falls.
Memory trick: "mgh" — Mass × Gravity × Height. Gravity is always 9.8 on Earth — you never change it. The only things that differ between problems are mass and height. Taller + heavier = more GPE.
Write the formula.
GPE = m × g × hSubstitute: m = 2 kg, g = 9.8, h = 5 m.
GPE = 2 × 9.8 × 5Multiply: 2 × 9.8 = 19.6 → 19.6 × 5 = 98.
GPE = 98 JoulesAt the Top of the First Hill — Maximum GPE
As the coaster is pulled up to the highest point, it gains GPE (GPE = m × g × h). At the very top, height is maximum, so GPE is maximum. The coaster is barely moving, so kinetic energy (KE) is nearly zero.
As the Coaster Descends — GPE Converts to KE
Going downhill, height decreases → GPE decreases. That lost GPE converts into kinetic energy (motion). The coaster accelerates. The total mechanical energy (GPE + KE) stays constant — energy is not lost, just transformed.
At the Bottom — Minimum GPE, Maximum KE
At the lowest point, height ≈ 0, so GPE ≈ 0. All the energy is now kinetic — the coaster is at its maximum speed. For a 1,000 kg car dropped 45 m, this equals a speed of about 30 m/s (108 km/h)!
Subsequent Hills — Why Each Must Be Lower
As the coaster climbs the next hill, KE converts back to GPE and the car slows. In a real coaster, friction and air resistance slowly convert some mechanical energy to heat, so each successive hill must be lower than the last — the coaster can't climb as high as it started.
Still
zero KE
Speeding
Max speed
MAX KE
- Coaster at top of hill
- Book on a high shelf
- Rock at cliff edge
- Water behind a dam
- Coaster flying downhill
- Book falling off shelf
- Rock falling from cliff
- Water flowing through turbines
Key Points to Remember
GPE is stored energy due to height — no motion required.
Formula: GPE = m × g × h — always use g = 9.8 m/s² on Earth.
Double the height → double the GPE. Mass and height are both directly proportional.
On a roller coaster, GPE converts to KE going down, and KE converts back to GPE going up.
Friction converts some mechanical energy to heat — that's why each hill must be lower than the last.
Total mechanical energy (GPE + KE) stays constant if we ignore friction.
See GPE and KE Trade Off in Real Time
Drag the red car along the track — or tap a step button — and watch the energy bars update instantly. Adjust mass and hill height with the sliders to see how GPE = m × g × h changes.
Gravitational Potential Energy of a Roller Coaster
Drag the car along the track — or tap a step to explore each phase
GPE → KE as the car descends · KE → GPE as the car climbs · Total energy stays constant (ignoring friction)
Try the Formula Yourself
Enter mass and height — gravity is locked at 9.8 m/s² for Earth. Every step of the calculation is shown so you can follow the method for any GED problem.
GPE = 2 × 9.8 × 5 = 98 J. Move it to h = 10 m: GPE = 2 × 9.8 × 10 = 196 J.
🔑 Doubling height doubled GPE — direct proportion.
GPE = 1,000 × 9.8 × 45 = 441,000 J at the top. At the bottom (h = 0): GPE = 0, all energy is KE.
Speed at bottom: v = √(2 × KE ÷ m) = √(2 × 441,000 ÷ 1,000) ≈ 29.7 m/s (107 km/h)!
🔑 All GPE stored at the top converts to kinetic energy at the bottom — that's what makes roller coasters fast.
GPE = 500 × 9.8 × 30 = 147,000 J
🔑 A massive object at height stores enormous energy — which is why falling boulders are so destructive.