Potential Energy, Work, and Centripetal Force Explained
Three core physics formulas — gravitational potential energy, mechanical work, and centripetal force — worked through with real numbers.
Potential energy, work, and centripetal force are three distinct physics concepts that share a common thread: each converts a physical setup into a single energy or force number using nothing more than multiplication.
Gravitational potential energy
PE = mgh. An object with a mass of 5kg held at a height of 10 meters: PE = 5 × 9.8 × 10 = 490 joules of stored energy, entirely due to its position in a gravitational field. Drop it, and (ignoring air resistance) that same 490 joules converts almost entirely into kinetic energy right before impact.
Mechanical work
W = F × d. Applying a 20N force to move an object 5 meters in the direction of that force: W = 20 × 5 = 100 joules of work done. Notably, if the force and the direction of motion aren't aligned, only the component of force in the direction of movement counts — pushing at an angle wastes some effort that doesn't contribute to useful work.
Centripetal force
F = mv²/r. Keeping a 2kg object moving in a circular path of radius 2 meters at 5 m/s requires: F = (2 × 5²)/2 = (2×25)/2 = 25 newtons of force directed toward the circle's center. Double the speed to 10 m/s (same mass and radius), and required force becomes (2×100)/2 = 100N — quadruple the original, because velocity is squared in the formula, the same squared relationship seen in kinetic energy.
What connects all three
Each formula ultimately traces back to Newton's laws and the definition of energy as force applied over distance. Potential energy, kinetic energy, and work are all measured in the same unit (joules) precisely because they're different forms or transfers of the same underlying quantity — energy — while centripetal force is a force (newtons) required to maintain circular motion, not a form of energy itself.
Common mistakes to avoid
- Forgetting that centripetal force isn't a separate, additional force acting on an object — it's whatever existing force (tension, gravity, friction) happens to be providing the center-directed pull
- Assuming work is done any time force is applied — if there's no resulting displacement (like pushing against an immovable wall), zero work is done by definition, regardless of effort exerted
- Mixing up mass and weight when calculating potential energy — the formula needs mass in kilograms, with gravity as a separate multiplied term, not weight (a force) substituted directly
Calculate your own scenarios with the potential energy calculator, work calculator, and centripetal force calculator.