Gravitational Potential Energy

Gravitational potential energy: Ep = m·g·h

Lift a body against gravity and it banks energy. That stored amount is the gravitational potential energy, Ep = m·g·h, measured in joules, with mass in kg, gravity g ≈ 9.81 m/s² near Earth's surface, and height in meters from whatever reference you pick. Put a 2 kg book on a 5 m shelf and it holds Ep ≈ 98 J relative to the floor. Let it fall and those 98 J show up as kinetic energy when it lands. Notice the result hangs on the reference you chose. The zero level is up to you, so what actually matters physically is the difference, ΔEp. When there's no friction and the system is conservative, Ec + Ep = constant, which is where mechanical energy conservation comes from.

Applications

It shows up in hydroelectric plants, where Itaipu's ~14 GW comes from turning the Ep of dammed water into electricity, and in pumped-storage hydropower. A roller coaster's first climb sets the energy budget the rest of the ride has to spend. The same idea drives free-fall problems, pile drivers, and gravitational batteries that hoist heavy weights to release the energy later.

FAQ

Does g change with location? It does. You get about 9.78 m/s² at the equator and 9.83 m/s² at the poles, a consequence of how the Earth spins and how it's shaped. For everyday problems, 9.81 m/s² is close enough.

What is the reference height? You decide where h = 0, whether that's the floor, sea level, or a table top. The physical results only depend on differences in Ep, never the absolute value.

Is mgh valid at any altitude? Only while the height stays small next to Earth's radius. Once you're dealing with satellites or space, switch to the general form Ep = -G·M·m/r.