Understanding Potential Energy

Potential energy is stored energy that an object has due to its position, configuration, or condition. Unlike kinetic energy which depends on motion, potential energy represents the potential for doing work.

Gravitational Potential Energy

The formula PE = mgh calculates the energy stored in an object due to its height above a reference point. Here, m is mass, g is gravitational acceleration (9.8 m/s² on Earth), and h is height. The higher an object is lifted, the more potential energy it stores.

Elastic Potential Energy

Springs and elastic materials store energy when stretched or compressed. The formula PE = ½kx² shows that elastic potential energy depends on the spring constant (k) and the displacement (x) from the equilibrium position. Note that energy increases with the square of displacement.

Electric Potential Energy

Two charged particles have potential energy due to their electrostatic interaction. The formula PE = kq₁q₂/r uses Coulomb's constant (k ≈ 8.99×10⁹ N·m²/C²), the two charges, and the distance between them. Like charges result in positive (repulsive) energy, while opposite charges give negative (attractive) energy.

Conservation of Energy

Potential energy can be converted to kinetic energy and vice versa. A falling object converts gravitational PE to kinetic energy. A compressed spring releases its elastic PE as kinetic energy. Total mechanical energy (PE + KE) remains constant in an isolated system.

Examples of Potential Energy

• Water behind a dam: Gravitational PE converted to electrical energy
• Drawn bow: Elastic PE stored in the bent limbs
• Roller coaster at top: Maximum gravitational PE
• Compressed car spring: Elastic PE for suspension

Gravity on Different Bodies

Gravitational potential energy varies with location. On the Moon (g = 1.62 m/s²), an object has less gravitational PE at the same height compared to Earth. On Jupiter (g = 24.79 m/s²), it would have much more.