Kinetic and potential energy
Kinetic energy is the energy of motion, given by KE = ½mv², while potential energy is stored energy due to position or configuration, such as gravitational potential energy PE = mgh. In a system with no friction, the two convert back and forth while their total stays constant.
Kinetic and potential energy are the two fundamental forms of mechanical energy. Kinetic energy is the energy an object has because it is moving: KE = ½mv², where m is mass and v is speed. Potential energy is stored energy an object has because of its position or configuration — energy with the potential to become motion.
The two most common types of potential energy are gravitational and elastic. Gravitational potential energy near Earth's surface is PE = mgh — lift a 2 kg book 1.5 m and you store about 29 J (2 × 9.8 × 1.5). Elastic potential energy stored in a stretched or compressed spring is PE = ½kx², where k is the spring constant and x the displacement from equilibrium. Note that kinetic energy depends on speed squared: doubling an object's speed quadruples its kinetic energy.
The power of these ideas comes from conservation of energy. In the absence of friction and air resistance, total mechanical energy (KE + PE) stays constant, so energy simply shifts between forms. A dropped ball trades height for speed; a pendulum swings between maximum potential energy at its endpoints and maximum kinetic energy at the bottom; a mass on a spring oscillates between elastic potential energy and kinetic energy. When friction acts, mechanical energy is not destroyed but converted to thermal energy.
The AP Physics 1 exam tests kinetic and potential energy throughout its work, energy, and oscillations units — energy bar charts, conservation problems, and energy in simple harmonic motion. The FE Civil exam applies the same principles in its dynamics section, using work-energy methods to solve engineering motion problems.
Key takeaways
- Kinetic energy is energy of motion: KE = ½mv²; doubling speed quadruples kinetic energy.
- Potential energy is stored by position: gravitational PE = mgh, elastic PE = ½kx².
- Without friction, total mechanical energy is conserved as KE and PE convert into each other.
- Friction converts mechanical energy to thermal energy rather than destroying it.
- AP Physics 1 and the FE Civil exam both test energy conservation and work-energy problem solving.