Energy Transformations, Conservation of Energy, and Waves

Energy Transformations, Conservation of Energy, and Waves

Law of Conservation of Energy

Energy cannot be created or destroyed; it can only be transformed from one form to another. The total energy in an isolated system remains constant.

Forms of Mechanical Energy

1. Kinetic Energy ($KE$): Energy of motion. $$KE = \frac{1}{2}mv^2$$
2. Potential Energy ($PE$): Stored energy due to position or height. $$PE = mgh$$

At the top of a roller coaster hill, potential energy is at its maximum and kinetic energy is near zero. At the bottom of the drop, potential energy transforms completely into maximum kinetic energy.

Wave Properties

• Wavelength ($\lambda$): Distance between successive crests or troughs.
• Frequency ($f$): Number of waves passing a point per second (measured in Hertz, Hz).
• Wave Speed Equation: $$v = f \cdot \lambda$$