# Conservation of Energy

## Conservation of Energy Principle

- The
**Conservation of Energy Principle**is a key concept in physics that asserts that energy can neither be created nor destroyed; rather, it only changes from one form to another. - This principle is derived from the
**first law of thermodynamics**, which concerns the balance of energy in a system: if a system is closed (i.e., no energy in and out), the total energy remains constant. - The main types of energy that can be interconverted are
**kinetic energy**,**potential energy**,**heat energy**,**chemical energy**,**electrical energy**, and**nuclear energy**.

## Kinetic Energy and Potential Energy

**Kinetic energy (K)**is the energy of motion. The kinetic energy of an object can be calculated from its mass (m) and velocity (v) using the equation K = 0.5mv^2.**Potential energy (P)**is stored energy, which can be converted into kinetic energy. For example, the potential energy in a raised object will be converted into kinetic energy as it falls.- The potential energy can be calculated from the object’s mass (m), the acceleration due to gravity (g), and the height (h) using the formula P = mgh.

## Principle of Conservation of Mechanical Energy

- The
**Principle of Conservation of Mechanical Energy**relates to the sum of kinetic and potential energy. It states that, in a closed system with no non-conservative forces acting (like friction), the total mechanical energy is constant. - This principle gives us the equation: K_initial + P_initial = K_final + P_final.
- This tells us that the total energy at the start (K_initial + P_initial) is equal to the total energy at the end (K_final + P_final).

## Applications of Conservation of Energy

- Understanding the Conservation of Energy Principle is crucial for comprehending and solving various physical phenomena and real-world situations.
- It is applied in many fields, such as engineering, mechanics, thermal physics, and even biology.
- For instance, in roller-coaster rides, the total energy (potential + kinetic) of the cart is conserved, with potential energy being converted into kinetic energy as the cart descends.
- Similarly, in oscillating systems like pendulums or springs, the inter-conversion of potential and kinetic energy occurs continuously, leading to the observed oscillatory motion.