Conservation of Mechanical Energy

What is Conservation of Energy?

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system, the total energy remains constant.

For example, when a ball is thrown into the air, its energy transforms between kinetic and potential energy, but the total mechanical energy remains the same.

Types of Mechanical Energy

• Kinetic Energy (KE): The energy of motion. Calculated using the formula: $$KE = \frac{1}{2}mv^2$$ where $m$ is mass and $v$ is velocity.
• Potential Energy (PE): The energy stored due to an object's position or condition. For gravitational potential energy: $$PE = mgh$$ where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height.

Conservation of Mechanical Energy

In the absence of non-conservative forces (like friction), the total mechanical energy (sum of kinetic and potential energy) in a system remains constant:

$$\text{Total Mechanical Energy} = KE + PE = \text{constant}$$