# Conservation of Energy

**Conservation of Energy**

**Fundamentals**

- The law of
**conservation of energy**states that the total energy of a closed system is constant. - It can be inferred that energy can neither be created nor destroyed, but it can be converted from one form to another.
- The sum of kinetic and potential energy in the system is always the same, representing the
*mechanical energy*of an object.

**Kinetic Energy and Work**

- The
**kinetic energy**of an object is the energy it possesses due to its motion. - Described mathematically, kinetic energy (K.E) = 1/2 mv^2 where m is the mass of the object and v is its speed.
- The work done by forces, excluding the force of gravity, is equal to the change in kinetic energy of an object. This is the basis of work-energy theorem.
- Physically,
**work**done on an object transfers energy to the object.

**Potential Energy**

- The
**potential energy**of an object is the energy it possesses due to its position relative to other objects. - Potential energy usually refers to energy that an object has because of its position in a force field, such as gravitational potential energy, or due to its configuration, like elastic potential energy.
- Gravitational potential energy is given by P.E = mgh where m is the mass of the object, g is acceleration due to gravity, and h is height above the ground.

**Energy Transformations**

- Due to the law of conservation of energy, energy may be converted between different forms.
- For example, an object in free fall will convert potential energy into kinetic energy as it falls towards the Earth.
- In an ideal, frictionless system, the sum of the kinetic and potential energies will remain constant, signifying
**conservation of mechanical energy**.

**Power**

**Power**is the rate at which energy is transferred, or the amount of energy per unit time.- The unit of power is Joule per second (J/s), which is also known as a Watt (W).
- The power resulting from force F moving an object at velocity v is given by P=Fv.

Remember, understanding the principles of energy conservation and how to apply them in problem-solving scenarios is crucial for mastering this topic.