# Energy

## Energy

# Energy

### Introduction to Energy

**Energy**, in the field of mechanics, is defined as the capacity to do work.- There are two primary categories of energy:
**potential energy**and**kinetic energy**.

### Potential Energy

- Potential energy is the
**stored**energy in an object or system due to its position or configuration. - It is given by
**PE = mgh**, where`m`

is mass,`g`

is the acceleration due to gravity, and`h`

is height above the reference level. - Another form of potential energy used in mechanics is
**elastic potential energy**, which is the energy stored in an object when it is stretched or compressed.

### Kinetic Energy

- Kinetic energy is the energy that an object possesses due to its
**motion**. - It is given by
**KE = 0.5mu²**, where`m`

is mass and`u`

is the velocity of the object.

### Work-Energy Theorem

- The work-energy theorem states that the
**work done**on an object equals the change in its kinetic energy. - Mathematically,
**Work = ΔKE**, where`ΔKE`

is the change in kinetic energy. - Work done is also calculated as the
**force multiplied by the displacement**and the cosine of the angle between the force and displacement vectors.

### Conservation of Energy

- The law of conservation of energy, a fundamental concept in physics, states that
**energy cannot be created or destroyed**; it can only change from one form to another. - In mechanics, this is often simplified to potential energy plus kinetic energy being constant, provided no external work is done.

### Applications of Energy in Mechanics

- Energy concepts are crucial in understanding various mechanical phenomena, such as
**collisions**,**oscillations**, and**rotational motion**. - For example, in an
**elastic collision**, both momentum and kinetic energy are conserved. - In systems containing springs and/or pendulum, the
**exchange of energy**between potential energy and kinetic energy forms the basis of oscillatory motion.

### Energy Problem Solving

- To tackle energy-based problems effectively, start by identifying all the forms of energy at the beginning and end of the process.
- Apply the
**conservation laws**appropriately, respecting that energy cannot be lost. - For problem solving in energy context, understanding of
**forces**and their impact is crucial. - Always check the physical reality of your calculated answer by thinking about whether it is reasonable.

Understanding energy and its principles does not only unlock a vast array of mechanics problems, but it also deepens appreciation and comprehension of physics in general.