# 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.