# Conservation of Energy

### Introduction to Conservation of Energy

• The Law of Conservation of Energy states that energy can neither be created nor destroyed. It can only be transferred from one form to another.

• This principle implies that the total energy within a closed system remains constant over time, regardless of individual changes to its components.

• The law is fundamental in understanding the motion of objects and prediction of their future states.

### Forms of Energy

• Potential energy (U) is energy an object possesses due to its position in a gravitational field (like a raised weight), or in an elastic target.

• Kinetic energy (K) is energy an object has as a result of its motion. It depends on both the object’s mass and velocity, formulated as 0.5mv².

• Mechanical energy is the sum of an object’s kinetic and potential energy. It remains constant in an isolated system where only conservative forces, like gravity, are involved.

### Energy Transformation and Work

• In an ideal, frictionless system, the potential and kinetic energy can transform into each other, whilst keeping the mechanical energy constant. An object falling under gravity, for example, gradually exchanges its gravitational potential energy for kinetic energy.

• Work done (W) on an object can transfer energy into or out of the system, changing the object’s speed and thus its kinetic energy.

### Conservation of Energy in Practical Mechanics

• Applying the conservation of energy can solve problems in mechanics by equating the initial total energy to the final total energy.

• The principle helps to predict how objects will behave when they interact. For example, when considering two colliding objects, if we know the total kinetic energy before the collision, this will equal the total kinetic energy after the collision if no external forces are acting on the system (In a purely elastic collision).

• Beware cases where non-conservative forces are involved (like friction or air resistance). They transform mechanical energy into thermal energy, causing the total mechanical energy to decrease.

### Understanding Conservation of Energy

• Get comfortable with the different forms of energy and how they transform into each other, keeping the total energy constant in an ideal frictionless system.

• Be able to identify when work has been done on a system, and account for this when calculating changes in energy.

• Learn how to apply the conservation of energy principle to practical mechanics problems. Such as those that require you to calculate changes in speed, height or mechanical work.

A solid grasp of the Conservation of Energy principle is at the heart of many mechanics topics and problems. It underpins a deep understanding of the interactions and transformations that shape the physical world.