Energy can be defined as the ability to do work. It is a fundamental concept in physics. The sun is a core source of energy. Energy is a scaler quantity and it is measured in Joules. A person running down a field or throwing a ball possesses energy which makes it possible to do work.

1. Mechanical Energy: Associated with the motion or position of an object, combining kinetic and potential energy.
2. Chemical Energy: Stored in the bonds between atoms and molecules, released during chemical reactions.
3. Nuclear Energy: Released during nuclear reactions, either fission (splitting) or fusion (combining) of atomic nuclei.
4. Thermal Energy: Related to the internal motion of particles within a substance, often referred to as heat.
5. Hydro Energy: Derived from the movement of water, often harnessed in dams or flowing rivers.
6. Light Energy: Emitted by the sun and other sources, it can be converted into other forms of energy.
7. Electrical Energy: Resulting from the movement of electrons, commonly produced and used for various applications.

Kinetic energy is the energy possessed by an object due to its motion. An example of kinetic energy is the energy possessed by a stone shot from a catapult which is able to kill a bird. The amount of kinetic energy depends on both its mass and velocity, and it can be calculated using the formula
$$ KE = \frac{1}{2} m v^2 $$
where \( m \) is the mass
and \( v \) is the velocity of the object.

Potential energy is the stored energy an object possesses due to its position or state in a force field. A mango fruit falling from a tree has the ability to break a glass beneath it due to the potential energy stored by the fruit when at rest. It can be converted into kinetic energy when the object is set in motion.

Forms of Potential Energy:

• Gravitational Potential Energy: Associated with an object's height relative to a reference point. Example: a raised weight. $${PE_{grav}} = mgh $$
• Elastic Potential Energy: Stored in objects that can be stretched or compressed. Example: a stretched spring. $$ {PE_{elastic}} = \frac{1}{2}ke² = \frac{1}{2}Fe $$
• Chemical Potential Energy: Stored in the chemical bonds of substances. Example: a charged battery.
• Phosphates: Mined for fertilizer production.
• Heavy Metals (e.g., Copper, Iron): Extracted for manufacturing and construction.
• Rock Salt: Mined for various industrial and domestic uses.

The law of conservation of energy states that energy can neither be created nor destroyed but can be transformed from one form to another. According to the principle of conservation of energy, the total energy of an isolated system remains constant. This means that energy can transform from one form to another, but the total amount remains unchanged.

Consider a fruit falling from a tree. As it falls, it experiences a transformation of energy from kinetic energy (\(KE\)) to gravitational potential energy (\(PE_{\text{grav}}\)). Consider three points A, B and C describing the motion of the falling fruit from the tree

At point A, the fruit of mass m is on the tree at a height, h above the ground. The total energy possessed by fruit is \(PE_{\text{grav}}\) since it possesses no velocity $$ v = 0 $$ $$ KE = 0 $$ $$ \text{Total energy }= KE + PE = mgh $$

At point B, the fruit is falling down with a velocity v, and having a height h, above the ground. The total energy possessed by the body is the sum of KE and PE_grav $$\text{Total energy} = KE + {PE_{grav}} $$ $$ \text{Total energy} = \frac{1}{2}mv² + mgh $$

At Point C, the fruit has gotten to the ground. The fruit still possesses velocity with which it hits the ground but has no height above the ground. At point C, velocity is maximum. Hence the total energy attained by the fruit is kinetic energy only. $$ h = 0 $$ $$ P.E = 0 $$ $$ \text{Total energy} = PE + KE $$ $$ \text{Total energy} = \frac{1}{2}mv² $$

$$\text {Therefore, from point A to point C} $$ $$ PE = KE $$ $$\text{At point C, where velocity is max} $$ $$ mgh = \frac{1}{2}mv²_{max} $$ $$ 2mgh = mv²_{max} $$ $$ 2gh = v²_{max} $$ $$ v_{max} = \sqrt{2gh} $$ $$ \text{Also, h} = \frac{V²_{max}}{2g} $$

Note: For a swinging simple pendulum, KE is max at midpoint ay zero at both ends while P.E is max at the end where it has the highest displacement, and zero at the midpoint

• Hydro to Electric Energy: Energy from flowing water is harnessed by water turbines, and the mechanical energy is then transformed into electrical energy by generators in hydroelectric power plants.
• Solar to Thermal Energy: Solar energy is absorbed by solar panels, and the absorbed energy is converted into thermal energy, which can be used for heating purposes in various applications.
• Chemical to Thermal Energy: Chemical energy from burning fossil fuels is converted into thermal energy in combustion engines or boilers, which is then used to generate electricity or provide heat.
• Wind to Mechanical to Electrical Energy: Wind energy is captured by wind turbines, and the mechanical energy from the rotation of the turbines is transformed into electrical energy by generators.
• Nuclear to Thermal to Electrical Energy: Nuclear reactions release thermal energy in nuclear reactors. This thermal energy is used to produce steam, which drives turbines connected to generators, converting it into electrical energy.
• Geothermal to Electrical Energy: Geothermal energy, derived from the Earth's internal heat, is used to generate steam. The steam then drives turbines connected to generators, converting geothermal energy into electrical energy.

Renewable Resources: Renewable resources are sources of energy that can be naturally replenished over time. They are considered sustainable and have minimal environmental impact.

• Solar Energy: Derived from the sun's radiation using solar panels.
• Wind Energy: Captured by wind turbines to generate electricity.
• Hydropower: Harnessing energy from flowing water in rivers or dams.
• Geothermal Energy: Tapping into the Earth's internal heat for power generation.
• Biomass: Organic materials like wood, crops, and waste used for energy.
• Ocean Energy: Extracting energy from tides, waves, and ocean currents.
• Hydrogen Fuel: Producing energy through hydrogen fuel cells.
• Biogas: Generated from organic waste and used for heating or electricity.
• Tidal Energy: Capturing energy from the rise and fall of tides.
• Wave Energy: Utilizing the energy from ocean waves to generate power.

Non-Renewable Resources: Non-renewable resources are finite and depletable over time. They are typically fossil fuels formed over millions of years.

• Coal: Extracted from underground mines and used for power generation.
• Oil (Petroleum): Extracted from the ground and refined for various energy products.
• Natural Gas: Extracted from underground reservoirs and used for heating and electricity.
• Nuclear Fuels: Uranium and plutonium used for nuclear power generation.
• Natural Asphalt: Formed from ancient plants and used in road construction.
• Peat: Partially decayed organic matter used as fuel in some regions.
• Mineral Oil: Extracted for various industrial applications.
• Phosphates: Mined for fertilizer production.
• Heavy Metals (e.g., Copper, Iron): Extracted for manufacturing and construction.
• Rock Salt: Mined for various industrial and domestic uses.

Example 1: An object of mass 0.25kg moves at a height h, above the ground with a speed of 4m/s. If its mechanical energy at this height is 12J, determine the value of h (g = 10m/s²) (WAEC)

Example 2: An object of mass 100g projected vertically upwards from the ground level has a velocity of 20m/s at a height of 10m. Calculate its initial kinetic energy at the ground level (g = 10m/s²) (JAMB)

Example 3: A ball of mass 200g falls from a height of 5m on to a hard floor and rebounds to a height of 3m. What energy is lost by the ball as a result of the impact on the floor (g = 10m/s²) (NECO)

Example 4: A body of mass 5kg falls from a height of 10m above the ground. What is the kinetic energy of the body just before it strikes the ground? [Neglect energy losses and take g as 10m/s²](WAEC)