Work, Energy and Power

Work

Work is done when a force moves an object through a certain distance in the direction of the force. Mathematically, it is expressed as:

$$ W = F * D $$

or when lifting a body against gravity:

$$ W = mgh $$

If a force is applied at an angle θ to the horizontal:

Example:

A boy of mass 50 kg runs up a set of steps with a total height of 3.0 m. Calculate the work done against gravity.

Solution:

Given: m = 50 kg, h = 3 m, g = 10 m/s²

Work done: W = mgh = 50 × 10 × 3 = 1500 Joules

Energy

Energy is the ability to do work. It is a scalar quantity measured in Joules.

Types of Energy:

  1. Mechanical Energy
  2. Thermal Energy
  3. Chemical Energy
  4. Electrical Energy
  5. Nuclear/Atomic Energy
  6. Solar/Light Energy
  7. Sound Energy

Types of Mechanical Energy:

1. Potential Energy (PE)

Stored energy due to position or state.

$$ E_p = mgh $$

2. Kinetic Energy (KE)

Energy of a moving object.

$$ E_k = \frac{1}{2} mv^2 $$

Example:

An object of mass 5 kg moves at a velocity of 15 m/s. Calculate its kinetic energy.

Solution:

KE = ½ × 5 × 15 × 15 = 562.5 J

Example:

A boy of mass 10 kg stands on a building floor 10 m above the ground. Find his potential energy.

Solution:

PE = 10 × 10 × 10 = 1000 J

Power

Power is the rate of doing work or transferring energy. It is a scalar quantity measured in watts (W).

$$ Power = \frac{Work Done}{Time}$$

or

$$ Power = \frac{F * D}{T} = F * V $$

Example:

A boy of mass 10 kg climbs 10 steps, each 0.2 m high, in 20 seconds. Calculate his power.

Solution:

Height climbed: 10 × 0.2 = 2 m

Work done: 10 × 10 × 2 = 200 Joules

Power: 200 / 20 = 10 watts

Conservation & Transformation of Energy

Energy can be converted from one form to another within a closed system. The law of conservation of energy states that in an isolated system, energy cannot be created or destroyed, only transformed from one form to another.

Examples of Energy Conversion

World Energy Resources

Global energy resources are categorized into two main types:

1. Renewable Energy Resources

These are energy sources that can be replenished naturally as they are used. Examples include:

2. Non-Renewable Energy Resources

These are energy sources that cannot be replaced once they are depleted. Examples include:

Source How Energy is Generated Renewable (R) or Non-Renewable (NR) Availability Environmental Impact
Fossil Fuels Chemical energy stored in fuels is released when burned, heating water in a boiler to produce steam. The steam turns a turbine, which drives a generator. Non-Renewable Oil and gas supplies are depleting; coal is expected to last for about 200 more years. Burning produces carbon dioxide (causes global warming) and sulfur dioxide (causes acid rain).
Hydroelectric Power Gravitational potential energy from water behind a dam is converted into kinetic energy as water flows through turbines, driving a generator. Renewable Only available in areas with suitable water sources. Loss of habitat due to flooding, affecting farming and forestry.
Tidal Energy Works on the same principle as hydroelectric power, using tidal movements to drive turbines and generate electricity. Renewable Only suitable in specific coastal areas. Destroys wildlife habitats and affects shipping routes.
Wave Energy Harnesses the movement of waves to drive a generator. Renewable Useful for island communities. Can create problems for shipping.
Geothermal Energy Cold water is pumped into hot underground rocks, producing steam that turns turbines to drive a generator. Renewable Only feasible in regions where hot rocks are near the surface. Some open-loop systems emit carbon dioxide and hydrogen sulfide, contributing to global warming and acid rain. Closed-loop systems avoid emissions.
Nuclear Energy Nuclear fission releases energy, which is used to generate steam, turning turbines that drive a generator. Non-Renewable Available to countries with nuclear power plants. Produces radioactive waste that must be stored for thousands of years.
Solar Energy Solar cells convert sunlight directly into electricity. Renewable Can be used anywhere. Requires large areas of land, potentially reducing land available for agriculture.
Wind Turbine turned directly by the wind. Renewable Best in coastal and Upland sites Noisy. wind farms at sea can cause problems for shipping. Hazard to migrating birds.
Biomass Chemical energy store in the biofuels. Renewable Works anywhere Produces carbon dioxide but is carbon neutral as carbon dioxide absorbed as biomass grows. Land used for food production may be lost to biofuel growth.