In everyday life, “work” and “energy” are used loosely. In physics they have precise meanings that are central to WAEC calculations.
Work
Work is done when a force moves an object through a distance in the direction of the force.
If the force is at an angle θ to the displacement, W = F × d × cos θ.
Energy
Energy is the ability to do work. It is measured in joules (J).
- Kinetic energy (K.E.) = ½mv² — energy due to motion.
- Potential energy (P.E.) = mgh — energy due to position (height).
- Other forms: heat, light, sound, electrical, chemical, nuclear.
The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.
Power
Power is the rate of doing work.
Efficiency
Efficiency = (useful work output ÷ total energy input) × 100%. No machine is 100% efficient because some energy is always lost as heat or sound (due to friction).
Worked Example
A mass of 2 kg is raised through a height of 5 m. Taking g = 10 m/s², find (a) the work done and (b) the potential energy gained.
- Force = weight = mg = 2 × 10 = 20 N
- Work = F × d = 20 × 5 = 100 J
- P.E. = mgh = 2 × 10 × 5 = 100 J (equal to the work done)
Summary
Work is force × distance. Energy is the capacity to do work (kinetic = ½mv², potential = mgh). Power is the rate of doing work (W/t), and efficiency compares useful output to input energy.
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