Learning Objectives
- Understand the scientific definition of work
- Learn about kinetic energy and potential energy
- Derive expressions for kinetic and potential energy
- Understand the law of conservation of energy
- Define and calculate power
Key Concepts
Work
Work is done when a force acts on an object and the object is displaced in the direction of the force.
W = F × s × cos θ where F is force, s is displacement, and θ is the angle between force and displacement.
When force and displacement are in the same direction (θ = 0°): W = F × s
SI unit: Joule (J). 1 Joule = 1 Newton × 1 metre.
Conditions for work: (1) A force must be applied, (2) The object must be displaced, (3) There must be a component of force along the displacement.
Positive work: Force and displacement in the same direction. Negative work: Force and displacement in opposite directions (e.g., friction). Zero work: Force perpendicular to displacement (e.g., carrying a bag while walking horizontally).
Energy
Energy is the capacity to do work. SI unit: Joule (J). An object that can do more work possesses more energy.
Kinetic Energy
Energy possessed by an object due to its motion.
KE = (1/2)mv²
Kinetic energy is always positive. It depends on mass and the square of velocity.
Work-Energy Theorem: The work done on an object equals the change in its kinetic energy. W = (1/2)mv² - (1/2)mu².
Potential Energy
Energy possessed by an object due to its position or configuration.
Gravitational PE = mgh where m is mass, g is acceleration due to gravity, and h is height above the reference level.
Potential energy is relative — it depends on the chosen reference point.
Law of Conservation of Energy
Energy can neither be created nor destroyed. It can only be transformed from one form to another. The total energy of an isolated system remains constant.
For a freely falling object: At any point during the fall, KE + PE = constant = mgh (initial height). As the object falls, PE decreases and KE increases, but their sum remains the same.
Power
Power is the rate of doing work or the rate of transfer of energy.
Power = Work / Time = Energy / Time
SI unit: Watt (W). 1 Watt = 1 Joule / 1 second.
1 kilowatt (kW) = 1000 W.
Commercial unit of energy: kilowatt-hour (kWh). 1 kWh = 3.6 × 10⁶ J.
Summary
Work is done when force causes displacement. Energy is the capacity to do work and exists in various forms — kinetic (motion) and potential (position). The work-energy theorem relates work done to change in kinetic energy. The law of conservation of energy states that total energy remains constant. Power measures how quickly work is done.
Important Terms
- Work: Product of force and displacement in the direction of force; SI unit: Joule
- Kinetic Energy: Energy of motion, KE = (1/2)mv²
- Potential Energy: Energy of position, PE = mgh
- Power: Rate of doing work; SI unit: Watt
- Conservation of Energy: Energy cannot be created or destroyed, only transformed
- Kilowatt-hour: Commercial unit of energy; 1 kWh = 3.6 × 10⁶ J
Quick Revision
- Work = Force × Displacement (when in same direction); unit: Joule
- KE = (1/2)mv²; PE = mgh
- Work-energy theorem: W = change in KE
- Total energy is conserved: KE + PE = constant (for free fall)
- Power = Work / Time; unit: Watt; 1 kWh = 3.6 × 10⁶ J