PRELIMS

03. Work, Energy and Power

1. Work

• Definition: If a body is displaced when a force acts on it, work is said to be done.
• Formula:
  • = Force applied.
  • = Displacement.
  • = Angle between force and displacement.
• Characteristics: Scalar quantity; SI unit is joule.

2. Energy

• Definition: Capacity of doing work.
• Characteristics: Scalar quantity; SI unit is joule.
• Mechanical Energy: Divided into two types:
  • Potential Energy (PE): Capacity of doing work due to position or configuration.
    • Examples: Energy of a stretched/compressed spring, water collected at a height, spring in a watch.
    • Gravitational PE: ( ).
  • Kinetic Energy (KE): Energy possessed by a body due to its motion.
    • Formula: .

3. Conservation & Transformation of Energy

• Principle of Conservation of Energy: Energy can neither be created nor destroyed; it only transforms from one form to another. Total energy of the universe remains constant.

Equipments for Energy Transformation:

• Dynamo: Mechanical Electrical
• Candle: Chemical Light and Heat
• Microphone: Sound Electrical
• Loud Speaker: Electrical Sound
• Solar Cell: Solar Electrical
• Tube light: Electrical Light
• Electric Bulb: Electrical Light and Heat
• Battery: Chemical Electrical
• Electric motor: Electrical Mechanical
• Sitar: Mechanical Sound

4. Momentum & KE Relationship

• Formula: (where ).
• Fact: If momentum is doubled, kinetic energy becomes four times.

5. Power

• Definition: Rate of doing work ( ).
• Units:
  • SI Unit: watt (W) = 1 joule/sec.
  • Horse Power (HP): .
• Energy Units (Time-based):
  • .
  • .
  • .

6. Work-Energy Theorem & Collisions

• Work-Energy Theorem: The work done by the net force on a body equals the change in its kinetic energy ( ).
• Collisions:
  • Elastic Collision: Both momentum and kinetic energy are conserved (e.g., collision between subatomic/gas particles is nearly elastic).
  • Inelastic Collision: Momentum is conserved, but kinetic energy is not conserved (some energy converts to heat/sound/deformation).
  • Perfectly Inelastic Collision: Colliding bodies stick together and move with a common velocity after collision; maximum KE loss.

7. Commonly Confused Pairs

• Work vs. Power: Work is the total effort delivered ( ), independent of time; Power is the rate at which work is done ( ) — two agents can do the same work but differ in power if the time taken differs.
• Energy vs. Power: Energy is the capacity to do work (joule); Power is the rate of using/producing that energy (watt); a kWh is a unit of energy, not power.
• Potential Energy vs. Kinetic Energy: PE depends on position/configuration; KE depends on motion — total mechanical energy (PE+KE) is conserved in the absence of friction/air resistance (e.g., a swinging pendulum or a freely falling body).

UPSC Relevance

Energy transformations and power units are frequent in competitive exams.

• Key Focus: Distinguishing between Power (rate) and Energy (capacity).
• Practical Application: Efficiency of motors, household electricity billing (kWh), and the physics of simple machines/instruments (Sitar, Dynamo).
• Concept Check: Why doubling momentum quadruples KE (the square relationship).
• Collisions: Elastic vs. inelastic — a recurring conceptual distinction (KE conservation is the differentiator, not momentum).