Work, Energy, and Power

Work

• Definition: Work is the transfer of energy from one object to another through a force applied over a distance.
• Formula: W = F × d × cos(θ)
  • W: work done
  • F: force applied
  • d: distance over which the force is applied
  • θ: angle between the force and displacement vectors
• Units: Joules (J)
• Types of work:
  • Positive work: force and displacement are in the same direction
  • Negative work: force and displacement are in opposite directions
  • Zero work: force and displacement are perpendicular

Energy

• Definition: Energy is the ability to do work.
• Types of energy:
  • Kinetic energy (K): energy of motion
    • Formula: K = 1/2 × m × v^2
      • m: mass
      • v: velocity
  • Potential energy (U): energy of position or stored energy
    • Formula: U = m × g × h (gravitational potential energy)
      • m: mass
      • g: acceleration due to gravity
      • h: height
  • Thermal energy (Q): energy of heat
  • Electrical energy (E): energy associated with electric charges
  • Chemical energy (E): energy stored in chemical bonds
• Law of conservation of energy: energy cannot be created or destroyed, only converted from one form to another

Power

• Definition: Power is the rate at which work is done or energy is transferred.
• Formula: P = W / t
  • P: power
  • W: work done
  • t: time over which the work is done
• Units: Watts (W)
• Types of power:
  • Instantaneous power: power at a given instant
  • Average power: power over a period of time
• Examples of power:
  • Mechanical power: power transmitted through mechanical systems
  • Electrical power: power transmitted through electrical circuits