Work and Energy

• Work

  • Scientific Conception
    • Force must act on an object
    • Object must be displaced
  • Conditions for Work
    • Force ($F$) is applied
    • Displacement ($s$) occurs
    • Angle between force and displacement ($W = Fs \cos\theta$)
  • Types of Work
    • Positive Work: Force and displacement in the same direction ($\theta = 0^\circ$)
    • Negative Work: Force and displacement in opposite directions ($\theta = 180^\circ$)
    • Zero Work: Force and displacement are perpendicular ($\theta = 90^\circ$)
  • Unit of Work
    • Joule (J) or Newton-meter ($N\cdot m$)
    • Scalar quantity

• Energy

  • Definition
    • Capacity to do work
    • Scalar quantity
    • SI Unit: Joule (J)
  • Forms of Energy
    • Mechanical Energy (Kinetic + Potential)
    • Heat Energy
    • Light Energy
    • Chemical Energy
    • Electrical Energy

• Kinetic Energy (KE)

  • Definition
    • Energy possessed due to motion
  • Examples
    • Moving car, flowing water, running athlete
  • Formula derivation
    • $KE = \frac{1}{2}mv^2$
    • $m$ = mass, $v$ = velocity
  • Work-Energy Theorem
    • Work done = Change in Kinetic Energy

• Potential Energy (PE)

  • Definition
    • Energy possessed due to position or shape
  • Gravitational Potential Energy
    • Stored due to height above ground
    • Formula: $PE = mgh$
    • $m$ = mass, $g$ = acceleration due to gravity, $h$ = height
  • Elastic Potential Energy
    • Stored in stretched/compressed springs or rubber bands

• Law of Conservation of Energy

  • Statement
    • Energy can neither be created nor destroyed, only transformed from one form to another
  • Total Mechanical Energy
    • $PE + KE = \text{Constant}$
  • Example
    • Free falling body (Potential energy converts into Kinetic energy)

• Power

  • Definition
    • Rate of doing work or rate of transfer of energy
  • Formula
    • $P = \frac{W}{t}$
    • $W$ = Work, $t$ = Time
  • Unit of Power
    • Watt (W) or Joule per second ($J/s$)
    • Larger unit: Kilowatt (kW)
  • Commercial Unit of Energy
    • Kilowatt-hour (kWh) or Board of Trade (BOT) unit
    • $1 \text{ kWh} = 3.6 \times 10^6 \text{ Joules}$