Work, Energy, and Power

Work

• Definition: Work is accomplished by the action of a force.
• Calculation: Work = Force x Displacement (W = Fd)
  • If force and displacement are not parallel, use: W = Fd cos(θ)
  • θ = angle between force and displacement vectors.
• Examples: Pulling a block with tension at an angle.

Energy

• Definition: The ability to do work.
• Types of Energy:
  • Kinetic Energy: Energy of motion.
    • Formula: KE = 1/2 mv^2
  • Potential Energy: Stored energy.
    • Gravitational Potential Energy: U = mgh
    • Other forms: Elastic, Electric, Chemical

Work-Energy Principle

• Total work is equal to change in kinetic energy: W = ΔKE
• Positive Work: Force increases kinetic energy and speeds up the object.
• Negative Work: Force decreases kinetic energy and slows down the object.

Forces and Energy Transfer

• Newton's Third Law: For every action, there is an equal and opposite reaction.
• Energy Transfer: During collision, energy transfers between objects.
• Work by Forces:
  • Positive work when force and displacement align.
  • Negative work when force opposes displacement.
  • No work when force and displacement are perpendicular.

Power

• Definition: Rate at which work is done or energy is transferred.
• Formula: Power (P) = Work (W) / Time (t)
• Units: Watts (W) = Joules/second
• Examples: Lifting weights versus time taken.

Conservation of Energy

• Mechanical Energy: Sum of kinetic and potential energy.
• Conservative Forces: Do not change total mechanical energy. (e.g., gravity)
• Non-Conservative Forces: Change mechanical energy (e.g., friction).

Practical Problems and Calculations

• Kinetic Energy: Calculate using mass and speed.
  • Doubling mass doubles KE.
  • Doubling speed increases KE by a factor of four.
• Potential Energy: Depends on height and mass.
  • Example calculation with a book above ground.
• Power: Illustrated by comparing two people doing work at different rates.

Problem Solving Steps

• Use formulas to calculate energy, work, and power.
• Apply concepts of conservative and non-conservative forces.
• Use graphical methods to understand force-displacement relations.