Lecture on Work and Energy - MCAT General Physics and Math Review

Introduction

• Instructor: Iman
• Topics Covered:
  • Energy (Kinetic and Potential Energy, Total Mechanical Energy, Conservation of Energy)
  • Work (Force, Displacement, Pressure, Volume, Power, Work-Energy Theorem)
  • Mechanical Advantage (Simple Machines, Pulleys)

Energy

• Definition: A system's ability to do work or make something happen.
• Einstein's Quote: Energy is fundamental to reality; E=mc² shows interchangeability of matter and energy.
• Forms of Energy: Kinetic, Potential, Heat, Light, Nuclear, etc.
  • Energy cannot be created or destroyed, only transformed.

Kinetic Energy

• Definition: Energy of motion.
• Equation: ( KE = \frac{1}{2}mv^2 )
  • Units: Joules
  • Speed Relationship: If speed doubles, kinetic energy quadruples.
• Example Calculation:
  • Given: Mass = 5 kg, Velocity = 2 m/s
  • ( KE = \frac{1}{2} \times 5 \times 2^2 = 10 ) Joules
  • Doubling velocity (4 m/s) results in ( KE = 40 ) Joules

Potential Energy

• Definition: Energy due to position in space or intrinsic qualities.
  • Types: Gravitational Potential Energy, Chemical Potential Energy, Elastic Potential Energy
• Gravitational Potential Energy:
  • Equation: ( PE = mgh )
  • Example Calculation:
    • Mass = 2 kg, g = 9.8 m/s², Height = 10 m
    • ( PE = 2 \times 9.8 \times 10 = 196 ) Joules
    • Doubling height to 20m results in ( PE = 392 ) Joules

Elastic Potential Energy

• Springs/Energy Storage:
  • Equation: ( PE = \frac{1}{2}kx^2 )
  • Variables: k = Spring constant, x = Displacement from equilibrium

Total Mechanical Energy

• Definition: Sum of potential and kinetic energy ( E = U + K )
• Conservation of Energy: First law of thermodynamics - energy isn't created/destroyed, only transformed.
• Conservative vs Non-Conservative Forces:
  • Conservative: Path independent, do not dissipate energy (e.g., weight, spring)
  • Non-Conservative: Cause energy loss (e.g., friction, air drag)

Conservation of Mechanical Energy

• Expression: ( \Delta E = \Delta U + \Delta K = 0 )
  • Holds when non-conservative forces are absent.
• Example Problem: Baseball thrown with initial speed and returns with a different speed due to air resistance.
  • Calculate Work by Air Resistance: Use energy conservation equations, identify non-conservative forces.
  • Result: Energy dissipated due to non-conservative forces.

Conclusion

• Next Steps: Continue discussion on work and energy, practice problems.
• Engagement: Encouragement for questions/comments and reminder for ongoing study.