Lecture on Work, Energy, and Power

Work

• Definition: Accomplished by the action of a force.
• Calculation: Product of the magnitude of force and displacement.
• When Vectors Are Not Parallel: Use the formula (W = Fd \cos \theta) where (\theta) is the angle between force and displacement vectors.

Energy

• General: An object with energy can perform work; force transfers energy when acting on an object.
• Kinetic Energy: Associated with motion.
  • Formula: (KE = \frac{1}{2}mv^2)
  • Units: Joules ((\text{J}))
• Potential Energy: Stored energy, notably gravitational potential energy.
  • Formula: (PE = mgh)
  • Variants: Elastic, electric, chemical potential energy.

Work-Energy Theorem

• Network: Equal to the change in kinetic energy.
• Positive Work: Force increases kinetic energy.
• Negative Work: Force decreases kinetic energy.
• Forces and Work:
  • Parallel vectors result in positive work.
  • Opposite direction vectors result in negative work.
  • Perpendicular vectors: No work done.

Energy Conservation

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

Power

• Definition: Rate at which work is done or energy is transferred.
• Formula: (P = \frac{W}{t})
• Units: Watts ((\text{W})), where 1 watt = 1 joule/second.
• Alternate Formula: (P = Fv)
• Example: Power displayed by lifting weights quickly vs. slowly.

Practice Problems

1. Kinetic Energy Calculation:
   • 5 kg block at 12 m/s: (KE = 360 \text{ J}).
2. Effect of Mass and Speed on Kinetic Energy:
   • Doubling mass doubles KE.
   • Doubling speed quadruples KE.
   • Tripling speed increases KE by factor of 9.
3. Gravitational Potential Energy Calculation:
   • 2.5 kg book 10m above ground: (GPE = 245 \text{ J}).
4. Speed and Energy Transformation:
   • Analyze ball falling and energy conversions.
   • Mechanical energy conserved under gravity.
5. Work Done Calculations:
   • Constant force: Direct calculation.
   • Varying force: Use average force or graphically calculate area under force-displacement curve.