Lecture Notes: Work, Energy, and Power

Key Concepts

• Work: Accomplished by the action of a force, defined as the product of force magnitude and displacement.

  • Formula: ( W = Fd )
  • When force and displacement vectors aren't parallel, use ( W = Fd \cos\theta ).

• Energy: The capacity to do work.

  • Kinetic Energy (KE): Energy due to motion.
    • Formula: ( KE = \frac{1}{2} mv^2 )
  • Potential Energy (PE): Stored energy, with gravitational potential energy as ( PE = mgh ).
  • Multiple types: Gravitational, Elastic, Electric, Chemical.

Work-Energy Theorem

• Theorem: The network done on an object equals the change in its kinetic energy.
• Positive Work: When force increases kinetic energy.
• Negative Work: When force decreases kinetic energy.

Forces and Energy Transfer

• Action and reaction forces transfer energy between objects.
• Network is connected to changes in kinetic energy, governed by the direction of force and displacement vectors.

Power

• Definition: Rate at which work is done or energy is transferred.
  • Formula: ( P = \frac{W}{t} ) or ( P = Fv )
  • Units: Watts (W), with conversions like 1 kW = 1000 W.
• Power is higher when work is done faster.

Mechanical Energy

• Conservation: Total mechanical energy (kinetic + potential) is conserved in systems with only conservative forces (e.g., gravity).
• Non-Conservative Forces: Friction and applied forces can change mechanical energy.

Practice Problems

Problem 1: Kinetic Energy Calculation

• Given: Block of 5 kg at 12 m/s.
• Solution: ( KE = \frac{1}{2} (5)(12^2) = 360 ) Joules.

Problem 2: Effects of Mass and Speed

• Doubling mass doubles kinetic energy.
• Doubling speed increases kinetic energy by a factor of four.

Problem 3: Gravitational Potential Energy

• Given: Book of 2.5 kg, 10 m above ground.
• Solution: ( PE = 2.5 \times 9.8 \times 10 = 245 ) Joules.

Problem 4: Falling Ball

• Calculated height, speed, and energy changes over time to show energy conservation.
• Confirmed gravity as a conservative force.

Problem 5: Work and Force

• Calculated work done by a constant force and a varying force over a displacement, using graph area for verification.

Important Formulas

• Work: ( W = Fd )
• Kinetic Energy: ( KE = \frac{1}{2} mv^2 )
• Potential Energy: ( PE = mgh )
• Power: ( P = \frac{W}{t} ), ( P = Fv )

Summary

Understanding how work, energy, and power interact is crucial in analyzing physical systems, predicting energy changes, and applying appropriate equations to solve practical problems. Remembering the relationships between force, displacement, and energy forms aids in grasping complex concepts in physics.