Lecture Notes: Conservative Forces

Definition of Conservative Forces

• Conservative forces are those where the work done depends only on the initial and final positions of the object, not on the path taken.
• Examples include:
  • Gravitational Force
  • Spring Force

Characteristics of Conservative Forces

• Work done is path-independent.
• Such forces conserve mechanical energy (kinetic + potential energy).
• Potential energy can be defined for these forces.

Example: Gravitational Force

• Force on a 5 kg mass: 49 N
• Work done moving down 6 m: 294 J
• If moving back up 6 m, work becomes -294 J.
• Total work remains 294 J regardless of path, confirming gravity as a conservative force.

Example: Spring Force

• Work done by a spring depends only on initial and final positions, similar to gravity.

Non-Conservative Forces

• Friction and Air Resistance
  • Work done depends on the path taken.
  • Do not conserve mechanical energy.
  • No potential energy can be defined.

Example: Friction

• Moving a mass from point A to B:
  • Friction does negative work, creating thermal energy.
  • Work increases with repeated back-and-forth movement.
• Non-reversible: energy lost as thermal energy cannot be easily recovered.

Implications of Conservative vs Non-Conservative Forces

• Potential Energy
  • Conservative forces allow potential energy to turn into kinetic energy and vice versa.
  • Non-conservative forces dissipate energy (e.g., thermal energy from friction) which cannot be recovered easily.

Conclusion

• Understanding force types (conservative vs non-conservative) is crucial for analyzing energy conservation in physical systems.