Conservative and Non-conservative Forces
Understanding the types of forces for which the concept of potential energy is defined, distinguishing them by work done over a closed path.
What is Conservative and Non-conservative Forces?
A force for which the work done in moving an object between two points is independent of the path taken, and the work done over a closed path is zero.
Key formula / rule: Work done by conservative force
Key points
- Differentiate between conservative and non-conservative forces.
- Understand the conditions for a force to be conservative.
- Relate potential energy to conservative forces.
- Identify examples of both types of forces.
Common exam trap
Confusing potential energy with work done by non-conservative forces.
Definitions
- Term
Conservative Force
- Meaning
A force for which the work done in moving an object between two points is independent of the path taken, and the work done over a closed path is zero.
- Term
Non-conservative Force
- Meaning
A force for which the work done in moving an object between two points depends on the path taken, and the work done over a closed path is generally not zero.
- Term
Potential Energy
- Meaning
Energy possessed by an object due to its position or configuration, defined only for conservative forces.
- Term
Mechanical Energy
- Meaning
The sum of kinetic energy and potential energy of an object.
Learning objectives
Differentiate between conservative and non-conservative forces.
Understand the conditions for a force to be conservative.
Relate potential energy to conservative forces.
Identify examples of both types of forces.
Analyze the work done by different forces in various scenarios.
Formulae
- Name
Work done by conservative force
- Note
Change in potential energy is the negative of work done by the conservative force.
- Expression
$Wc = -\Δ U = Ui - Uf$
- Name
Total Mechanical Energy
- Note
Sum of kinetic and potential energy.
- Expression
$E = K + U$
- Name
Work-Energy Theorem (with non-conservative forces)
- Note
Net work done equals change in kinetic energy. $Wnc = \Δ K - Wc = \Δ K + \Δ U = \Δ E$.
- Expression
$Wnet = Wc + Wnc = \Δ K$
- Name
Condition for Conservative Force
- Note
Work done over any closed path is zero.
- Expression
$\oint \vec{F} \· d\vec{l} = 0$
Prerequisites
Work and Energy
Types of Forces
Displacement and Velocity
Common mistakes
Confusing potential energy with work done by non-conservative forces.
Assuming potential energy can be defined for forces like friction.
Incorrectly applying the closed-path work condition to non-conservative forces.
Forgetting that work done by friction is always negative.
Keywords
Conservative Force
Non-conservative Force
Work Done
Path Independence
Closed Path
Potential Energy
Mechanical Energy
Friction
Gravity
Spring Force
Practice preview
The work done by a conservative force is:…
easy
A particle is subjected to a force F = (2y + 3)i + (3x + 2)j. If the particle moves from (0,0) to (1,1) along the path y = x, calculate the work done by this force.…
hard
If the work done by a force in moving a particle from point P to point Q is W_PQ, and the work done in moving it from Q to P is W_QP, then for a conservative force, which relation holds true?…
hard