Work, Energy and Power - Lecture 10 (Potential Energy and Conservative Forces)

Vocabulary flashcards covering conservative vs. non-conservative forces, potential energy, and equilibrium concepts from the lecture notes.

Conservative force

A force whose work is independent of path; work around a closed loop is zero; examples include gravitation, spring, and electrostatic forces; a potential energy function exists for such forces.

Non-conservative force

A force whose work depends on the path between initial and final positions; examples include friction, air resistance, and viscous forces.

Potential energy (U)

Energy associated with the configuration of a system due to conservative forces; defined as the negative of the work done by internal conservative forces; change in U is path- and frame-independent.

ΔU = -Wbyconservative_forces

Change in potential energy equals the negative of the work done by internal conservative forces.

dU = - F · dr

Infinitesimal change in potential energy is the negative of the differential work done by the force along displacement dr.

F = - dU/dx

Conservative force is the negative gradient of the corresponding potential energy with respect to position.

Potential energy reference point

The zero of potential energy is arbitrary; only changes in U have physical meaning.

Kinetic energy (KE)

Energy of motion; KE = 1/2 m v^2.

Mechanical energy (ME)

Sum of kinetic and potential energy: ME = KE + PE; conserved when only conservative forces do work.

Work-Energy Theorem

Net work done on a body equals the change in its kinetic energy.

Conservation of mechanical energy

If only conservative forces act, mechanical energy KE + PE remains constant.

Equilibrium position (MP)

Position where the potential energy has zero slope: dU/dx = 0 (the derivative with respect to x is zero).

Stable equilibrium

At the equilibrium point, d²U/dx² > 0; small displacement leads to a restoring force (energy minimum).

Unstable equilibrium

At the equilibrium point, d²U/dx² < 0; small displacement leads away from equilibrium (energy maximum).

Neutral equilibrium

At the equilibrium point, d²U/dx² = 0 while dU/dx = 0; no restoring or opposing force.

Second derivative test (in U-x plot)

Sign of d²U/dx² at MP determines stability: >0 stable, <0 unstable, =0 neutral.

ΔU is frame-independent

The change in potential energy is independent of the reference frame.

Conservative force examples

Gravitational force, spring force, and electrostatic force.

Non-conservative force examples

Friction, air resistance, and viscous forces.

Path independence of work by conservative forces

The work done by a conservative force between two points depends only on the endpoints, not the path taken.

Reference line for potential energy

The zero of potential energy can be chosen arbitrarily; only differences in U matter for dynamics.

Energy components (ME)

Mechanical energy comprises kinetic and potential energy (ME = KE + PE); it is conserved under conservative forces.