AcademyPotential Energy and Conservation

Academy

Nonconservative Forces

Level 1 - Physics topic page in Potential Energy and Conservation.

Principle

Nonconservative forces change mechanical energy rather than storing it in a recoverable potential energy function.

Notation

\(W_{nc}\)
work by nonconservative forces
\(\mathrm{J}\)
\(E\)
mechanical energy
\(\mathrm{J}\)
\(f_k\)
kinetic friction force
\(\mathrm{N}\)
\(d\)
path length
\(\mathrm{m}\)

Rules

Mechanical energy change
\[W_{nc}=\Delta K+\Delta U\]
Energy accounting
\[K_i+U_i+W_{nc}=K_f+U_f\]
Kinetic friction work
\[W_f=-f_k d\]

Method

Start with energy
\[K_i+U_i+W_{nc}=K_f+U_f\]
Insert losses
\[W_f=-f_kd\]
Solve remaining quantity
\[\Delta E_{mech}=W_{nc}\]
blockNmgfkd
Kinetic friction does negative work when it points opposite the displacement.

Examples

Question
A block slides \(d\) on a rough horizontal surface with kinetic friction \(f_k\). Find the mechanical energy change.
Answer
\[W_f=-f_kd\]
so
\[\Delta E_{mech}=-f_kd\]
Mechanical energy is transferred away from the block-surface mechanical system.

Checks

  • Friction work depends on path length.
  • Nonconservative work changes mechanical energy.
  • Negative nonconservative work removes mechanical energy.
  • Positive applied work can add mechanical energy.