Key idea
Path Independence of Work
For conservative forces, work depends only on endpoints, not the path taken.
- Two paths, same work
- Closed-loop work is zero
- Energy storage meaning
Work & Energy · Physics
Conservative and Non-Conservative Forces
Conservative forces store energy (potential). Non-conservative forces remove mechanical energy (like friction).
This topic includes
Subtopics to master
Learn the test for conservative forces and how to account for energy loss.
Identification
Identifying Conservative Forces
Check whether a potential \(U\) exists such that \(\vec F=-\nabla U\), or test closed-loop work.
- Potential-function test
- Closed-loop test
- Common examples
Loss
Energy Loss from Non-Conservative Forces
Friction, drag, and deformation convert mechanical energy into thermal/internal energy.
- Work by friction is negative
- Mechanical energy decreases
- Where the energy “goes”
Compare
Examples: Gravity vs Friction
Gravity is conservative; friction is non-conservative. They behave differently in loops and energy equations.
- Gravity stores \(U_g\)
- Friction dissipates
- Typical motion examples
Practice
Practice & Exercises
Decide whether forces are conservative and compute energy changes with dissipation.
- Conservative/non-conservative sorting
- Closed-loop work checks
- Energy accounting with friction
- Mixed-force problems
- Concept questions: “where did energy go?”
Bridge
Toward Conservation of Mechanical Energy
If only conservative forces do work, mechanical energy \(K+U\) stays constant. Otherwise, include \(W_{nc}\).
- \(K_i+U_i=K_f+U_f\)
- When it applies
- Next topic setup