Work & Energy · Physics

Conservation of Mechanical Energy

If only conservative forces do work, mechanical energy stays constant: \(K_i+U_i=K_f+U_f\).

This topic includes

Subtopics to master

Learn when you can use conservation and why it’s often faster than Newton’s laws.

Conditions

When Mechanical Energy Is Conserved

Mechanical energy is conserved when non-conservative work is negligible or absent.

Systems

Isolated Systems

Pick the right system so external work is zero (or accounted for). Then energy methods become clean.

Mixed

Mixed Kinetic–Potential Problems

Solve for speed or height using \(K+U=\text{constant}\) for gravity/springs.

Compare

Comparison with Newton’s-Law Approach

Energy is scalar and often removes time and vector complexity; Newton’s laws give more detail but can be longer.

Practice

Practice & Exercises

Solve conservation problems and decide when conservation is valid.

Bridge

Adding Friction and Dissipation

When friction acts, mechanical energy is not conserved — but energy accounting still works with \(W_{nc}\).