Lesson 03
Work, energy, and conservation
Energy methods often solve motion problems faster than force-by-force analysis. When you can compare an initial state to a final state, conservation of energy turns a long path into a short one.
Core relationships
Kinetic energy
KE = 0.5 m v^2
Energy of motion
Potential energy
PE = m g h
Stored by height
Work
W = F d
For force aligned with displacement
Conservation
KE_i + PE_i = KE_f + PE_f
When no non-conservative work acts
When energy beats forces
- Use work-energy when you know forces and displacement but do not care about the full time history.
- Use conservation when friction is negligible and you can compare two states cleanly.
- Use power when the rate of doing work matters.
Worked example
A cart starts from rest at height h and slides down a frictionless ramp. Use m g h = 0.5 m v^2. Mass cancels, leaving v = sqrt(2 g h). Conservation lets us avoid finding acceleration and time.
Next step
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Mark this lesson complete when the main idea feels clear, then move straight into practice while it is fresh.
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Quick reference
- Mechanical energy
- E = KE + PE
- Power
- P = W / t
- Gravity
- g = 9.8 m/s^2