Lesson 2 · 14 min
Kinetic and potential
Two ledgers. Motion, and configuration. Springs and heights are the configuration ledger.
The work–energy theorem
The net work on a particle equals its change in kinetic energy. That is a rearrangement of Newton’s second law, integrated along the path. KE = ½mv² is not an independent axiom — it is what you get when you integrate F = ma.
h is measured from a datum you choose. k is the spring stiffness in N/m. x is displacement from the unloaded length (or from equilibrium, carefully).
Conservative forces
Gravity and ideal springs are conservative: work between two points does not depend on the path, so you can hide that work inside a potential. Friction, drag, and inelastic deformation are not. They move energy into thermal microscopic motion, which this course will not give back.
Check
A 3.0 kg mass on a 400 N/m spring is pulled 12 cm from equilibrium and released. Maximum speed?
Bench
Spring–mass
E = ½kA²
- ω
- 6.32 rad/s
- T
- 0.99 s
- E
- 1.30 J
- f
- 1.01 Hz