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Mechanics · Physics

Work, Energy & Power

Learn how forces transfer energy (work), how motion stores energy (kinetic), how systems store energy (potential), and how fast energy is transferred (power).

Work, Energy & Power topics

Core topics in this unit

Work through these in order for maximum clarity, or jump to the concept you need right now.

1
Work Done by a Force
Define work using the dot product and line integral language. Learn why direction matters.
  • Definition of work as a line integral
  • Work by a constant force
  • Directional dependence of work
  • Zero work and perpendicular forces
Start topic Foundation for energy methods.
2
Work by Constant and Variable Forces
Use graphs and integration to compute work when the force changes with position.
  • Work from force–position graphs
  • Variable forces and integration
  • Spring force as a variable force
  • Area interpretation of work
Start topic Key visual + calculus link.
3
Kinetic Energy
Define energy of motion and learn how it depends on speed and reference frame.
  • Translational kinetic energy
  • Dependence on reference frame
  • Kinetic energy in one and two dimensions
  • Kinetic energy of systems of particles
Start topic Energy of motion.
4
Work–Energy Theorem
Connect net work to change in kinetic energy: the fastest path through many motion problems.
  • Derivation from Newton’s second law
  • Net work and change in kinetic energy
  • Applications to motion problems
  • Advantages over force-based methods
Start topic High-yield problem tool.
5
Potential Energy
Learn energy storage in fields, how reference levels work, and how forces relate to potential.
  • Definition and reference choice
  • Potential energy functions
  • Force as the gradient of potential energy
  • One-dimensional potential wells
Start topic Energy storage viewpoint.
6
Conservative and Non-Conservative Forces
Decide when energy conservation works — and when you must include losses via non-conservative work.
  • Path independence of work
  • Identifying conservative forces
  • Energy loss from non-conservative forces
  • Examples: gravity vs friction
Start topic Key classification step.
7
Gravitational Potential Energy
Use near-Earth and universal gravity potentials, and connect potential to force.
  • Near-Earth gravitational potential
  • General gravitational potential energy
  • Potential energy and force relationship
  • Escape energy (intro level)
Start topic Gravity as energy storage.
8
Elastic Potential Energy (Springs)
Model springs with Hooke’s law and connect work, potential energy, and stored energy release.
  • Hooke’s law
  • Spring potential energy function
  • Systems with multiple springs
  • Energy storage and release
Start topic Classic energy model.
9
Energy Diagrams and Energy Methods
Use bar charts and potential curves to predict motion, turning points, and stability.
  • Energy bar charts
  • Potential energy curves
  • Turning points and equilibrium
  • Stability analysis
Start topic Visual reasoning.
10
Conservation of Mechanical Energy
Solve many problems with \(K+U=\text{constant}\) when only conservative forces do work.
  • Conditions for conservation
  • Isolated systems
  • Mixed kinetic–potential energy problems
  • Comparison with Newton’s-law approach
Start topic The big shortcut.
11
Energy with Friction and Dissipative Forces
Include energy losses by tracking work done by friction/drag and the conversion to thermal/internal energy.
  • Work done by friction
  • Mechanical energy loss
  • Thermal energy considerations
  • Real-world system modeling
Start topic Realistic systems.
12
Power
Power measures how fast energy changes. Learn average vs instantaneous power and \(P=\vec F\cdot\vec v\).
  • Average vs instantaneous power
  • Power as force–velocity dot product
  • Power in mechanical systems
  • Efficiency and energy transfer rates
Start topic Finish the unit.
Practice
Practice & Exercises
Mixed practice across work, energy, conservation, friction losses, and power.
  • Work & dot-product drills
  • Work–energy theorem sets
  • Potential energy + conservation problems
  • Friction/drag energy loss questions
  • Power & efficiency problems
  • Exam-style mixed review
Open practice Unit-wide mastery.