📘 How does energy actually get spent?

What you’ll learn

1. Defining Energy in PhysicsEstablish the precise physical definition of energy and distinguish it from everyday usage.Energy quantifies the capacity to do work within a system. The joule serves as the SI unit linking force and displacement. This foundation supports every subsequent calculation of mechanical and thermal processes.
2. Kinetic Energy DerivationDerive the kinetic energy formula and compute values for linear motion.Work done by net force equals change in kinetic energy. Substituting kinematics equations produces the ½mv² relation. Worked examples include a 1500 kg car reaching 20 m/s.
3. Gravitational Potential EnergyDefine gravitational potential energy and relate it to height and mass.U = mgh follows from integrating the constant gravitational force. Reference levels are chosen arbitrarily but must remain consistent. The expression connects directly to work against gravity.
4. Elastic Potential EnergyCalculate elastic potential energy stored in Hooke's-law springs.U = ½kx² arises from integrating the variable restoring force. Energy is released as the spring returns to equilibrium. Real mechanisms include vehicle suspensions and archery bows.
5. Work-Energy TheoremApply the work-energy theorem to relate net work and kinetic energy change.The theorem states W_net = ΔK for any system. Both conservative and non-conservative forces contribute to the total work. Vector components must be resolved when forces act at angles.
6. Conservation of Mechanical EnergyApply conservation of mechanical energy between kinetic and potential forms.Total mechanical energy remains constant when only conservative forces act. Initial and final states are equated without explicit force integration. Frictionless ramps and roller coasters illustrate the principle.
7. Non-Conservative Forces and DissipationAccount for energy lost to friction and other non-conservative work.The energy equation becomes K_f + U_f = K_i + U_i + W_non-conservative. Thermal energy generated equals the magnitude of negative work. Realistic problems always include this term.
8. Power and Rate of Energy TransferCalculate instantaneous and average power from work or force and velocity.Power equals work per unit time or F·v. The watt and horsepower units are compared. Efficiency is introduced as useful power output divided by input.
9. Energy in One-Dimensional CollisionsDistinguish elastic and inelastic collisions using kinetic energy conservation.Elastic collisions conserve both momentum and kinetic energy. Inelastic cases lose kinetic energy to deformation and heat. The coefficient of restitution quantifies the energy retained.
10. Thermal Energy and the First LawIntroduce internal thermal energy and connect it to the first law of thermodynamics.ΔU = Q − W links heat added, work done, and change in internal energy. Temperature change relates to specific heat capacity. This extends mechanical energy accounting to molecular scales.
11. Energy Efficiency and Real SystemsEvaluate efficiency as the ratio of useful output energy to total input energy.Efficiency never reaches 100 % because of unavoidable thermal losses. Sankey diagrams illustrate energy flow branches. Design improvements target the largest loss pathways.
12. Relativistic Energy RelationExtend the energy concept to special relativity for high-speed particles.Rest energy mc² appears as the zero-velocity limit. Total energy includes both rest and kinetic contributions via the Lorentz factor. This prepares students for nuclear and particle applications.

Questions this course answers

Grounded in trusted sources

• OpenStax
• National Institute of Standards and Technology
• American Association of Physics Teachers
• OpenStax University Physics Volume 1 — Work and Kinetic Energy; Potential Energy and Conservation of Energy
• NIST — SI units: the joule
• American Association of Physics Teachers — energy instruction resources

Every Wunder lesson is built from real, reputable sources — never invented.

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