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InformationUDP datagram service

UDP exchanges addressed messages without adding reliable stream delivery.

DefinitionInformationDNS names, records and caching

DNS distributes typed resource records through a delegated naming hierarchy.

DefinitionInformationCombinational digital-circuit model

A combinational output depends on current valid inputs after a bounded settling delay.

ModelInformationBoolean gates and truth tables

Logic gates compute Boolean functions with truth values 0 and 1.

DefinitionInformationClocked storage and sequential state

Sequential circuits retain state, so current inputs alone do not determine their behavior.

ModelInformationStored programs and instruction sets

Stored instructions control computation through a specified hardware/software interface.

ModelPhysicsDisplacement, distance and average speed

Displacement compares endpoints; distance measures the travelled path.

ModelPhysicsConstant-acceleration kinematics

Closed formulas require constant acceleration over the interval.

ModelPhysicsInertial reference frames and inertia

Newtonian force balances need an inertial frame or explicit inertial terms.

ModelPhysicsCircular motion and centripetal acceleration

A constant speed can still have an acceleration.

ModelPhysicsMass, gravitational weight and apparent weight

Mass is in kilograms; gravitational weight is a force.

ModelPhysicsNormal forces and tension

Contact geometry determines the force direction.

ModelPhysicsFree-body diagrams and system boundaries

List forces on the selected body once.

ModelPhysicsStatic and kinetic dry friction

Static friction is a responsive force with an approximate limit.

ModelPhysicsFluid drag and terminal speed

Terminal speed depends on the chosen drag model.

ModelPhysicsImpulse and momentum transfer

Time-integrated net force changes momentum.

ModelPhysicsElastic and inelastic collisions

Momentum conservation and kinetic-energy conservation are different.

ModelPhysicsConservative forces and potential energy

Potential-energy differences encode path-independent work.

ModelPhysicsMechanical-energy conservation and dissipation

Mechanical energy is only part of the total energy.

ModelPhysicsHooke’s spring model and elastic energy

A linear spring restores displacement toward equilibrium.

ModelPhysicsMechanical power

Power measures the rate of work or energy transfer.

ModelPhysicsRigid-body rotational kinetic energy

Rotation stores kinetic energy determined by mass distribution.

ModelPhysicsRolling without slipping

No slip constrains velocity at the contact point.

ModelPhysicsStatic equilibrium and torque balance

Zero net force alone does not prevent rotation.

ModelPhysics · Earth & cosmosYoung, shear and bulk elastic moduli

Stress and strain need a loading geometry and a constitutive range.

ModelPhysicsDensity and fluid pressure

Density is mass per volume; pressure is normal force per area.

ModelPhysicsAbsolute, gauge and differential pressure

A zero gauge reading need not be a vacuum.

ModelPhysicsPascal’s principle and ideal hydraulics

A pressure change is transmitted; pressure need not be equal at different heights.

ModelPhysicsNewtonian viscosity and Poiseuille flow

Viscosity relates shear stress to velocity gradient.

ModelPhysics · ChemistrySurface tension and capillary rise

Interface forces can support pressure jumps and capillary columns.

Model
ModelSource checked

Hooke’s spring model and elastic energy

Physics

A linear spring restores displacement toward equilibrium.

Key knowledge

An ideal one-dimensional spring has restoring force F=−kx and potential energy U=kx²/2 relative to equilibrium. The force law is an approximate material/geometry model valid over its linear elastic range, not a universal response of every deformable object.

Values and equations

F=−kx; U=½kx²

F
Axial restoring force N
k
Spring stiffness N m⁻¹
x
Displacement from spring equilibrium m
U
Stored elastic potential relative to equilibrium J

Conditions and scope

  • k>0; x measures extension or compression from the equilibrium length along the model’s axis.
  • Fixed spring parameters, negligible hysteresis and loading within the reversible linear range; beyond this range deformation can be nonlinear or permanent.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Samuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)2 sources
    1. University Physics Volume 1, §15.1: simple harmonic motionSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source
    2. University Physics Volume 1, §8.1: potential energy of a systemSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §15.1 Hooke restoring-force model and §8.1 elastic potential-energy integral. This is a one-dimensional spring model, not a complete elastic constitutive tensor.

2026-10-10 · /root/audit_life_earth_chemistry — independent Chemistry/Life/Earth editor. Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–4 of 4 relationships

Scientific relationships · 4 / 4

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 2

    Linked statements

    • An ideal one-dimensional spring has restoring force F=−kx and potential energy U=kx²/2 relative to equilibrium. The force law is an approximate material/geometry model valid over its linear elastic range, not a universal response of every deformable object.

    This relation concerns the stated hooke’s spring model and elastic energy claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  2. Uses definition
    Relationship sources · 2

    Linked statements

    • An ideal one-dimensional spring has restoring force F=−kx and potential energy U=kx²/2 relative to equilibrium. The force law is an approximate material/geometry model valid over its linear elastic range, not a universal response of every deformable object.

    This relation concerns the stated hooke’s spring model and elastic energy claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  3. Related to
    Relationship sources · 1

    Linked statements

    • For small reversible linear deformations, uniaxial stress σ=F_perp/A gives axial strain ε=ΔL/L₀ with σ=E_Yε. Simple shear obeys τ=Gγ, where γ is the engineering shear strain. Isotropic pressure compression has Δp=−K_BΔV/V₀. The moduli characterize different loading responses and are not interchangeable with strength or fracture limits.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

  4. Uses definition
    Relationship sources · 1

    Linked statements

    • Undamped one-dimensional motion obeying m ẍ=−kx has x=Acos(ωt+φ), with ω=√(k/m), period T=2π/ω and frequency f=1/T. Acceleration is −ω²x. Initial position and velocity determine amplitude and phase; frequency is independent of amplitude only within the ideal linear model.

    This relation concerns the stated simple harmonic motion and period claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

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