Kinetic Energy and WorkEnergy Theorem
The workenergy theorem states that the work done by all forces acting on a particle equals the change in the particle's kinetic energy.
Learning Objective

Outline the derivation of the workenergy theorem
Key Points
 The work W done by the net force on a particle equals the change in the particle's kinetic energy KE:
$W=\Delta KE=\frac{1}{2} mv_f^2\frac{1}{2} mv_i^2$ .  The workenergy theorem can be derived from Newton's second law.
 Work transfers energy from one place to another or one form to another. In more general systems than the particle system mentioned here, work can change the potential energy of a mechanical device, the heat energy in a thermal system, or the electrical energy in an electrical device.
Term

torque
A rotational or twisting effect of a force; (SI unit newtonmeter or Nm; imperial unit footpound or ftlb)
Full Text
The WorkEnergy Theorem
The principle of work and kinetic energy (also known as the workenergy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle. This definition can be extended to rigid bodies by defining the work of the torque and rotational kinetic energy.
Kinetic Energy
A force does work on the block. The kinetic energy of the block increases as a result by the amount of work. This relationship is generalized in the workenergy theorem.
The work W done by the net force on a particle equals the change in the particle's kinetic energy KE:
where v_{i} and v_{f} are the speeds of the particle before and after the application of force, and m is the particle's mass.
Derivation
For the sake of simplicity, we will consider the case in which the resultant force F is constant in both magnitude and direction and is parallel to the velocity of the particle. The particle is moving with constant acceleration a along a straight line. The relationship between the net force and the acceleration is given by the equation F = ma (Newton's second law), and the particle's displacement d, can be determined from the equation:
obtaining,
The work of the net force is calculated as the product of its magnitude (F=ma) and the particle's displacement. Substituting the above equations yields:
Key Term Reference
 Law
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 acceleration
 Appears in these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Scientific Applications of Quadratic Functions, and Centripetial Acceleration
 application
 Appears in these related concepts: Introduction to Elementary operations and Gaussian Elimination, Physics and Other Fields, and XRay Imaging and CT Scans
 displacement
 Appears in these related concepts: Calculus with Parametric Curves, Reference Frames and Displacement, and Introduction to Human Language
 energy
 Appears in these related concepts: Surface Tension, Energy Transportation, and Introduction to Work and Energy
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 force
 Appears in these related concepts: Force of Muscle Contraction, Force, and First Condition
 heat
 Appears in these related concepts: Heat and Work, Work, and The First Law
 kinetic
 Appears in these related concepts: Friction: Static, The Kinetic Molecular Theory of Matter, and Postmodernist Sculpture
 kinetic energy
 Appears in these related concepts: Solid Solubility and Temperature, Pressure, and Types of Energy
 magnitude
 Appears in these related concepts: Multiplying Vectors by a Scalar, Roundoff Error, and Components of a Vector
 mass
 Appears in these related concepts: Mass Spectrometer, Pop Art, and Mass
 net force
 Appears in these related concepts: Diffusion, ProblemSolving With Friction and Inclines, and The Second Law: Force and Acceleration
 parallel
 Appears in these related concepts: Resistors in Parallel, Combination Circuits, and How Skeletal Muscles Are Named
 potential
 Appears in these related concepts: What is Potential Energy?, Conservative and Nonconservative Forces, and Linear Expansion
 potential energy
 Appears in these related concepts: Problem Solving With the Conservation of Energy, Escape Speed, and Defining Graviational Potential Energy
 resultant
 Appears in these related concepts: Adding and Subtracting Vectors Graphically, TwoComponent Forces, and Forces in Two Dimensions
 rigid
 Appears in these related concepts: Connected Objects, The Physical Pendulum, and Center of Mass and Translational Motion
 rigid body
 Appears in these related concepts: Stability, Balance, and Center of Mass, Center of Mass and Inertia, and Motion of the Center of Mass
 velocity
 Appears in these related concepts: Velocity of Blood Flow, RootMeanSquare Speed, and Rolling Without Slipping
 work
 Appears in these related concepts: Force at an Angle to Displacement, Free Energy and Work, and The First Law of Thermodynamics
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