Introduction to Work and Energy
Work is the energy associated with the action of a force.
Learning Objective

Describe relationship between work, energy, and force
Key Points
 Work is the transfer of energy by a force acting on an object as it is displaced.
 The work done by a force is zero if the displacement is either zero or perpendicular to the force.
 The work done is positive if the force and displacement have the same direction, and the work done is negative if they have opposite direction.
Term

energy
A quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent.
Example
 An example of work is a pitcher throwing a ball. A baseball pitcher does positive work on the ball by applying a force to it over the distance it moves while in his grip.
Full Text
The work done on a system by a constant force is the product of the component of the force in the direction of motion times the distance through which the force acts. For oneway motion in one dimension, this is expressed in equation form as W=Fdcosθ, where W is work, F is the magnitude of the force on the system, d is the magnitude of the displacement of the system, and θ is the angle between the force vector F and the displacement vector d .
Take this example of work in action from : (A) The work done by the force F on this lawn mower is Fdcosθ. Note that Fcosθ is the component of the force in the direction of motion. (B) A person holding a briefcase does no work on it, because there is no motion. No energy is transferred to or from the briefcase. (C) The person moving the briefcase horizontally at a constant speed does no work on it, and transfers no energy to it. (D) Work is done on the briefcase by carrying it up stairs at constant speed, because there is necessarily a component of force F in the direction of the motion. Energy is transferred to the briefcase and could, in turn, be used to do work. (E) When the briefcase is lowered, energy is transferred out of the briefcase and into an electric generator. Here the work done on the briefcase by the generator is negative, removing energy from the briefcase, because F and d are in opposite directions .
Examples of Work
This is how work in progress and energy coexist and operate. Work is the energy associated with the action of a force.
In physics, a force is said to do work when it acts on a body so that there is a displacement of the point of application, however small, in the direction of the force. Thus a force does work when there is movement under the action of the force. The work done by a constant force of magnitude F on a point that moves a distance d in the direction of the force is the product:
For example, if a force of 10 newton (F = 10 N) acts along point that travels two meters (d = 2 m), then it does the work W = (10 N)(2 m) = 20 N m = 20 J. This is approximately the work done lifting a 1 kg weight from the ground to over a person's head against the force of gravity. Notice that the work is doubled either by lifting twice the weight in the same distance or by lifting the same weight twice the distance.
Work is closely related to energy. The conservation of energy states that the change in total internal energy of a system equals the added heat minus the work performed by the system (see the first law of thermodynamics, and ):
Baseball Pitcher
A baseball pitcher does work on a baseball by throwing the ball at some force, F, over some distance d, which for the average baseball field, is about 60 feet.
Also, from Newton's second law for rigid bodies, it can be shown that work on an object is equal to the change in kinetic energy of that object:
The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative. Therefore work on an object moving in a conservative force field is equal to minus the change of potential energy of the object:
This shows that work is the energy associated with the action of a force, and so has the physical dimensions and units of energy.
Key Term Reference
 Component
 Appears in these related concepts: Adding and Subtracting Vectors Using Components, Cathode Ray Tube, TV and Computer Monitors, and the Oscilloscope, and Position, Velocity, and Acceleration as a Function of Time
 Law
 Appears in these related concepts: Damped Harmonic Motion, Photon Interactions and Pair Production, and Models, Theories, and Laws
 Newton's Second Law
 Appears in these related concepts: Momentum, Force, and Newton's Second Law, Centripetal Force, and Matter Exists in Space and Time
 application
 Appears in these related concepts: Introduction to Elementary operations and Gaussian Elimination, Physics and Other Fields, and XRay Imaging and CT Scans
 conservation
 Appears in these related concepts: Conservation of Mechanical Energy, Museums and Private Collections, and Linear Momentum
 conservative force
 Appears in these related concepts: Gravity, Springs, and Fundamental Theorem for Line Integrals
 dimension
 Appears in these related concepts: TwoDimensional Space, Length, and Dimensional Analysis
 displacement
 Appears in these related concepts: Position, Displacement, Velocity, and Acceleration as Vectors, Reference Frames and Displacement, and Introduction to Human Language
 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
 gravity
 Appears in these related concepts: Defining Graviational Potential Energy, Key Points: Range, Symmetry, Maximum Height, and Properties of Electric Charges
 heat
 Appears in these related concepts: Heat and Work, Work, and The Greenhouse Effect
 internal energy
 Appears in these related concepts: The First Law, Isotherms, and Internal Energy
 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: Newton and His Laws, Roundoff Error, and Components of a Vector
 motion
 Appears in these related concepts: Motion Diagrams, TwoComponent Forces, and Moving Source
 perpendicular
 Appears in these related concepts: The Cross Product, Tangent Vectors and Normal Vectors, and Circular Motion
 potential
 Appears in these related concepts: What is Potential Energy?, Conservative and Nonconservative Forces, and Linear Expansion
 potential energy
 Appears in these related concepts: The Chain Rule, Problem Solving With the Conservation of Energy, and Escape Speed
 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
 thermodynamics
 Appears in these related concepts: Absolute Zero, The Effect of a Catalyst, and Solutions and Heats of Hydration
 vector
 Appears in these related concepts: Multiplying Vectors by a Scalar, Series and Sigma Notation, and Translations
 weight
 Appears in these related concepts: Gauge Pressure and Atmospheric Pressure, Weight of the Earth, and B.9 Chapter 9
 work
 Appears in these related concepts: Free Energy and Work, Energy Transportation, and The First Law of Thermodynamics
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