Chapter 5Chapter 5

EnergyEnergy

Forms of EnergyForms of Energy

MechanicalMechanical focus for nowfocus for now

chemicalchemical electromagneticelectromagnetic nuclearnuclear

Using Energy Using Energy ConsiderationsConsiderations

Energy can be transformed from Energy can be transformed from one form to anotherone form to another Essential to the study of physics, Essential to the study of physics,

chemistry, biology, geology, chemistry, biology, geology, astronomyastronomy

Can be used in place of Newton’s Can be used in place of Newton’s laws to solve certain problems laws to solve certain problems more simplymore simply

WorkWork

Provides a link between force and Provides a link between force and energyenergy

The work, The work, WW, done by a constant , done by a constant force on an object is defined as the force on an object is defined as the product of the component of the product of the component of the force along the direction of force along the direction of displacement and the magnitude displacement and the magnitude of the displacementof the displacement

x)cosF(W

Work, cont.Work, cont.

F cos θ is the F cos θ is the

component of the component of the force in the force in the direction of the direction of the displacementdisplacement

Δ x is the Δ x is the displacementdisplacement

x)cosF(W

Work, cont.Work, cont.

This gives no information aboutThis gives no information about the time it took for the displacement the time it took for the displacement

to occurto occur the velocity or acceleration of the the velocity or acceleration of the

objectobject

Units of WorkUnits of Work

SISI Newton • meter = JouleNewton • meter = Joule

N • m = JN • m = J

US CustomaryUS Customary foot • poundfoot • pound

ft • lbft • lb– no special nameno special name

More About WorkMore About Work

Scalar quantityScalar quantity The work done by a force is zero when The work done by a force is zero when

the force is perpendicular to the the force is perpendicular to the displacementdisplacement cos 90° = 0cos 90° = 0

If there are multiple forces acting on an If there are multiple forces acting on an object, the total work done is the object, the total work done is the algebraic sum of the amount of work algebraic sum of the amount of work done by each forcedone by each force

More About Work, cont.More About Work, cont.

Work can be positive or negativeWork can be positive or negative Positive if the force and the Positive if the force and the

displacement are in the same displacement are in the same directiondirection

Negative if the force and the Negative if the force and the displacement are in the opposite displacement are in the opposite directiondirection

When Work is ZeroWhen Work is Zero

Displacement is Displacement is horizontalhorizontal

Force is verticalForce is vertical cos 90° = 0cos 90° = 0

Work Can Be Positive or Work Can Be Positive or NegativeNegative

Work is positive Work is positive when lifting the when lifting the boxbox

Work would be Work would be negative if negative if lowering the boxlowering the box

Kinetic EnergyKinetic Energy

Energy associated with the motion Energy associated with the motion of an objectof an object

Scalar quantity with the same units Scalar quantity with the same units

as workas work Work is related to kinetic energyWork is related to kinetic energy

2mv2

1KE

Work-Kinetic Energy Work-Kinetic Energy TheoremTheorem

When work is done by a net force When work is done by a net force on an object and the only change on an object and the only change in the object is its speed, the work in the object is its speed, the work done is equal to the change in the done is equal to the change in the object’s kinetic energyobject’s kinetic energy

Speed will increase if work is positiveSpeed will increase if work is positive Speed will decrease if work is Speed will decrease if work is

negativenegative

KEKEKEW ifnet

Work and Kinetic EnergyWork and Kinetic Energy

An object’s kinetic An object’s kinetic energy can also be energy can also be thought of as the thought of as the amount of work amount of work the moving object the moving object could do in coming could do in coming to restto rest The moving The moving

hammer has kinetic hammer has kinetic energy and can do energy and can do work on the nailwork on the nail

Potential EnergyPotential Energy

Potential energy is associated with Potential energy is associated with the position of the object within the position of the object within some systemsome system Potential energy is a property of the Potential energy is a property of the

system, not the objectsystem, not the object A system is a collection of objects or A system is a collection of objects or

particles interacting via forces or particles interacting via forces or processes that are internal to the processes that are internal to the systemsystem

Gravitational Potential Gravitational Potential EnergyEnergy

Gravitational Potential Energy is Gravitational Potential Energy is the energy associated with the the energy associated with the relative position of an object in relative position of an object in space near the Earth’s surfacespace near the Earth’s surface Objects interact with the earth Objects interact with the earth

through the gravitational forcethrough the gravitational force Actually the potential energy of the Actually the potential energy of the

earth-object systemearth-object system

Work and Gravitational Work and Gravitational Potential EnergyPotential Energy

PE = mgyPE = mgy Units of Potential Units of Potential

Energy are the Energy are the same as those of same as those of Work and Kinetic Work and Kinetic EnergyEnergy

figravity PEPEW

Reference Levels for Reference Levels for Gravitational Potential Gravitational Potential EnergyEnergy

A location where the gravitational A location where the gravitational potential energy is zero must be chosen potential energy is zero must be chosen for each problemfor each problem The choice is arbitrary since the change in the The choice is arbitrary since the change in the

potential energy is the important quantitypotential energy is the important quantity Choose a convenient location for the zero Choose a convenient location for the zero

reference heightreference height often the Earth’s surfaceoften the Earth’s surface may be some other point suggested by the problemmay be some other point suggested by the problem

Conservative ForcesConservative Forces

A force is conservative if the work it A force is conservative if the work it does on an object moving between does on an object moving between two points is independent of the path two points is independent of the path the objects take between the pointsthe objects take between the points The work depends only upon the initial The work depends only upon the initial

and final positions of the objectand final positions of the object Any conservative force can have a Any conservative force can have a

potential energy function associated potential energy function associated with itwith it

More About Conservative More About Conservative ForcesForces

Examples of conservative forces Examples of conservative forces include:include: GravityGravity Spring forceSpring force Electromagnetic forcesElectromagnetic forces

In general:In general: fic PEPEW

Nonconservative ForcesNonconservative Forces

A force is nonconservative if the A force is nonconservative if the work it does on an object depends on work it does on an object depends on the path taken by the object the path taken by the object between its final and starting points.between its final and starting points.

Examples of nonconservative forcesExamples of nonconservative forces kinetic friction, air drag, propulsive kinetic friction, air drag, propulsive

forcesforces

Friction as a Friction as a Nonconservative ForceNonconservative Force

The friction force is transformed The friction force is transformed from the kinetic energy of the from the kinetic energy of the object into a type of energy object into a type of energy associated with temperatureassociated with temperature the objects are warmer than they the objects are warmer than they

were before the movementwere before the movement Internal EnergyInternal Energy is the term used for is the term used for

the energy associated with an the energy associated with an object’s temperatureobject’s temperature

Friction Depends on the Friction Depends on the PathPath

The blue path is The blue path is shorter than the shorter than the red pathred path

The work required The work required is less on the blue is less on the blue path than on the path than on the red pathred path

Friction depends Friction depends on the path and on the path and so is a so is a nonconservative nonconservative forceforce

Conservation of Conservation of Mechanical EnergyMechanical Energy

Conservation in generalConservation in general To say a physical quantity is To say a physical quantity is conservedconserved is to is to

say that the numerical value of the quantity say that the numerical value of the quantity remains constantremains constant

In Conservation of Energy, the total In Conservation of Energy, the total mechanical energy remains constantmechanical energy remains constant In any isolated system of objects that In any isolated system of objects that

interact only through conservative forces, interact only through conservative forces, the total mechanical energy of the system the total mechanical energy of the system remains constant. remains constant.

Conservation of Energy, Conservation of Energy, cont.cont.

Total mechanical energy is the Total mechanical energy is the sum of the kinetic and potential sum of the kinetic and potential energies in the systemenergies in the system

Other types of energy can be added Other types of energy can be added to modify this equationto modify this equation

ffii

fi

PEKEPEKE

EE

Problem Solving with Problem Solving with Conservation of EnergyConservation of Energy

Define the systemDefine the system Select the location of zero gravitational Select the location of zero gravitational

potential energypotential energy Do Do notnot change this location while solving change this location while solving

the problemthe problem Determine whether or not Determine whether or not

nonconservative forces are presentnonconservative forces are present If only conservative forces are present, If only conservative forces are present,

apply conservation of energy and solve apply conservation of energy and solve for the unknownfor the unknown

Potential Energy Stored in Potential Energy Stored in a Springa Spring

Involves the Involves the spring constantspring constant (or (or force constant), kforce constant), k

Hooke’s Law gives the forceHooke’s Law gives the force F = - k xF = - k x

F is the restoring forceF is the restoring force F is in the opposite direction of xF is in the opposite direction of x k depends on how the spring was k depends on how the spring was

formed, the material it is made from, formed, the material it is made from, thickness of the wire, etc.thickness of the wire, etc.

Potential Energy in a Potential Energy in a SpringSpring

Elastic Potential EnergyElastic Potential Energy related to the work required to related to the work required to

compress a spring from its compress a spring from its equilibrium position to some final, equilibrium position to some final, arbitrary, position xarbitrary, position x

2s kx

2

1PE

Conservation of Energy Conservation of Energy including a Springincluding a Spring

The PE of the spring is added to The PE of the spring is added to both sides of the conservation of both sides of the conservation of energy equationenergy equation

fsgisg )PEPEKE()PEPEKE(

Nonconservative Forces Nonconservative Forces with Energy with Energy ConsiderationsConsiderations

When nonconservative forces are When nonconservative forces are present, the total mechanical energy present, the total mechanical energy of the system is of the system is notnot constant constant

The work done by all nonconservative The work done by all nonconservative forces acting on parts of a system forces acting on parts of a system equals the change in the mechanical equals the change in the mechanical energy of the systemenergy of the system

EnergyW ativenonconserv

Nonconservative Forces Nonconservative Forces and Energyand Energy

In equation form:In equation form:

The energy can either cross a boundary The energy can either cross a boundary or the energy is transformed into a form or the energy is transformed into a form not yet accounted fornot yet accounted for

Friction is an example of a Friction is an example of a nonconservative forcenonconservative force

)PEKE()PEKE(W

or)PEPE(KEKEW

iiffnc

fiifnc

Transferring EnergyTransferring Energy

By WorkBy Work By applying a By applying a

forceforce Produces a Produces a

displacement of displacement of the systemthe system

Transferring EnergyTransferring Energy

HeatHeat The process of The process of

transferring heat transferring heat by collisions by collisions between between moleculesmolecules

Transferring EnergyTransferring Energy

Mechanical Mechanical WavesWaves a disturbance a disturbance

propagates propagates through a mediumthrough a medium

Examples include Examples include sound, water, sound, water, seismicseismic

Transferring EnergyTransferring Energy

Electrical Electrical transmissiontransmission transfer by means transfer by means

of electrical of electrical currentcurrent

Transferring EnergyTransferring Energy

Electromagnetic Electromagnetic radiationradiation any form of any form of

electromagnetic electromagnetic waveswaves

Light, microwaves, Light, microwaves, radio wavesradio waves

Notes About Conservation Notes About Conservation of Energyof Energy

We can neither create nor destroy We can neither create nor destroy energyenergy Another way of saying energy is Another way of saying energy is

conservedconserved If the total energy of the system does If the total energy of the system does

not remain constant, the energy must not remain constant, the energy must have crossed the boundary by some have crossed the boundary by some mechanismmechanism

Applies to areas other than physicsApplies to areas other than physics

Problem Solving with Problem Solving with Nonconservative ForcesNonconservative Forces

Define the systemDefine the system Write expressions for the total Write expressions for the total

initial and final energiesinitial and final energies Set the WSet the Wncnc equal to the difference equal to the difference

between the final and initial total between the final and initial total energyenergy

Follow the general rules for solving Follow the general rules for solving Conservation of Energy problemsConservation of Energy problems

PowerPower

Often also interested in the Often also interested in the raterate at at which the energy transfer takes placewhich the energy transfer takes place

PowerPower is defined as this rate of energy is defined as this rate of energy transfertransfer

SI units are Watts (W)SI units are Watts (W)

vFt

WP

2

2

s

mkg

s

JW

Power, cont.Power, cont.

US Customary units are generally hpUS Customary units are generally hp need a conversion factorneed a conversion factor

Can define units of work or energy in Can define units of work or energy in terms of units of power:terms of units of power:

kilowatt hours (kWh) are often used in kilowatt hours (kWh) are often used in electric billselectric bills

W746s

lbft550hp1

Center of MassCenter of Mass

The point in the body at which all The point in the body at which all the mass may be considered to be the mass may be considered to be concentratedconcentrated When using mechanical energy, the When using mechanical energy, the

change in potential energy is related change in potential energy is related to the change in height of the center to the change in height of the center of massof mass

Work Done by Varying Work Done by Varying ForcesForces

The work done by The work done by a variable force a variable force acting on an acting on an object that object that undergoes a undergoes a displacement is displacement is equal to the area equal to the area under the graph under the graph of F versus xof F versus x

Spring ExampleSpring Example

Spring is slowly Spring is slowly stretched from 0 stretched from 0 to xto xmaxmax

FFappliedapplied = -F = -Frestoringrestoring = = kxkx

W = ½kx²W = ½kx²