chapter 5 energy. forms of energy mechanical mechanical focus for now focus for now chemical...
TRANSCRIPT
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