Chapter 7Chapter 7

Work and EnergyWork and Energy

Conservation LawsConservation Laws

MassMass Electric ChargeElectric Charge Conservation of EnergyConservation of Energy Sum of all forms of energy is conservedSum of all forms of energy is conserved

Energy: ability to do work

Forms of EnergyForms of Energy

MechanicalMechanical• Focus for nowFocus for now• May be kinetic (associated with motion) May be kinetic (associated with motion)

or potential (associated with position)or potential (associated with position) ChemicalChemical ElectromagneticElectromagnetic NuclearNuclear

Some Energy ConsiderationsSome Energy Considerations

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

chemistry, biology, geology, astronomychemistry, biology, geology, astronomy From one body to another – Work!From one body to another – Work! Can be used in place of Newton’s Can be used in place of Newton’s

laws to solve certain problems more laws to solve certain problems more simplysimply

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 the product of force on an object is the product of the force times the distance through the force times the distance through which the force acts.which the force acts.

FsW

Units of WorkUnits of Work

SISI• Newton Newton • meter = Joule• meter = Joule

N N • m = J• m = J J = kg • mJ = kg • m22 / s / s22

US CustomaryUS Customary• foot foot • pound• pound

ftft • lb• lb• no special nameno special name

Work, cont.Work, cont.

In generalIn general

• F F is the magnitude of the forceis the magnitude of the force• s is the distance of the object moveds is the distance of the object moved is the angle between force and direction of is the angle between force and direction of

motionmotion

sFW )cos(

Work, cont.Work, cont.

This gives no information aboutThis gives no information about• the time it took for the motion to occurthe time it took for the motion to occur• the velocity or acceleration of the objectthe velocity or acceleration of the object

Work is a scalar quantityWork is a scalar quantity

More About WorkMore About Work

The work done by a force is zero when the The work done by a force is zero when the force is perpendicular to the displacementforce is perpendicular to the displacement• F=0F=0• s=0s=0• 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 algebraic object, the total work done is the algebraic sum of the amount of work done by each sum of the amount of work done by each forceforce

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

Work can be positive or negativeWork can be positive or negative• Positive if s is in the same direction as FPositive if s is in the same direction as F• Negative if s is in opposite direction to FNegative if s is in opposite direction to F• Zero if s is perpendicular to FZero if s is perpendicular to F

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• The force would The force would

still be upward, still be upward, but the but the displacement displacement would be would be downwarddownward

ExampleExample

50N force pulls a 20 kg object at 30° 50N force pulls a 20 kg object at 30° above horizontal and moves it 2m, above horizontal and moves it 2m, friction f=15N. Acceleration along friction f=15N. Acceleration along the ground? Work done? Work done the ground? Work done? Work done by friction?by friction?

Kinetic EnergyKinetic Energy

Energy associated with the motion of Energy associated with the motion of an objectan 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 TheoremWork-Kinetic Energy Theorem

When work is done by the resultant When work is done by the resultant external force on an object and the external force on an object and the only change in the object is its only change in the object is its speed, the work done is equal to the speed, the work done is equal to the change in the object’s kinetic energychange in the object’s kinetic energy

• Speed will increase if work is positiveSpeed will increase if work is positive• Speed will decrease if work is negativeSpeed will decrease if work is negative

net fiW KE KE KE

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 the amount of work the moving object 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

ExampleExample

50N force pulls a 20 kg object at 30° 50N force pulls a 20 kg object at 30° above horizontal and moves it 2m, above horizontal and moves it 2m, friction f=15N. Find vfriction f=15N. Find vff if v if vi=i=4m/s.4m/s.

PowerPower

Often also interested in the Often also interested in the raterate at which at which the energy transfer takes placethe 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)

•

t

WP

3

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

kilowatt hours (kWh) are often used in electric bills kilowatt hours (kWh) are often used in electric bills 1kWh=3.6x10^6 J1kWh=3.6x10^6 J

This is a unit of energy, not powerThis is a unit of energy, not power

W746s

lbft550hp1

ExampleExample

An 80hp outboard motor, operating at An 80hp outboard motor, operating at full speed, can drive at speed boat at full speed, can drive at speed boat at 11 m/s. What is the forward 11 m/s. What is the forward thrust(force) of the motor?thrust(force) of the motor?

Fvt

Fs

t

WP

Potential EnergyPotential Energy

Potential energy is associated with Potential energy is associated with the shape or position of the objectthe shape or position of the object• 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 A system is a collection of objects

interacting via forces or processes that interacting via forces or processes that are internal to the systemare internal to the system

Elastic Potential EnergyElastic Potential Energy

Compression of a springCompression of a spring Restoring forceRestoring force

Elastic potential energy Elastic potential energy

Energy is available to do work: Energy is available to do work:

constant) spring :(k

kxF

2

2

1kxPE

Gravitational Potential EnergyGravitational Potential Energy

Lift object vertically, work is done Lift object vertically, work is done against the force of gravity of Earth against the force of gravity of Earth and energy is stored in the object in and energy is stored in the object in the form of Gravitational Potential the form of Gravitational Potential Energy (PE)Energy (PE)• Falling object: PE is changed to KEFalling object: PE is changed to KE• PE of water in reservoir is used to PE of water in reservoir is used to

generate electricitygenerate electricity

mghPE

ExampleExample

A 1500kg pile driver lifted 20 m in the A 1500kg pile driver lifted 20 m in the air have PE …air have PE …

Energy ConservationEnergy Conservation

Energy is never created or destroyed. Energy is never created or destroyed. Energy can be transformed from one Energy can be transformed from one kind into another, but the total kind into another, but the total amount of energy remains constant.amount of energy remains constant.

Example: PendulumExample: Pendulum

Conservation of Mechanical Conservation of Mechanical EnergyEnergy

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

is to say that the numerical value of the is to say that the numerical value of the quantity remains constant throughout quantity remains constant throughout any physical processany physical process

In Conservation of Energy, the total In Conservation of Energy, the total mechanical energy remains constantmechanical energy remains constant

constant KEPEE

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

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

• Other types of potential energy Other types of potential energy functions can be added to modify this functions can be added to modify this equationequation

ffii

fi

PEKEPEKE

EE

Work and EnergyWork and Energy

If a force (other than gravity) acts on If a force (other than gravity) acts on the system and does workthe system and does work

Need Work-Energy relationNeed Work-Energy relation

oror

ffii KEPEWKEPE

22

2

1

2

1ffii mvmghWmvmgh

ExampleExample

Cart on a roller-coaster…Cart on a roller-coaster…

ExampleExample

Two cars each with mass 2000kg andTwo cars each with mass 2000kg and

speed 80km/h collide. speed 80km/h collide.

ExampleExample

Child on a slideChild on a slide

If a child of 25kg slides down and If a child of 25kg slides down and reaches only 3m/s. What work was reaches only 3m/s. What work was done by the frictional force acting on done by the frictional force acting on the child?the child?