Chapter 5Chapter 5

Work, Power and Work, Power and EnergyEnergy

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 (or d) is the distance of the object moveds (or d) 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 and 50N force pulls a 20 kg object and moves it 2m, friction f=15N. moves it 2m, friction f=15N. Acceleration along the ground? Work Acceleration along the ground? Work done? Work done by friction? Total done? Work done by friction? Total work?work?

What about pulling at 30What about pulling at 30??

PowerPower

PowerPower is defined as this rate of work is defined as this rate of work•

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

A crane lifts a 5000 kg object 800 m in A crane lifts a 5000 kg object 800 m in 10 min. How much power must the 10 min. How much power must the engine produce?engine produce?

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

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

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

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 (EEnergy (Epp))• PE of water in reservoir is used to PE of water in reservoir is used to

generate electricitygenerate electricity

mghEp

Reference Levels for Gravitational Reference Levels for Gravitational Potential EnergyPotential Energy

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

• Once the position is chosen, it must remain Once the position is chosen, it must remain fixed for the entire problemfixed for the entire problem

ExampleExample

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

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

2

2

1mvEk

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

Consider energy of a falling ball of Consider energy of a falling ball of mass m from height of h.mass m from height of h.

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 kp EEE

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

kfpfkipi

fi

EEEE

EE

Conservation of (Conservation of (mechanicalmechanical) Energy) Energy

True if only conservative forces are True if only conservative forces are presentpresent• Conservative forces: gravity, springsConservative forces: gravity, springs• Non-conservative forces: push, pull, friction, Non-conservative forces: push, pull, friction,

air-resistanceair-resistance Apply the conservation of energy equation Apply the conservation of energy equation

to the systemto the system• Immediately substitute zero values, then do Immediately substitute zero values, then do

the algebra before substituting the other the algebra before substituting the other valuesvalues

Solve for the unknown(s)Solve for the unknown(s)

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

WWncnc work done by non-cons. forces work done by non-cons. forces

22

2

1

2

1ffii mvmghWmvmgh

kfpfnckipi EEWEE

ExampleExample

Cart on a roller-coaster with no friction. Cart on a roller-coaster with no friction. Start from rest at h=30m. What is Start from rest at h=30m. What is the speed at the end hthe speed at the end hAA=15m.=15m.

ExampleExample

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

speed 80km/h collide and come to speed 80km/h collide and come to rest. rest.

ExampleExample

Child on a 3 m high slide (no friction),Child on a 3 m high slide (no friction),what is the speed at the end?what is the speed at the end?

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

If the slide is 10 m long, how large was If the slide is 10 m long, how large was the average friction force?the average friction force?

ExampleExample

Same child is on a swing with 6m rope Same child is on a swing with 6m rope and starts at 60° with respect to and starts at 60° with respect to vertical direction. Maximum speed?vertical direction. Maximum speed?

If the child starts with speed of 1 m/s If the child starts with speed of 1 m/s with a push, what is the max speed?with a push, what is the max speed?