Chapter 6Chapter 6

Work, Energy, PowerWork, Energy, Power

WorkWorkThe The workwork done by force is defined as the done by force is defined as the product of the magnitude of the product of the magnitude of the displacement and the component of the displacement and the component of the force parallel to the displacementforce parallel to the displacement

The unit of work is the newton-meter, The unit of work is the newton-meter, called a joule (J)called a joule (J)

Work is a scalarWork is a scalar

W = F∙d∙cosθ

WorkWork

F

d

)cos d(F W

F cos

EnergyEnergyEnergyEnergy– The ability to do workThe ability to do work

Sources of energy?Sources of energy?

Mechanical energyMechanical energy– energy due to position or movement. energy due to position or movement.

Types of EnergyTypes of EnergyKinetic Energy = “Motion Energy”Kinetic Energy = “Motion Energy”

Potential Energy = “Stored Energy”Potential Energy = “Stored Energy”

Kinetic EnergyKinetic EnergyKinetic EnergyKinetic Energy is the energy is the energy possessed by an object because possessed by an object because it is in motion.it is in motion.

What would the unit be?What would the unit be?

(Translational Kinetic energy)

KE = ½ mv2

Work Energy TheoremWork Energy Theorem

The amount of kinetic energy transferred The amount of kinetic energy transferred to the object is equal to the work done. to the object is equal to the work done. KE = WKE = W– Many of the problems can be worked from Many of the problems can be worked from

herehere

Ex:Ex:

How much force is required to stop a 1500kg How much force is required to stop a 1500kg car traveling 60.0 km/hr in a distance of 20m?car traveling 60.0 km/hr in a distance of 20m?

Gravitational Gravitational Potential EnergyPotential Energy

Gravitational Potential EnergyGravitational Potential Energy is the energy is the energy possessed by an object because of a possessed by an object because of a gravitational interaction.gravitational interaction.– Product of it’s weight and its height above Product of it’s weight and its height above

some reference level.some reference level.

PEG = mghy

Properties of GravitationalProperties of GravitationalPotential EnergyPotential Energy

Arbitrary Zero PointArbitrary Zero Point– You need to select a zero levelYou need to select a zero level

Independent of PathIndependent of Path– All that matters is the vertical height changeAll that matters is the vertical height change

– Example: which has more potential, which Example: which has more potential, which requires more workrequires more work

Elastic Potential EnergyElastic Potential EnergyElastic potential energyElastic potential energy– Energy stored elastically by stretching or Energy stored elastically by stretching or

compressing. compressing. – Examples?Examples?

SpringsSpringsThe more you compress or stretch them, The more you compress or stretch them, the more force you need to stretch or the more force you need to stretch or compress.compress.

Hooke’s LawHooke’s Law– FFspringspring=k x=k x

k is the spring constant which is a measure of k is the spring constant which is a measure of stiffnessstiffness

x is the displacement from equilibriumx is the displacement from equilibrium

P.E. P.E. springspring= ½ k x= ½ k x22

– Practice problemPractice problem

Conservation of Conservation of Mechanical EnergyMechanical Energy

Energy can neither be created or destroyed, but Energy can neither be created or destroyed, but only transformed from one form to another.only transformed from one form to another.

Total initial energy = Total final energyTotal initial energy = Total final energy

finalinital PEKEPEKE )()(

Works for systems with no losses (friction, air resistance, etc.)

Problem Solution GuidelinesProblem Solution Guidelines

Determine that energy can be conserved Determine that energy can be conserved (no losses)(no losses)– Pick the zero level for potential energyPick the zero level for potential energy

Pick two interesting places in the problemPick two interesting places in the problem– Write kinetic and potential energies at these Write kinetic and potential energies at these

placesplaces– Conserve energyConserve energy

(KE + PE)(KE + PE)11 = (KE + PE) = (KE + PE)22

ExampleExample

If a boulder is pushed off of a 15.0 m high cliff by Wile E. If a boulder is pushed off of a 15.0 m high cliff by Wile E. Coyote, and the road runner is 1.50 m tall, find the velocity Coyote, and the road runner is 1.50 m tall, find the velocity of the boulder when it reaches the road runners head.of the boulder when it reaches the road runners head.

Forces Work and EnergyForces Work and Energy

Conservative forces- work done by these Conservative forces- work done by these forces is independent of the pathforces is independent of the path– Examples: gravity, elastic, electricExamples: gravity, elastic, electric

Non-conservative forces- work done by Non-conservative forces- work done by these forces is dependant upon the paththese forces is dependant upon the path– Examples: friction, air resistanceExamples: friction, air resistance

Law of conservation with Law of conservation with dissipative forcesdissipative forces

Dissipative forces- forces that reduce the Dissipative forces- forces that reduce the total mechanical energy of a systemtotal mechanical energy of a system• Example: friction (loss to thermal energy)Example: friction (loss to thermal energy)

Swinging pendulum of pain demo. Swinging pendulum of pain demo. In real situationsIn real situations• T.E.= K.E.+P.E+ Energy lost to n.c. ForcesT.E.= K.E.+P.E+ Energy lost to n.c. Forces

WWNCNC= = ΔΔKE+ KE+ ΔΔPEPE

-F-Ffrictionfriction d = d = ΔΔKE+ KE+ ΔΔPEPE• Example 6-15 pg 168Example 6-15 pg 168

PowerPowerPowerPower is the rate at which work is done. is the rate at which work is done.The unit of power is a joule per second, called a Watt (W).The unit of power is a joule per second, called a Watt (W).1hp = 746 Watts1hp = 746 Watts

Velocity * Force

*

t

W P

Time

DoneWork Power Average

t

dF

ExampleExampleA 70.0 kg football player runs up a flight of stairs in 4.0 A 70.0 kg football player runs up a flight of stairs in 4.0 seconds while training. The vertical height of the stairs is seconds while training. The vertical height of the stairs is 4.5 m. 4.5 m. – What is the power output of the player in W & hpWhat is the power output of the player in W & hp– How much energy was required to climb the stairs?How much energy was required to climb the stairs?