WORK AND ENERGY

http://www.physics.umd.edu/lecdem/services/avmats/slides/C4.%20SECOND%20LAW%20OF%20MOTION/C4%20Cartoon%20-%20FoxTrot%20-%20F=MA.gif

WORK ANDENERGY

WORK

•Work is done when an object ismoved through a distance. It isdefined as the product of thecomponent of force applied alongthe direction of displacement and themagnitude of the displacement.

•W = F • d cos

$C:\Users\Rich\Desktop\Physics Figs\07_Figures\07_01_Figure.jpg$

Units of Work

•Look at the equation:

•W = F • d cos, the units are theunits of force times displacement.

•So, Newton • meter

•A Newton • meter is called a Joule

•1 Joule = 1 Newton • meter

•1 J = 1 N • m

Units of Work

•SI or MKSNewton•meterJoule

•CGSDyne•centimeterErg

•EnglishPound•footft•lb

•The unit is named after the Englishphysicist James P. Joule

James Joule(1818-1889)

•Not formally trainedas a physicist.

•He ran experimentsduring hishoneymoon.

•He later found themechanicalequivalent of heat.

•Heat is energy not asubstance.

$C:\Users\Rich\Desktop\Physics Figs\07_Figures\07_02_Figure.jpg$

Work: positive or negative?

•Work is a scalar quantity

•Work is positive when thecomponent of force and thedisplacement are in the samedirection.

•Work is negative when thecomponent of force and thedisplacement are in theopposite directions.

$C:\Users\Rich\Desktop\Physics Figs\07_Figures\07_04_Figure.jpg$

$C:\Users\Rich\Desktop\Physics Figs\07_Figures\07_05_Figure.jpg$

Displacement

Force

Area under Curve is Work

$C:\Users\Rich\Desktop\Physics Figs\07_Figures\07_06_Figure.jpg$

Can you determine the workdone?

$C:\Users\Rich\Desktop\Physics Figs\07_Figures\07_19_Figure.jpg$

Who’s Doing Work?

Try this problem

•A horse pulls a stationary 300 kg cart for 55 m.The horse pulls on the cart at an angle of 35o with a450 N constant force.

–Find the force along the direction of motion.

–Find the work done by the horse.

–Find the acceleration of the cart.

–Find the total time this takes.

–Find the weight of the cart.

–What would the d-t, v-t, a-t, F-d graphs looklike?

POWER !

•Power is the rate of doing work.

Power is measured in units called Watts

Units of Power

•The units of power are:

The Inclined PlaneA Simple Machine

$C:\Users\Rich\Desktop\Physics Figs\07_Figures\07_conceptualcheckpt_01.jpg$

Independence of Path

Force applied

Length of ramp

Work is thesame

Height

Forms ofEnergyForms ofEnergy

http://www.greenearthproject.com/Forms8xllb.jpg

Chemical EnergyChemical Energy

Solar EnergySolar Energy

Electrical EnergyElectrical Energy

Wind EnergyWind Energy

Sound EnergySound Energy

Nuclear EnergyNuclear Energy

Heat EnergyHeat Energy

Kinetic EnergyKinetic Energy

Kinetic Energy is energy of motion.Kinetic Energy is energy of motion.

Work-Energy TheoremWork-Energy Theorem

The result of work is that there is achange of speed, or an acceleration.The result of work is that there is achange of speed, or an acceleration.

W=F•dW=F•d

W=ma•dW=ma•d

vf2 = vi2 + 2ad and solve for advf2 = vi2 + 2ad and solve for ad

ad = (vf2 – vi2)/2ad = (vf2 – vi2)/2

Insert into W=madInsert into W=mad

W=m(vf2 – vi2)/2W=m(vf2 – vi2)/2

Work-Energy TheoremWork-Energy Theorem

Work-Energy TheoremWork-Energy Theorem

Gravitational Potential EnergyGravitational Potential Energy

The force of gravity does work. Itaccelerates objects.The force of gravity does work. Itaccelerates objects.

W = Fg • dW = Fg • d

W = mg • dW = mg • d

W = mg • hW = mg • h

(h = height above a referencepoint)(h = height above a referencepoint)

Gravitational Potential EnergyGravitational Potential Energy

Note: AP Physics uses thesymbol U for potentialenergy

Potential Energy and WorkPotential Energy and Work

When work is done by gravity oragainst it, the change in PE is equalto the work done.When work is done by gravity oragainst it, the change in PE is equalto the work done.

Work and Gravity

$C:\Users\Rich\Desktop\Physics Figs\Energy\08_01_Figure.jpg$

Work and Friction

$C:\Users\Rich\Desktop\Physics Figs\Energy\08_02_Figure.jpg$

Conservation of EnergyConservation of Energy

Energy is conserved in all systems.This means that in the Universe,all the energy that was at thebeginning of time is still in theUniverse today.Energy is conserved in all systems.This means that in the Universe,all the energy that was at thebeginning of time is still in theUniverse today.

As we isolate systems, we find thatthe total energy before is equal tothe total energy after.As we isolate systems, we find thatthe total energy before is equal tothe total energy after.

The energy just changes form.The energy just changes form.

Mechanical Energy

Try this Problem

Find the final speedof the object as ithits the pavement.

35m

The Roller Coaster

$C:\Users\Rich\Desktop\Physics Figs\Energy\08_05_Figure.jpg$

$C:\Users\Rich\Desktop\Physics Figs\Energy\08_11_Figure.jpg$

Conservation of Energy-The Roller Coaster

The Roller CoasterProblem

40 m

20 m

30 m

Find the Speeds at points A-F

25 m

Atwood’s Machine Revisited

$C:\Users\Rich\Desktop\Physics Figs\Energy\08_23_Figure.jpg$

Spring Potential EnergySpring Potential Energy

•Springs possess potential energy ifthey are elongated or compressedfrom their rest positions.•Springs possess potential energy ifthey are elongated or compressedfrom their rest positions.

•This is called spring (or elastic)potential energy.•This is called spring (or elastic)potential energy.

•The formula is derived from Hooke’sLaw:•The formula is derived from Hooke’sLaw:

Spring Potential EnergySpring Potential Energy

Conservative Force

•A conservative force is such that the workdone on the object is independent of thepath.

The force does NO work as the objectmoves around a closed path from start tofinish.

Conservative vs. Non-conservativeForce

•Conservative

–Gravity

–Elastic Spring

–Electric

•Non-conservative

–Friction

–Air resistance

–Tension

–Normal force

Conservative Force

$C:\Users\Rich\Desktop\Physics Figs\Energy\08_03_Figure.jpg$

Non-Conservative Force

$C:\Users\Rich\Desktop\Physics Figs\Energy\08_04_Figure.jpg$

Internal Energy

•The total energy contained within athermodynamic system.

•Basically we are talking about heat when weuse the term internal energy

•Usually in mechanical systems, heat iscreated because of friction, air resistance, orwater resistance

•Energy in this form is typically wastedenergy

Non-Conservative Forces

•A force is non-conservative if the workdone on an object is dependent upon thepath of travel.

Review QuestionsReview Questions

Write responses to each question on a separatesheet of paper to be handed in.Write responses to each question on a separatesheet of paper to be handed in.

There are 6 questions.There are 6 questions.

Some are equations, some require written responsesand deep thought, while some are graphical.Some are equations, some require written responsesand deep thought, while some are graphical.

Question 1

What is the definition ofWork in Physics?

Question 2

•Name two ways in which Work and Energyare related.

Question 3Question 3

What equation equatesWork with Kinetic Energy?What equation equatesWork with Kinetic Energy?

Question 4

•Explain how thispicture shows that:

Question 5Question 5

How does the statement, “the Earth getsall its energy from the Sun,” explain howyou can be awake here today?How does the statement, “the Earth getsall its energy from the Sun,” explain howyou can be awake here today?

Question 6

•Draw a graph that shows how PE and KEchange while riding this roller coaster.Label points W, X, and Y on the graph.

In Summary

•Work is Force times a displacement.

•Kinetic Energy is 1/2 mv2.

•Gravitational Potential Energy

is mgh.

•The work-energy theorem is

W=  K.

•Conservation of energy

•Spring potential energy is 1/2 kx2