Note for PH 101 at UA-General Physics I (6)
Note for PH 101 at UA-General Physics I (6)
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Date Created: 02/06/15
GIANCOLI Lecture PowerPoints Chapter 6 Physics Principles with Applications 6 edition Giancoli Chapter 6 Work and Energy Units of Chapter 6 Work Done by a Constant Force Work Done by a Varying Force Kinetic Energy and the WorkEnergy Principle Potential Energy Conservative and Nonconservative Forces Mechanica Energy and Its Conservation Problem Solving Using Conservation of Mechanical Energy Units of Chapter 6 Other Forms of Energy Energy Transformations and the Law of Conservation of Energy Energy Conservation with Dissipative Forces Solving Problems Power Importance of Energy and Work In this chapter we will meet our first conservation law This gives us a powerful new way to analyse certain aspects of motion Energy and Work are also scalar quantities so they can be easier to work with than vectors Definition of Work In physics work has a very specific meaning o When a force acts on an object and the object then moves through some distance then we say that the force did work on the object 61 Work Done by a Constant Force The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement W Fd 0036 61 Copyright 2005 Pearson Prentice Hall Inc 61 Work Done by a Constant Force In the SI system the units of work are joules Copyright 2005 Pearson Prentice Hall Inc 1 1an As long as this person does not lift or lower the bag of groceries he is doing no work on it The force he exerts has no component in the direction of motion 61 Work Done by a Constant Force Work done by forces that oppose the direction of motion such as friction will be negative ltl Moon Copyright 2005 Pearson Prentice Hall Inc Centripetal forces do no work as they are always perpendicular to the direction of motion 62 Work Done by a Varying Force For a force that varies the work can be approximated by dividing the distance up into small pieces finding the work done during each and adding them up As the pieces become very narrow the work done is the area under the force vs distance curve dA dB Distance d Distance d Definition of Energy Energy is a really important concept but its hard to write a simple precise definition of it Instead we will examine different types of energy and see how they relate The traditional definition of energy is as the ability to do work 63 Kinetic Energy and the WorkEnergy Principle Energy was traditionally defined as the ability to do work We now know that not all forces are able to do work however we are dealing in these chapters with mechanical energy which does follow this definition 63 Kinetic Energy and the WorkEnergy Principle If we write the acceleration in terms of the velocity and the distance we find that the work done here is 1 l Wnet Emvg inf 6392 We define the kinetic energy 63 Copyright 2005 Pearson Prentice Hall Inc 63 Kinetic Energy and the WorkEnergy Principle This means that the work done is equal to the change in the kinetic energy 64 If the net work is positive the kinetic energy increases If the net work is negative the kinetic energy decreases 63 Kinetic Energy and the WorkEnergy Principle Because work and kinetic energy can be equated they must have the same units kinetic energy is measured in joules 3 JL a on hammer on nail lt K 64 Potential Energy An object can have potential energy by virtue of its surroundings Familiar examples of potential energy A woundup spring A stretched elastic band An object at some height above the ground 64 Potential Energy yz quot l1 In raising a mass m to a height exerted h the work done by the by hand external force Is gt h Wext Fextd cos 039D mgh F a mgy2 y1 m G g 65a y1 Lu quotl We therefore define the Copyright 2005 Pearson Prentice Halnc 66 64 Potential Energy This potential energy can become kinetic energy if the object is dropped Potential energy is a property of a system as a whole not just of the object because it depends on external forces quot where do we measure yfrom It turns out not to matter as long as we are consistent about where we choose y 0 Only changes in potential energy can be measured 64 Potential Energy Potential energy can also be stored in a spring when it is compressed the figure below shows potential energy yielding kinetic energy b Copyright 2005 Pearson Prentice Hall Inc 64 Potential Energy The force required to 39 x0 compress or stretch a VWWWV l spring is a 15 S kx 68 x where k is called the FF spring constant and needs to be measured for each spring 3 Hooke s Law F12 0 Copyright 2005 Pearson Prentice Hall Inc 64 Potential Energy The force increases as the spring is stretched or compressed further We find that the potential energy of the compressed or stretched spring measured from its equilibrium position can be written 69 Copyright 2005 Peamon Prentice Hali inc Conservative Forces When the work done does not depend on the path taken but only on the start and end points we say that a force is conservative Example is gravity Work done is same for direct lift as any other path between the same heights Same Height h 65 Conservative and Nonconservative Forces If friction is present the work done depends not only on the starting and ending points but also on the path taken Friction is called a nonconservative force Copyright 2005 Pearson Prentice Hall Inc Recap Work W Fd c056 Kinetic energy KE md Doing work on an object changes its KE Wm AKE Potential stored energy PEgrav quot18y elastic PE ch 65 Conservative and Nonconservative Forces TABLE 6 1 Conservative POtential energy can and Nonconservative Forces only be defined for Conservative Nonconservative conservatlve forces Forces Forces Gravitational Friction Elastic Air resistance Electric Tension in cord Motor or rocket propulsion Push or pull by a person Copyright 2005 Pearson Prentice Hall Inc 65 Conservative and Nonconservative Forces Therefore we distinguish between the work done by conservative forces and the work done by nonconservative forces We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies 610 66 Mechanical Energy and Its Conservation If there are no nonconservative forces the sum of the changes in the kinetic energy and in the potential energy is zero the kinetic and potential energy changes are equal but opposite in sign This allows us to define the total mechanical energy E KE PE And its conservation 612b 67 Problem Solving Using Conservation of Mechanical Energy all PE y1h In the image on the left the total I H mechanical energy is l39 3212 E K13 PE W my Hllll Ty VZO yzmeEl 420 Ill l The energy buckets right V 63mS y 10 show how the energy H H l moves from all potential to V 77mS y o Ty all kinetic Copyright 2005 P eeee on Prentice Hall Inc 67 Problem Solving Using Conservation of Mechanical Energy If there is no friction the speed of a roller coaster will depend only on its height compared to its starting height 9 94949494 9 949 949 94949494 4 4 Copyright 2005 Pearson Prentice Hall Incl Prb gm Mgmamm Emgsn gy Fm am elastic forceg m3 m ti m f mrgy fzea g MES 1 2 1 2 jm vl 3106 msv2 kx 614 Copyright 2005 Pearson Pfentice Hall Inc Worked Example A block mass m falls from a height h on top of a spring of spring constant k natural length I By how much is the spring compressed 68 Other Forms of Energy Energy Transformations and the Conservation of Energy Some other forms of energy Electric energy nuclear energy thermal energy chemical energy Work is done when energy is transferred from one object to another Accounting for all forms of energy we find that the total energy neither increases nor decreases Energy as a whole is conserved 69 Energy Conservation with Dissipative Processes Solving Problems If there is a nonconservative force such as friction where do the kinetic and potential energies go They become heat the actual temperature rise of the materials involved can be calculated 69 Energy Conservation with Dissipative Processes Solving Problems Problem Solving 1 Draw a picture 2 Determine the system for which energy will be conserved 3 Figure out what you are looking for and decide on the initial and final positions 4 Choose a logical reference frame 5 Apply conservation of energy 6 Solve 610 Power Power is the rate at which work is done work energy transfom39leci P average power time time 617 In the SI system the units of power are watts 1 W 1 Js K I I The difference between walking L 39 and running up these stairs is V I power the change in quot gravitational potential energy is I the same 610 Power Power is also needed for acceleration and for moving against the force of gravity The average power can be written in terms of the force and the average velocity 617 Copyright 2005 Pearson Prentice Hailv inc Summary of Chapter 6 Work W Fd c056 1 2 KInetIc energy Is energy of motIon KE 2m Potential energy is energy associated with forces that depend on the position or configuration of objects The net work done on an object equals the change in its kinetic energy If only conservative forces are acting mechanical energy is conserved Power is the rate at which work is done
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