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# 428 Class Note for PHYS 250 at PSU

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This 33 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 20 views.

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Date Created: 02/06/15

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 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 Copyright 2005 Pearson Prentice Hall Inc Work Done by a Constant Force In the SI system the units of work are joules 1J 1N m No work on it Why Copyright 2005 Pearson Prentice Hall Inc Work Done by a Constant Force Solving work problems 1 Draw a freebody diagram coordinate system 2 Apply Newton s laws to determine any unknown forces 3 To find the net work either find the net force and then find the work it does or find the work done by each force and add Cagculate the work done C Copyright 2005 Pearson Prentice Hall Inc Work Done by a Constant Force Work done by forces that oppose the direction of motion such as friction will be negative lt1 Moon quot Copyright 2005 Pearson Prentice Hali Inc Centripetal forces do no work as they are always perpendicular to the direction of motion 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 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 l 1 W Fmvg mv2 62 net 2 2 2 1 We define the kinetic energy 63 Copyright 2005 Pearson Prentice Hall Inc 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 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 a it on hammer on nail lt K 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 Potential Energy In raising a mass m to a height h the work done by the E 5391 5 3L 0 O on CD 0 H m gh mgy2 yl 65a y1v I I We therefore define the Copyright 2005 Pearson Prentice Halllnc 66 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 I 3 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 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 Potential Energy The force required to x0 compress or stretch a I sp ngis 39 Fs kx 68 x where k is called the 17 1 spring constant and needs to be measured for each spring Copyright 2005 Pearson Prentice Hall Inc 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 d A dB Distance d Distance d 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 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 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 Conservative and Nonconservative Forces Therefore we distinguish between the work done by conservative forces and the work done by nonconservative forces 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 Energy Conservation Example 1 A 10 m g 0 DGDQD494949494D494D4D4gt4gt4gt4 Qk T 1 DQDQDGDQDQDQDQDQDQDQDQDQDQDQDQ NNNNMNNMNMNNMMNN lsnl DQDQDQDQDGDQDQDQDGDQDQDQDQDQD4DQDltD DQDGDQDQDQDQDQDGDQDQDQDGDQDQDQDGD4 ltgt DGDQDQDGDQDQDGDGDGDQDQDGDQDQDQDGDQDGD DGDQDQDGDGDGDQDQDGDQDQDQDGDQDGDQDGDQDQ QDQD D4 4 DGDQDQDQDQDQDQDGDQDQDQDGDQDQDQDQDQDQDQDQDQD Copyrlght 2005 Pearson Prentice Ha Inc D b Energy Conservation Example T 39I Y b C Copyright 2005 Pearson Prentice Hall lnc y0 Energy Conservation Example HW prob Copyright 2005 Pearson Prentice Hall Inc 351 Prb m Saving Ug mg WWf im 031 Mmhamma Ewarng Fm am elastic forceg mwati m mgnqu tcg g Mg r l mvi k mvg gkxg 614 Copyright 2005 Pearson Prentice HaH Inc 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 transformeci P average power trme tune 617 In the SI system the units of power are watts 1W llJs The difference between walking quot and running up these stairs is power the change in gravitational potential energy is l 1 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 Hall Inca

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