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Work and Energy Physics 100 Chapt 5

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Physicists definition of work dist Work = F x dist A scalar (not a vector) dist

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Atlas holds up the Earth But he doesnt move, dist = 0 Work= F x dist = 0 He doesnt do any work!

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Garcon does work when he picks up the tray but not while he carries it around the room dist is not zero, but dist is 0

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Why this definition? Newtons 2 nd law: F=m a Definition of work + a little calculus Work= change in ½mv 2 A scalar equation A vector equation This scalar quantity is given a special name: kinetic energy

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Work = change in KE This is called: the Work-Energy Theorem

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Units again… Kinetic Energy = ½mv 2 kg m2s2m2s2 work = F x dist Nm=kg ms2ms2 m =1Joule same!

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Work done by gravity start end dist W=mg Work = F x dist = - mg x change in height = - change in mg h change in vertical height

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Gravitational Potential Energy Work grav = -change in mgh This is called: Gravitational Potential Energy (or PE grav ) Work grav = -change in PE grav change in PE grav = -Work grav

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If gravity is the only force doing work…. -change in mgh = change in ½ mv 2 0 = change in mgh + change in ½ mv 2 change in (mgh + ½ mv 2 ) = 0 mgh + ½ mv 2 = constant Work-energy theorem:

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Conservation of energy mgh + ½ mv 2 = constant Gravitational Potential energy Kinetic energy If gravity is the only force that does work: PE + KE = constant Energy is conserved

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Free fall (reminder) V 0 = 0 t = 0s V 1 = 10m/s t = 1s V 2 = 20m/s t = 2s V 3 = 30m/s t = 3s V 4 = 40m/s t = 4s 75m 60m 35m 0m height 80m

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m=1kg free falls from 80m V 0 = 0 h 0 =80m t = 0s V 1 = 10m/s; h 1 =75m t = 1s V 2 = 20m/s; h 2 =60m 600J 200J 800J t = 2s V 3 = 30m/s; h 3 =35m 350J 450J 800J t = 3s V 4 = 40m/s; h 4 = J 800J t = 4s mgh ½ mv 2 sum 800J 0 800J 750J 50J 800J

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pendulum W=mg T Two forces: T and W T is always to the motion (& does no work)

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Pendulum conserves energy h max E=mgh max E=1/2 m(v max ) 2

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Roller coaster

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Work done by a spring Relaxed Position F=0 F x I compress the spring (I do + work; spring does -work) Work done by spring = - change in ½ kx 2

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Spring Potential Energy Work spring = -change in ½ kx 2 This is the: Springs Potential Energy (or PE spring ) Work spring = -change in PE spring change in PE spring = - Work spring

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If spring is the only force doing work…. -change in ½ kx 2 = change in ½ mv 2 0 = change in ½ kx 2 + change in ½ mv 2 change in ( ½ kx 2 + ½ mv 2 ) = 0 ½ kx 2 + ½ mv 2 = constant Work-energy theorem:

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Conservation of energy springs & gravity mgh + ½ kx 2 + ½ mv 2 = constant Gravitational potential energy Kinetic energy If elastic force & gravity are the only force doing work: PE grav + PE spring + KE = constant Energy is conserved spring potential energy

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example KineticE Spring PE grav PE

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Two types of forces: Conservative forces forces that do + & – work Gravity Elastic (springs, etc) Electrical forces … Dissipative forces forces that only do – work Friction Viscosity …. -work change in PE -work heat (no potential energy.)

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(-)Work done by friction heat

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Thermal atomic motion Heat energy = KE and PE associated with the random thermal motion of atoms Airsolid

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Work-energy theorem (all forces) Work fric = change in (PE+KE) Work done dissipative Forces (always -) Kinetic energy -Work fric = change in heat energy potential energy From all Conservative forces - change in Heat Energy = change in (PE+KE) Work fric = -change in heat energy

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Work – Energy Theorem (all forces) 0 = change in Heat Energy + change in (PE+KE) 0 = change in ( Heat Energy +PE+KE) Heat Energy + PE + KE = constant Law of Conservation of Energy

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Energy conversion while skiing Friction: energy gets converted to heat Potential energy Potential energy kinetic energy

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Units again Heat units: 1 calorie = heat energy required to raise the temp of 1 gram of H 2 O by 1 o C 1 calorie= 4.18 Joules Kg m 2 /s 2

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Food Calories 1 Calorie = 1000 calories = 1Kcalorie 1 Calorie= 4.18x10 3 Joules The Calories you read on food labels 8 x 10 5 J 7 x 10 6 J 2 x 10 6 J

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Power Rate of using energy: amout of energy elapsed time Units: Joule second 1= 1 Watt Power = A 100 W light bulb consumes 100 J of electrical energy each second to produce light

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Other units Over a full day, a work-horse can have an average work output of more than 750 Joules each second 1 Horsepower = 750 Watts

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Kilowatt hours energy time Power = energy = power x time power unit x time unit = energy unit Elec companies use: Kilowatts (10 3 W) hours (3600 s ) 1 kilowatt-hour = 1kW-hr = 10 3 W x 3.6x10 3 s = 3.6x10 6 WsJ HECO charges us about 15 cents /kW-hr x

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