Work and Energy
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Transcript of Work and Energy
![Page 1: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/1.jpg)
Work and Energy
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Physicist’s definition of “work”
dist
Work = F x dist∥
A scalar
(not a vector)
dist∥
![Page 3: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/3.jpg)
Atlas holds up the EarthBut he doesn’t move, dist∥ = 0
Work= Fx dist∥ = 0
He doesn’t do any work!
![Page 4: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/4.jpg)
Garcon does work whenhe picks up the tray
but not while hecarries it around
the room
dist is not zero,but dist∥ is 0
![Page 5: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/5.jpg)
Why this definition?
Newton’s 2nd law: F=m aDefinition of work+ a little calculus
Work= change in ½mv2
A scalarequation
A vector
equation
This scalar quantity is givena special name: kinetic energy
![Page 6: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/6.jpg)
Work = change in KE
This is called:
the Work-Energy Theorem
![Page 7: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/7.jpg)
Units again…
Kinetic Energy = ½mv2
kg
m2
s2work = F x dist∥
N m =kg
ms2 m
=1Joulesame!
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Work done by gravity
start
end
dist dist∥
W=mgWork = F x dist∥
= -mg x change in height= -change in mg h
change in vertical height
![Page 9: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/9.jpg)
Gravitational Potential Energy
Workgrav = -change in mgh
This is called:“Gravitational Potential Energy” (or PEgrav)
Workgrav = -change in PEgravchange in PEgrav = -Workgrav
![Page 10: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/10.jpg)
If gravity is the only force doing work….
-change in mgh = change in ½ mv2
0 = change in mgh + change in ½ mv2
change in (mgh + ½ mv2) = 0
mgh + ½ mv2 = constant
Work-energy theorem:
![Page 11: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/11.jpg)
Conservation of energy
mgh + ½ mv2 = constantGravitational
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)
V0 = 0t = 0s
V1 = 10m/s
t = 1s
V2 = 20m/s
t = 2s
V3 = 30m/s
t = 3s
V4 = 40m/s
t = 4s
75m
60m
35m
0m
height
80m
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m=1kg free falls from 80m
V0 = 0 h0=80m t = 0s
V1 = 10m/s; h1=75m
t = 1s
V2 = 20m/s; h2=60m 600J 200J 800J
t = 2s
V3 = 30m/s; h3=35m 350J 450J 800J
t = 3s
V4 = 40m/s; h4=0 0 800J 800J
t = 4s
mgh ½ mv2 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
hmax
E=mghmaxE=mghmax
E=1/2 m(vmax)2
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Roller coaster
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Work done by a springRelaxedPosition
F=0
F xI compressthe spring
(I do + work;spring does
-work)Work done by spring = - change in ½ kx2
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Spring Potential Energy
Workspring = -change in ½ kx2
This is the:“Spring’s Potential Energy” (or PEspring)
Workspring = -change in PEspring
change in PEspring = -Workspring
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If spring is the only force doing work….
-change in ½ kx2 = change in ½ mv2
0 = change in ½ kx2 + change in ½ mv2
change in ( ½ kx2 + ½ mv2) = 0
½ kx2 + ½ mv2 = constant
Work-energy theorem:
![Page 20: Work and Energy](https://reader036.fdocuments.in/reader036/viewer/2022062502/56813022550346895d95a389/html5/thumbnails/20.jpg)
Conservation of energysprings & gravity
mgh + ½ kx2 + ½ mv2 = constantGravitational
potential energyKinetic energy
If elastic force & gravity are the only force doing work: PEgrav + PEspring + KE = constant
Energy is conserved
springpotential energy
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Two types of forces:
“Conservative” forcesforces that do + & – work
•Gravity
•Elastic (springs, etc)
•Electrical forces
•…
“Dissipative” forcesforces that only do – work
•Friction
•Viscosity
•….
-work change in PE
-work heat(no potential energy.)
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(-)Work done by frictionheat
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Thermal atomic motion
Heat energy= KE and PE associated with the random thermal motion of atoms
Air solid
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Work-energy theorem(all forces)
Workfric = change in (PE+KE)Work done
dissipative
Forces(always -)
Kinetic energy
-Workfric = change in heat energy
potential energyFrom all
Conservative forces
-change in Heat Energy = change in (PE+KE)
Workfric = -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 energykinetic energy
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Units againHeat units:1 calorie = heat energy required to raise the temp of 1 gram of H2O by 1o C
1 calorie= 4.18 JoulesKg m2/s2
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Food Calories1 Calorie = 1000 calories = 1Kcalorie
1 Calorie= 4.18x103 JoulesThe Calories you read on food labels
8 x 105 J
7 x 106 J
2 x 106 J
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Power
Rate of using energy: amount of energyelapsed time
Units: Joulesecond 1 = 1
Watt
Power =
A 100 W light bulbconsumes 100 J of
electrical energy eachsecond 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
energytimePower = energy = power x time
power unit x time unit = energy unit
Elec companies use:Kilowatts(103 W)
hours(3600 s)
1 kilowatt-hour = 1kW-hr
= 103 W x 3.6x103 s = 3.6x106 WsJ
x