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Work and Energy
Physics 100 Chapt 5
Physicist’s definition of “work”
dist
Work = F x dist∥
A scalar
(not a vector)
dist∥
Atlas holds up the Earth
But he doesn’t move, dist∥ = 0
Work= Fx dist∥ = 0
He doesn’t do any work!
Garcon does work whenhe picks up the tray
but not while hecarries it around
the room
dist is not zero,but dist∥ is 0
Why this definition?
Newton’s 2nd law: F=m a
Definition of work+ a little calculus
Work= change in ½mv2
A scalar
equation
A vector
equation
This scalar quantity is givena special name: kinetic energy
Work = change in KE
This is called:
the Work-Energy Theorem
Units again…
Kinetic Energy = ½mv2
kg
m2
s2
work = F x dist∥
N m =kg
ms2
m=1Joule
same!
Work done by gravity
start
end
dist dist∥
W=mg
Work = F x dist∥
= -mg x change in height
= -change in mg h
change in vertical height
Gravitational Potential Energy
Workgrav = -change in mgh
This is called:“Gravitational Potential Energy” (or PEgrav)
Workgrav = -change in PEgravchange in PEgrav = -Workgrav
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:
Conservation of energy
mgh + ½ mv2 = constant
GravitationalPotential energy
Kinetic energy
If gravity is the only force that does work:
PE + KE = constant
Energy is conserved
Free fall (reminder)
V0 = 0
t = 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
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
pendulum
W=mg
T
Two forces: T and W
T is always ┴ to the motion
(& does no work)
Pendulum conserves energy
hmax
E=mghmaxE=mghmax
E=1/2 m(vmax)2
Roller coaster
Work done by a spring
RelaxedPosition
F=0
Fx
I compressthe spring
(I do + work;spring does
-work)
Work done by spring = - change in ½ kx2
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
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:
Conservation of energysprings & gravity
mgh + ½ kx2 + ½ mv2 = constant
Gravitationalpotential energy
Kinetic energy
If elastic force & gravity are the only force doing work:
PEgrav + PEspring + KE = constant
Energy is conserved
springpotential energy
example
KineticE
Spring PE
grav PE
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.)
(-)Work done by frictionheat
Thermal atomic motion
Heat energy= KE and PE associated with the random thermal motion of atoms
Air solid
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
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
Energy conversion while skiing
Friction: energy gets converted to heat
Potential energy
Potential energykinetic energy
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
Food Calories
1 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
Power
Rate of using energy:amout of energy
elapsed time
Units:Joule
second 1 = 1 Watt
Power =
A 100 W light bulbconsumes 100 J of
electrical energy eachsecond to produce light
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
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
HECO charges us about 15 cents /kW-hr
x