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Work and Energy
Physics 100 Chapt 5
Physicist’s definition of “work”
dist∥
dist
Work = F
x
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 when
he picks up the tray
but not while he
carries 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
This scalar quantity is given
a special name: kinetic energy
Work = change in KE
This is called:
the Work-Energy Theorem
Units again…
Kinetic Energy = ½mv2
work = F x dist∥
2
m
kg 2
s
same!
m
N m =kg 2 m
s
=1Joule
Work done by gravity
end
start
dist
dist∥
change in
vertical height
W=mg
Work = F
=
x
dist∥
-mg x change in height
= -change in mg h
Gravitational Potential Energy
Workgrav = -change in mgh
This is called:
“Gravitational Potential
Energy” (or PEgrav)
change
Workgrav
in =
PE-change
in PE
grav = -Work
grav
grav
If gravity is the only force
doing work….
Work-energy theorem:
-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
Conservation of energy
mgh + ½ mv2 = constant
Gravitational
Potential energy
Kinetic energy
If gravity is the only force that does work:
PE + KE = constant
Energy is conserved
Free fall
(reminder)
height
t = 0s
V0 = 0
t = 1s
80m
75m
V1 = 10m/s
60m
t = 2s
V2 = 20m/s
t = 3s
35m
V3 = 30m/s
t = 4s
V4 = 40m/s
0m
m=1kg free falls from 80m
t = 0s
V0 = 0 h0=80m
mgh
800J
½ mv2
sum
0
800J
50J
800J
t = 1s
V1 = 10m/s; h1=75m
750J
t = 2s
V2 = 20m/s; h2=60m
600J
200J
800J
350J
450J
800J
t = 3s
V3 = 30m/s; h3=35m
t = 4s
V4 = 40m/s; h4=0
0
800J
800J
pendulum
T
W=mg
Two forces: T and W
T is always
to the motion
(& does no work)
┴
Pendulum conserves energy
E=mghmax
E=mghmax
hmax
E=1/2 m(vmax)2
Roller coaster
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 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 = -
If spring is the only force doing
work….
Work-energy theorem:
-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
Conservation of energy
springs & gravity
mgh + ½ kx2 + ½ mv2 = constant
Gravitational
spring
potential energy potential energy
Kinetic energy
If elastic force & gravity are the only force doing work:
PEgrav + PEspring + KE = constant
Energy is conserved
example
grav PE
KineticE
Spring PE
Two types of forces:
“Conservative”
forces
forces that do + & – work
“Dissipative”
•Gravity
•Friction
•Elastic (springs, etc)
•Viscosity
•Electrical forces
•….
•…
-work  heat
-work 
change in PE
forces
forces that only do – work
(no potential energy.)
(-)Work done by frictionheat
Thermal atomic motion
Air
solid
Heat energy= KE and PE associated with
the random thermal motion of atoms
Work-energy theorem
(all forces)
Workfric =
Work done
dissipative
Forces
(always -)
change in
(PE+KE)
potential energy
From all
Conservative forces
Kinetic
energy
-Work
change in
in heat
heat energy
energy
Work
-change
fric = =
fric
-change
=
(PE+KE)
in Heat Energy
change in
Work – Energy Theorem
(all forces)
0 =
change in
0 =
+
(PE+KE)
change in Heat Energy
change in
Heat Energy
(Heat
Energy+PE+KE)
+ PE + KE = constant
Law of Conservation of Energy
Energy conversion while skiing
Potential energy
Potential energykinetic energy
Friction: energy gets
converted to heat
Units again
Heat units:
1 calorie = heat energy required to raise the
temp of 1 gram of H2O by 1o C
Kg m2/s2
1 calorie= 4.18 Joules
Food Calories
1 Calorie = 1000 calories = 1Kcalorie
The Calories you read on food labels
1 Calorie= 4.18x103 Joules
7 x 106 J
8 x 105 J
2 x 106 J
Power
Rate of using energy:
Units:
Joule
1 second
amout of energy
Power = elapsed time
= 1 Watt
A 100 W light bulb
consumes 100 J of
electrical energy each
second 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
energy
Power = time
 energy = power
 power unit
Elec companies use:
x
Kilowatts
(103 W)
x
time
time unit = energy unit
x
hours
(3600 s)
1 kilowatt-hour = 1kW-hr
= 103 W x 3.6x103 s = 3.6x106 Ws
J
HECO charges us about 15 cents /kW-hr