3. Atlas holds up the Earth
But he doesn’t move,
dist∥ = 0
Work= Fx dist∥ = 0
He doesn’t do any work!
4. 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
5. 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
6. Work = change in KE
This is called:
the Work-Energy Theorem
8. 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
9. Gravitational Potential Energy
Workgrav = -change in mgh
This is called:
“Gravitational Potential
Energy” (or PEgrav)
Workgrav = -change in PEgrav
change in PEgrav = -Workgrav
10. 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:
11. 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
12. 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
13. 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
17. 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
18. Spring Potential Energy
Workspring = -change in ½ kx2
This is the:
“Spring’s Potential
Energy” (or PEspring)
Workspring = -change in PEspring
change in PEspring = -
19. 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:
20. Conservation of energy
springs & gravity
mgh + ½ kx2 + ½ mv2 = constant
Gravitational
potential energy
Kinetic energy
If elastic force & gravity are the only force doing work:
PEgrav + PEspring + KE = constant
Energy is conserved
spring
potential energy
22. 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.)
24. Thermal atomic motion
Heat energy= KE and PE associated with
the random thermal motion of atoms
Air solid
25. Work-energy theorem
(all forces)
Workfric = change in (PE+KE)
Work done
dissipative
Forces
(always -)
Kinetic
energy
-Workfric = change in heat energy
potential energy
From all
Conservative forces
-change in Heat Energy =
change in (PE+KE)
Workfric = -change in heat energy
26. 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
27. Energy conversion while skiing
Friction: energy gets
converted to heat
Potential energy
Potential energykinetic energy
28. Units again
Heat units:
1 calorie = heat energy required to raise the
temp of 1 gram of H2O by 1o C
1 calorie= 4.18 Joules
Kg m2/s2
29. Food Calories
1 Calorie = 1000 calories = 1Kcalorie
1 Calorie= 4.18x103 Joules
The Calories you read on food labels
8 x 105 J
7 x 106 J
2 x 106 J
30. 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
31. 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
32. Kilowatt hours
energy
time
Power = 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 Ws
J
HECO charges us about 15 cents /kW-hr
x
