1. Work and Energy

2. Physicist’s definition of “work”
dist∥
A scalar
(not a vector)
dist
Work = F x dist∥

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. This scalar quantity is given a special name: kinetic energy
Why this definition?
A vector
equation
Newton’s 2nd law: F=m a
Definition of work
+ a little calculus
A scalar
equation
Work= change in ½mv2
This scalar quantity is given
a special name: kinetic energy

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

7. Units again… Kinetic Energy = ½mv2 m2 s2 kg work = F x dist∥ =1Joule m
same!
=1Joule m s2 N m
=kg m

8. change in vertical height
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

9. Gravitational Potential Energy
Workgrav = -change in mgh
This is called:
“Gravitational Potential
Energy” (or PEgrav)
change in PEgrav = -Workgrav
Workgrav = -change in PEgrav

10. 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

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) height t = 0s 80m V0 = 0 75m t = 1s V1 = 10m/s

13. m=1kg free falls from 80m mgh ½ mv2 sum t = 0s V0 = 0 h0=80m 800J 0
750J J
V1 = 10m/s; h1=75m
800J
t = 2s
V2 = 20m/s; h2=60m J J J
t = 3s
V3 = 30m/s; h3=35m J J J
t = 4s
V4 = 40m/s; h4= J J

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

15. Pendulum conserves energy
E=mghmax
E=mghmax
hmax
E=1/2 m(vmax)2

16. Roller coaster

17. Work done by spring = - change in ½ kx2
Work done by a spring
Relaxed
Position
F=0 x F
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 = -Workspring

19. 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

20. Conservation of energy springs & gravity
mgh + ½ kx2 + ½ mv2 = constant
Gravitational
potential energy
spring
potential energy
Kinetic energy
If elastic force & gravity are the only force doing work:
PEgrav + PEspring + KE = constant
Energy is conserved

21. example
grav PE
KineticE
Spring PE

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

23. (-)Work done by frictionheat

24. Thermal atomic motion Heat energy= KE and PE associated with Air solid
the random thermal motion of atoms

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

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
Potential energy
Potential energykinetic energy
Friction: energy gets
converted to heat

28. 1 calorie = heat energy required to raise the
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

29. 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

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

31. Other units 1 Horsepower = 750 Watts 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. HECO charges us about 15 cents /kW-hr
Kilowatt hours
energy
time
Power =
 energy = power x time
 power unit x time unit = energy unit
Kilowatts
(103 W)
hours
(3600 s)
Elec companies use: x
1 kilowatt-hour = 1kW-hr
= 103 W x 3.6x103 s = 3.6x106 Ws J
HECO charges us about 15 cents /kW-hr