Download Color - How Things Work

Falling Balls 1
Falling Balls 2
Observations about Skating

Skating
When you’re at rest on a level surface,
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without a push, you remain stationary
with a push, you start moving that direction
Wh you’re
When
’ moving
i on a level
l l surface,
f


without a push, you coast steady & straight
with a push, you change direction or speed
Turn off all electronic devices
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4 Questions about Skating

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
Why does a stationary skater remain stationary?
Why does a moving skater continue moving?
Why does a skater need ice or wheels to skate?
How does a skater start or stop moving?
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Question 1
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Physics Concept

Inertia (just the first part)

Why does a stationary skater remain stationary?
Question 2

Why does a moving skater continue moving?
A body at rest tends to remain at rest
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Physics Concept

Inertia (the whole thing)
A body at rest tends to remain at rest
 A body in motion tends to remain in motion
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Newton’s First Law (Version 1)
An object that is free of external influences moves
in a straight line and covers equal distances in
equal times.
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Question 3

Why does a skater need ice or wheels to skate?
Keeping It Simple
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Real-world complications mask simple physics
RealSolution: minimize or overwhelm complications
To demonstrate inertia:
work on level ground (minimize gravity’s effects)
use wheels, ice, or air support (minimize friction)
 work fast (overwhelm friction and air resistance)
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Physical Quantities

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Position – an object’s location
Velocity – its change in position with time
Velocity = speed plus direction of travel
Newton’s First Law (Version 2)
An object that is free of external influences moves
at a constant velocity.
I
Important
t t Note:
N t zero velocity
l it is
i a constant
t t velocity,
velocity
l it , so a
motionless object is moving at a constant velocity
2
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Physical Quantities

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Position – an object’s location
Velocity – its change in position with time
Force – a push or a pull
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Newton’s First Law
An object that is not subject to any outside forces
moves at a constant velocity.
Falling Balls 16
Question 4

How does a skater start or stop moving?
Physical Quantities
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Position – an object’s location
Velocity – change in position with time
Force – a push or a pull
Acceleration – change in velocity with time
Mass – measure of object’s inertia
Falling Balls 18
Newton’s Second Law
An object’s acceleration is equal to the net force
exert on it divided by its mass. That acceleration is
in the same direction as the net force.
acceleration 
About Units

Position – m (meters)
Velocity – m/s (meters
(meters--perper-second)
 Acceleration
A l r ti n – m/s
m/ 2 (meters
(
(meters-perper-secondd2)
 Force – N (newtons)
 Mass – kg (kilograms)


net force
mass
net force = mass  acceleration
SI or “metric” units:

Newton’s second law relates the units:
1 N (net force)
1 m/s 2 (acceleration) 
1 kg (mass)
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Summary about Skating

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Skates can free you from external forces
When you experience no external forces,
Falling Balls
You coast – you move at constant velocity
 If you’re
’ at rest, you remain
i at rest
 If you’re moving, you move steadily and straight

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When you experience external forces

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You accelerate – you move at a changing velocity
Acceleration depends on force and mass
Turn off all electronic devices
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Observations about Falling Balls

When you drop a ball, it
begins at rest, but acquires downward speed
 covers more and more distance each second

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Wh you tossed
When
dab
ballll straight
i h up, iit
rises to a certain height
 comes momentarily to a stop
 and then descends, much like a dropped ball
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5 Questions about Falling Balls
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A thrown ball travels in an arc
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Question 1

Why does a dropped ball fall downward?
Do different balls fall at different rates?
Would a ball fall differently on the moon?
Can a ball move upward and still be falling?
Does a ball’s horizontal motion affect its fall?
Why does a dropped ball fall downward?
Gravity and Weight
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Earth’s gravity exerts a force on the ball
That force is called the ball’s weight
The ball’s weight points toward earth’s center
A dropped ball’s weight causes it to accelerate
toward earth’s center (i.e., downward)
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Question 2

Do different balls fall at different rates?
Weight and Mass
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A ball’s weight is proportional to its mass
weight of ball
 constant
mass of ball
That constant
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is same for all balls (and other objects)!
is
newtons
9.8
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Why this strange name?
weight of ball
force

 acceleration
mass of ball
mass
Acceleration due to gravity is an acceleration!
newtons
meters
9.8
 9.8
 9.8 m/s2
kilogram
second 2
On earth’s surface, all falling balls accelerate
downward at 9.8 meter/second2
Falling Balls 29
Question 3
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Would a ball fall differently on the moon?
Answer: Yes!
Moon’s acceleration due to gravity is different!
Falling Balls 30
Question 4
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 9.8 N/kg
at earth’s surface
is called “acceleration due to gravity”
Acceleration Due to Gravity

kilogram
Can a ball move upward and still be falling?
A Falling Ball (Part 1)

A falling ball accelerates downward steadily
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Its acceleration is constant and downward
Its velocity increases in the downward direction
Wh ffalling
When
lli ffrom rest (stationary),
( i
) its
i
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velocity starts at zero and increases downward
altitude decreases at an ever faster rate
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Falling Downward
A Falling Ball (Part 2)
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A falling ball can start by heading upward!
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Its velocity starts in the upward direction
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Its velocity is momentarily zero
Its velocity continues in the downward direction
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Question 5
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Does a ball’s horizontal motion affect its fall?
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Throws and Arcs
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Its velocity becomes more and more downward
Its altitude decreases at ever faster rate
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Falling Upward First

Its velocity becomes less and less upward
Its altitude increases at an ever slower rate
Gravity only affects only
the ball’s vertical motion
The ball’s acceleration is
downward and constant
The ball coasts horizontally
while falling vertically
The ball’s overall path is a
parabolic arc
Summary About Falling Balls
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Without gravity, a free ball would coast
With gravity, an otherwise free ball
experiences its weight,
accelerates
l
d
downward,
d
 and its velocity becomes increasingly downward
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Whether going up or down, it’s still falling
Its horizontal coasting motion is independent of
its vertical falling motion
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Observations About Ramps
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Ramps
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It’s difficult to lift a heavy cart straight up
It’s easer to push a heavy cart up a ramp
That ease depends on the ramp’s steepness
Shallow ramps need gentler but longer pushes
Turn off all electronic devices
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5 Questions about Ramps
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Why doesn’t a cart fall through a sidewalk?
How does the sidewalk know how hard to push?
Why doesn’t a cart fall through a ramp?
Why is it easy to push the cart up the ramp?
What physical quantity is the same for any trip
up the ramp, regardless of its steepness?
Falling Balls 41
Question 1
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Why doesn’t a cart fall through a sidewalk?
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Support Forces
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On the sidewalk, the cart experiences two forces:
Adding up the Forces

(1) Its downward weight (from the earth)
 (2) An upward support force (from the sidewalk)
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Th support fforce
That
is exerted by sidewalk on cart
 acts perpendicular to sidewalk’s surface (i.e., upward)
 opposes cart’s downward weight
 prevents cart from penetrating the sidewalk’s surface
Since the cart isn’t accelerating,
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Thi balance
This
b l
only
l affects
ff
vertical
i l motion
i
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the sum of forces (the net force) on the cart is zero
so sidewalk’s support force balances cart’s weight!
The vertical component of net force on cart is zero
The horizontal component of net force can vary
The cart can still move or accelerate horizontally
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Question 2
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How does the sidewalk know how hard to push?
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
For every force that one object exerts on a second
object, there is an equal but oppositely directed force
that the second object exerts on the first object.
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Misconception Alert

Newton’s Third Law
While the forces two objects exert on one
another must be equal and opposite, the net
force on each individual object can be anything.
Each force within an equal
equal--but
but--opposite pair is
exerted on a different object, so they never
cancel directly.
The Cart and Sidewalk Negotiate
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If cart is not accelerating, it’s in equilibrium
the sidewalk pushes upward on the cart
the cart pushes downward on the sidewalk
The two objects
Th
bj
dent
d one another
h slightly
li h l
The more they’re dented, the harder they push
Cart moves up and down until it comes to rest
Cart is then in equilibrium (zero net force)
Falling Balls 48
The Cart and Sidewalk Negotiate

When the cart and sidewalk touch,
Question 3

Why doesn’t a cart fall through a ramp?
sidewalk’s support force on cart balances cart’s weight
 cart’s support force on sidewalk equals cart’s weight

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If cart is
i accelerating,
l i it’s
i ’ not in
i equilibrium
ilib i
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the two forces on the cart don’t balance
cart’s support force on sidewalk is not cart’s weight
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Forces on a Cart on a Ramp (Part 1)

Forces on a Cart on a Ramp (Part 2)
When the cart rests on the ramp’s surface,
support force
the ramp’s support force prevents the cart from
accelerating toward the ramp’s surface.
 cart
cart’ss weight prevents cart from accelerating away
from the ramp’s surface.
 so cart can only accelerate along the ramp’s surface
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Support force is perpendicular to ramp’s surface
and therefore doesn’t point directly upward,
so cart experiences a net force: a ramp force
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ramp force
f
(sum)
(
)
weight

Ramp force causes cart to accelerate downhill
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Question 4
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Why is it easy to push the cart up the ramp?
Balanced Cart on Ramp

If you balance the ramp force,
the net force on the cart will be zero,
so the cart won’t accelerate,
 and
nd it will
ill coastt uphill
phill orr downhill
d nhill orr remain
r m in att rest
r t
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The more gradual the ramp,
the more nearly its weight and the support balance,
the smaller the ramp force on the cart,
 and the easier it is to balance the ramp force!
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Question 5
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What physical quantity is the same for any trip
up the ramp, regardless of its steepness?
Energy and Work
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Energy – a conserved quantity
it can’t be created or destroyed
it can be transformed or transferred between objects
 is
i th
the capacity
p it to
t do
d work
rk
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Work – mechanical means of transferring energy
work = force · distance
(where force and distance in same direction)
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Work Lifting a Cart
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Going straight up: Force is large, Distance is small
Mechanical Advantage
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work = Force · Distance

Going up ramp: Force
F
is small
small, Distance is large

A ramp provides mechanical advantage
You can raise a heavy cart with a modest force,
but you must push that cart a long distance.
 Your work is independent of the ramp’s steepness

The work is the same, either way!
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Doing the same amount of work, but
altering the balance between force and distance
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work = Force · Distance
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Mechanical advantage:
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The Transfer of Energy
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Energy has two principal forms
Kinetic energy – energy of motion
 Potential energy – energy stored in forces

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Y
Your
workk transfers
f energy from
f
you to the
h cart
You do work on the cart
 Your chemical potential energy decreases
 The cart’s gravitational potential energy increases

Falling Balls 59
Summary about Ramps
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Ramp supports most of the cart’s weight
You can easily balance the ramp force
You do work pushing the cart up the ramp
Your work is independent of ramp’s steepness
The ramp provides mechanical advantage
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It allows you to push less hard
but you must push for a longer distance
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Wind Turbines
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Observations about
Wind Turbines
Wind turbines are symmetrical and balanced
A balanced wind turbine rotates smoothly
An unbalanced turbine settles heavyheavy-side down
Most wind turbines have three blades
Wind turbines start or stop spinning gradually
Wind turbines extract energy from the wind
and convert it into electrical energy
Turn off all electronic devices
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5 Questions about Wind Turbines
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How does a balanced wind turbine move?
Why does the wind turbine need a pivot?
Why do wind turbines have two or three blades?
Why do giant turbines start and stop so slowly?
How does energy go from wind to generator?
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Question 1

How does a balanced wind turbine move?
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Physics Concept

Rotational Inertia
A body at rest tends to remain at rest
 A body that’s rotating tends to keep rotating

Falling Balls 65
Newton’s First Law
of Rotational Motion
A rigid object that’s not wobbling and that is free
of outside torques rotates at a constant angular
velocity.
Physical Quantities



Angular Position – an object’s orientation
Angular Velocity – change in angular position with time
Torque – a twist or spin
Falling Balls 66
Rotation and Direction

Angular position/velocity and torque are vectors
Each quantity has an amount and a direction
Quantity’s direction points along a rotational axis,
 toward
t
rd th
the end
nd specified
p ifi d b
by th
the right
ri
rightht-hand
h nd rrule.
rule
l .


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Balanced Wind Turbine

A balanced wind turbine in calm air
Question 2

Why does the wind turbine need a pivot?
experiences zero net torque
 has a constant angular velocity (which may be zero)


E
Examples
l off constant angular
l velocity:
l i
motionless and horizontal
motionless and tilted
 turning steadily in a specific direction


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Falling Balls 70
Center of Mass


A turbine’s center of mass is its natural pivot
An unsupported turbine
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

Question 3

Why do wind turbines have two or three blades?
pivots about its center of mass
while
hil iits center off mass falls
f ll
A turbine supported at its center of mass
can spin freely (rotational motion is permitted)
 but doesn’t fall (translational motion is forbidden)

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A One
One--Blade Turbine (Part 1)

A oneone-blade turbine’s angular velocity fluctuates
It doesn’t obey Newton’s first law.
 Since it is rigid and doesn’t wobble,
 it must
m t be
b experiencing
p ri n in outside
t id torques.
t rq


Those torques change turbine’s angular velocity
Physical Quantities
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Angular Position – an object’s orientation
Angular Velocity – change in angular position with time
Torque – a twist or spin
Angular Acceleration – change in angular velocity with time
Rotational Mass – measure of rotational inertia
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Falling Balls 73
Newton’s Second Law
of Rotational Motion
An object’s angular acceleration is equal to the net
torque exerted on it divided by its rotational mass.
The angular acceleration is in the same direction as
the torque
torque.
angular acceleration =
net torque
rotational mass
Falling Balls 74
A One
One--Blade Turbine (Part 2)
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

Blade’s weight produces a torque on the blade
Weight is a force
force,, not a torque
Blade’s weight effectively acts at center of gravity
a lever arm separates center of gravity from pivot,
 so blade’s weight produces a torque about the pivot.


That torque is largest when

net torque  rotational mass  angular acceleration
Falling Balls 75

the blade’s weight acts farthest from pivot
and it acts perpendicular to the lever arm.
Falling Balls 76
Forces and Torques

Forces and torques are related:
A force can produce a torque
 A torque can produce a force

Balancing the Turbine



Installing a second blade adds a second torque
Net torque is the sum of all torques on turbine
The two torques point in opposite directions

torque = lever arm · force
(where the lever arm is perpendicular to the force)


Turbine is balanced when
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
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Falling Balls 77
those torques sum to zero or, equivalently,
equivalently, when
turbine’s center of gravity is located at the pivot
Three--blade turbine’s center of gravity is at pivot
Three
Falling Balls 78
Question 4

Left blade torque is ccw (points toward you)
Right blade torque is cw (points away from you)
Why do giant turbines start and stop so slowly?
A Blade’s Wind Torque

Wind torque on a blade is proportional to



the wind’s force on the blade
the blade’s effective lever arm
D bli the
Doubling
h llength
h off the
h bl
blade
d
increases its wind force by a factor of 2
increases its effective lever arm by a factor of 2
 increases its wind torque by a factor of 4

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Falling Balls 80
A Blade’s Rotational Mass

Rotational mass of blade is proportional to
Turbine Size and Responsiveness

the blade’s mass
 the square of blade’s effective lever arm


D bli the
Doubling
h llength
h off a bl
blade
d



increases its mass by a factor of 2
 increases its lever arm by a factor of 2
 increases its rotational mass by a factor of 8!

Falling Balls 81
A wind turbine blade’s
wind torque increases in proportion to its length2
rotational mass increases in proportion to its length3
Th larger
The
l
the
h wind
i d turbine,
bi


the slower its angular accelerations
the longer it takes to start or stop turning
Falling Balls 82
Question 5

How does energy go from wind to generator?
Falling Balls 83
Rotational Work

Falling Balls 84
Rotational Work

Wind does translational work on a turbine blade:
Summary about Wind Turbines

wind exerts a force on the blade
 blade moves a distance in direction of that force
 so energy
n r m
moves fr
from
m wind
ind tto tturbine
rbin

Turbine does rotational work on a generator



turbine exerts a torque on generator
generator turns an angle in direction of that torque
 so energy moves from wind turbine to generator


Work – mechanical means of transferring energy
work = torque · angle
(where torque and angle in same direction)
Without air or generator, balanced wind turbine




experiences zero gravitational torque
rotates at constant angular velocity
Wi d fforces produce
Wind
d
torques on turbine’s
bi ’ blades
bl d
Generator exerts opposing torque on turbine
Wind turbine turns at constant angular velocity
Energy goes from wind to turbine to generator
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Falling Balls 86
Observations about Wheels

Wheels



Friction makes wheel
wheel--less objects skid to a stop
Friction wastes energy
Wheels mitigate the effects of friction
Wheels can also propel vehicles
Turn off all electronic devices
Falling Balls 87
Falling Balls 88
5 Questions about Wheels





Why does a wagon need wheels?
Why do boxes seem to “break free” and then
slide easily when you shove them hard enough?
What
Wh happens
h
to energy as a box
b skids
kid to rest??
How do wheels help a wagon coast?
What energy does a wheel have?
Falling Balls 89
Question 1

Why does a wagon need wheels?
Falling Balls 90
Frictional Forces

A frictional force
opposes relative sliding motion of two surfaces
 points along the surfaces
 acts
t to
t bring
brin the
th two
t surfaces
rf
to
t one
n velocity
l it
The Two Types of Friction



Frictional forces always come in 3rd law pairs:
Pavement’s frictional force pushes cart backward
 Cart’s frictional force pushes pavement forward

Static Friction



Acts to prevent objects from starting to slide
Forces can range from zero to an upper limit
Slidi F
Sliding
Friction
i i


Acts to stop objects that are already sliding
Forces have a fixed magnitude
15
Falling Balls 91
Falling Balls 92
Question 2

Why do boxes seem to “break free” and then
slide easily when you shove them hard enough?
Frictional Forces

Frictional forces increase when you:



P k static
Peak
i force
f
may be
b greater than
h sliding
lidi force
f


Falling Balls 93
push the surfaces more tightly together
roughen the surfaces
Surface features can interpenetrate better
Friction force may drop when sliding begins
Falling Balls 94
Boxes and Friction

A stationary box
Question 3

What happens to energy as a box skids to rest?
experiences static friction
 won’t start moving until you pull very hard


A moving
i b
box
experiences sliding friction
needs to be pulled or it will slow down and stop
 experiences wear as it skids along the pavement


Falling Balls 95
Falling Balls 96
Friction, Energy, and Wear

Static friction
Both surfaces travel the same distance (often zero)
 No work “disappears” and there is no wear


The Many Forms of Energy



Slidi ffriction
Sliding
i i
The two surfaces travel different distances
 Some work “disappears” and becomes thermal energy
 The surfaces experience wear




A sliding box turns energy into thermal energy
Kinetic: energy of motion
Potential: stored in forces between objects


Gravitational
M
Magnetic
i
Electrochemical
Nuclear



Elastic
El i
Electric
Chemical
Thermal energy: the same forms of energy, but
divided up into countless tiny fragments
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Falling Balls 98
Energy and Order

A portion of energy can be
Question 4

How do wheels help a wagon coast?
Organized – ordered energy (e.g. work)
 Fragmented – disordered energy (e.g. thermal energy)


Turning ordered energy into disordered energy



is easy to do
is statistically likely
Turning disordered energy into ordered energy


is hard to do
is statistically so unlikely it never happens
Falling Balls 99
Falling Balls 100
Rollers


Eliminate sliding friction
at roadway
Are inconvenient because
they keep popping out
from under the object
Falling Balls 101
Wheels




Falling Balls 102
Bearings


Eliminate sliding friction at roadway
Convenient because they don’t pop out
Allow static friction to exert torques on wheels
and forces on vehicle
Wheel hubs still have sliding friction
Eliminate sliding
friction in wheel hub
Behave like
automatically recycling
rollers
Practical Wheels


Free wheels are turned
by the vehicle’s motion
Powered wheels propel
the vehicle as they turn.
turn
17
Falling Balls 103
Falling Balls 104
Question 5

What energy does a wheel have?
Falling Balls 105
Wheels and Kinetic Energy
A moving wheel has kinetic energy:
1
kinetic energy   mass  speed 2
2
 A spinning wheel has kinetic energy:
1
kinetic energy   rotational mass  angular speed 2
2
 A moving and spinning wheel has both forms

Falling Balls 106
Summary about Wheels

Sliding friction wastes energy




Wheels eliminate sliding friction
A vehicle with wheels coasts well
Bumper Cars
F wheels
Free
h l are turnedd by
b static
i ffriction
i i
Powered wheels use static friction to propel car
Turn off all electronic devices
Falling Balls 107
Falling Balls 108
Observations about Bumper Cars






Moving cars tend to stay moving
Changing a car’s motion takes time
Impacts alter velocities and angular velocities
Cars often appear to exchange their motions
The fullest cars are the hardest to redirect
The least
least--full cars get slammed during collisions
3 Questions about Bumper Cars



Does a moving bumper car carry a “force”?
Does a spinning bumper car carry a “torque”?
On an uneven floor, which way does a bumper
car accelerate?
l
?
18
Falling Balls 109
Falling Balls 110
Question 1

Does a moving bumper car carry a “force”?
Momentum


A translating bumper car carries momentum
Momentum
is a conserved quantity (can’t create or destroy)
i a di
is
directed
d (vector)
(
) quantity
i
 measures the translational investment the object
needed to reach its present velocity
momentum = mass · velocity


Falling Balls 111
Falling Balls 112
Exchanging Momentum


Bumper cars exchange momentum via impulses
An impulse is
the only way to transfer momentum
 a directed
di
d (vector)
(
) quantity
i


Head--On Collisions
Head




impulse = force · time
When car1 gives an impulse to car2, car2 gives an
equal but oppositely directed impulse to car1.
Falling Balls 113
Bumper cars exchange momentum via impulses
The total momentum never changes
Car with the least mass changes velocity most
The littlest riders get creamed
Falling Balls 114
Question 2

Does a spinning bumper car carry a “torque”?
Angular Momentum


A spinning car carries angular momentum
Angular momentum
is a conserved quantity (can’t create or destroy)
i a di
is
directed
d (vector)
(
) quantity
i
 measures the rotational investment the object
needed to reach its present angular velocity
angular momentum = rotational mass· angular velocity


19
Falling Balls 115
Newton’s Third Law
of Rotational Motion
For every torque that one object exerts on a
second object, there is an equal but oppositely
directed torque that the second object exerts on
the first object
object.
Falling Balls 116
Exchanging Angular Momentum


Bumper cars exchange angular momentum
via angular impulses
An angular impulse is



Falling Balls 117



Bumper cars exchange angular momentum
via angular impulses
Total angular momentum about a specific
inertial point in space remains unchanged
Bumper car with the smallest rotational mass
about that point changes angular velocity most
The littlest riders tend to get spun wildly
Falling Balls 119
Rotational Mass can Change


Mass can’t change, so the only way an object’s
velocity can change is if its momentum changes
Rotational mass can change, so an object that
changes shape can change its angular velocity
without changing its angular momentum
Falling Balls 120
Potential Energy, Acceleration,
and Force
Question 3

When car1 gives an angular impulse to car2, car2
gives an equal but oppositely directed angular
impulse to car1.
Falling Balls 118
Glancing Collisions

the only way to transfer angular momentum
a directed (vector) quantity
angular impulse = torque · time
On an uneven floor, which way does a bumper
car accelerate?



An object accelerates in the direction that
reduces its total potential energy as rapidly as
possible
Forces and potential energies are related!
A car on an uneven floor accelerates in whatever
direction reduces its total potential energy as
rapidly as possible
20
Falling Balls 121
Falling Balls 122
Summary about Bumper Cars

During collisions, bumper cars exchange



momentum via impulses
angular momentum via angular impulses
C lli i
Collisions
h
have lless effect
ff on


cars with large masses
cars with large rotational masses
Falling Balls 123





Static Electricity
Observations about
Static Electricity
Static electricity builds up on certain objects
Clothes in the dryer often develop static charge
Objects with static charge may cling or repel
Static electricity can cause shocks
Static electricity can make your hair stand up
Falling Balls 124






Falling Balls 125
Why do some clothes cling while others repel?
Why do clothes normally neither cling nor repel?
Why does distance reduce static effects?
Why do clingy clothes stick to uncharged walls?
Why do clingy clothes crackle as they separate?
Why do some things lose their charge quickly?
Falling Balls 126
Question 1

6 Questions about
Static Electricity
Why do some clothes cling while others repel?
Electric Charge (Part 1)


Clothes that cling or repel carry a physical
quantity called electric charge or simply “charge”
Charge comes in two types:
Charges
Ch
off the
h same type repell
 Charges of different types attract
 Franklin named the types “positive” and “negative”


Clothes acquire static charges while in the dryer


Clothes that cling evidently carry opposite charges
Clothes that repel evidently carry like charges
21
Falling Balls 127
Falling Balls 128
Question 2

Why do clothes normally neither cling nor repel?
Electric Charge (Part 2)

Electric charge





Electric charge is measured in coulombs
One fundamental charge is 1.6  10-19 coulombs
Charge is intrinsic to some subatomic particles


Falling Balls 129
is a conserved quantity
is quantized in multiples of the fundamental charge
Each proton has +1 fundamental charge
Each electron has –1 fundamental charge
Falling Balls 130
Net Charge

An object’s net charge
Charge Transfers

is the sum of all its individual charges
 tends to be zero or nearly zero





A electrically
An
l i ll neutrall object
bj

contains as many + charges as – charges
has zero net charge
Clothes tend to be neutral
Neutral clothes neither cling nor repel
Falling Balls 131
Contact can transfer electrons between objects
The object with the stronger affinity for electrons
gains electrons and becomes negatively charged
 The other object loses electrons and becomes
positively charged


Rubbing objects together ensures



A dryer charges clothes via these effects
Falling Balls 132
Question 3

excellent contact between their surfaces
significant charge transfer from one to the other.
Why does distance reduce static effects?
Electric Charge (Part 3)

Two charges push or pull on one another



Th electrostatic
These
l
i forces
f
are



with forces that are equal in magnitude
but opposite in direction.
proportional to the amount of each charge
inversely proportional to (distance between charges)2
Electrostatic forces obey Coulomb’s law:
Coulomb constant  charge1  charge 2
force =
(distance between charges)2
22
Falling Balls 133
Falling Balls 134
Question 4

Why do clingy clothes stick to uncharged walls?
Electric Polarization


A neutral wall contains countless charges
When a negatively charged sock nears the wall,
the wall’s positive charges shift toward the sock,
the
h wall’s
ll’ negative
i charges
h
shift
hif away from
f
it,
i
 and the wall becomes electrically polarized.





Falling Balls 135
Opposite charges are nearer and attract strongly
Like charges are farther and repel less strongly
The charged sock clings to the polarized wall
Falling Balls 136
Question 5

Why do clingy clothes crackle as they separate?
Voltage


Charge has electrostatic potential energy (EPE)
Voltage measures the EPE per unit of charge



Falling Balls 137
Separating opposite charges takes work,
Voltage is measured in volts (joules/coulomb)
Falling Balls 138
Separating Opposite Charges

Raising the voltage of positive charge takes work
Lowering
L
i the
h voltage
l
off negative
i charge
h
takes
k workk
Question 6

Why do some things lose their charge quickly?
so the positive charges undergo a rise in voltage
 and the negative charges undergo a drop in voltage.


P i i charge
Positive
h
at high
hi h voltage
l



can release EPE by moving to lower voltage
may move by way of a discharge or spark!
Negative charge at low voltage,

can release EPE by moving to higher voltage
23
Falling Balls 139
Falling Balls 140
Conductors and Insulators


Insulators have no mobile electric charges
Conductors have some mobile electric charges,
usually electrons (e.g., metals)
 but
b occasionally
i ll iions ((e.g., salt
l water))


In a conductor, the mobility of charge permits
like charges to disperse or escape
 opposite charges to aggregate and cancel








Summary about
Static Electricity
Even neutral objects contain countless charges
Objects can transfer charge during contact
Clothes often develop net charges during drying
Oppositely charged clothes cling to one another
and spark as separation raises their voltages.
Conductivity tends to let objects neutralize.
Conductors can lose their charges quickly
Falling Balls 141
Falling Balls 142
Observations About Copiers

Xerographic Copiers




Falling Balls 143



3 Questions about
Xerographic Copiers
How can light arrange colored powder on paper?
How does a copier spray charge onto a surface?
How does a copier make its copies permanent?
Copiers consume colored powder or “toner”
Copies consist of that powder stuck to paper
After jams, the powder sometimes wipes off
Copies are often warm after being made
Some copiers scan a light, some use a flash
Falling Balls 144
Question 1

How can light arrange colored powder on paper?
24
Falling Balls 145
Falling Balls 146
The Xerographic Concept

A xerographic copier or printer
Question 2

How does a copier spray charge onto a surface?
sprays electric charge onto a surface and
 projects an image of the document onto that surface.
 Wherever light
g hits the surface,, the charge
g escapes.
p
 The remaining charge attracts colored toner particles
 which are then bonded to paper to produce a copy.


The surface is a photoconductor,


an insulator that turns into a conductor in the light,
so illumination allows charge to move and escape.
Falling Balls 147
Falling Balls 148
Electric Fields (Part 1)


Consider these two views of electric forces:
The first view is charge
charge--onon-charge




is a structure in space that pushes on electric charge
is vector in character: it has magnitude and direction
 can
n vary
r with
ith p
position
iti n and
nd tim
time
Charge1 pushes directly on Charge2.
Charge1 creates an electric field and
that electric field pushes on Charge2.


The electric field at a given position and time
is proportional to the force on a + test charge
is often represented graphically by an arrow
 but is actually located at just one point on that arrow


This electric field isn’t a fiction; it actually exists!
Falling Balls 149
An electric field

The second view is charge
charge--electric fieldfield-charge


Electric Fields (Part 2)
Falling Balls 150
Electric Fields and…


Consider these two views of electric forces:
The first view is electric fieldfield-onon-charge

…Voltage Gradients

The second view is voltage gradientgradient-onon-charge
An object accelerates to reduce potential energy (PE)
so it experiences a force down the “gradient” of PE
 + test
t t charge
h r has
h electrostatic
l tr t ti potential
p t nti l energy
n r (EPE)
 + test charge’s EPE is proportional to its voltage
 + test charge experiences force down voltage gradient
 A voltage gradient exerts a force on a + test charge

An electric field exerts a force on a + test charge


A voltage gradient is an electric field!
25
Falling Balls 151

Electric Fields
In and Around Metals
Inside a metal, charges can move freely
Falling Balls 152
Corona Discharges

and can rearrange to minimize their EPE.
 At equilibrium, the metal has a uniform voltage,
 and
nd there
th r is
i no
n electric
l tri fi
field
ld in
inside
id th
the m
metal.
t l

Outside a metal, charges can’t move freely,



so they cannot rearrange to minimize their EPE.
 At equilibrium, voltages can vary with location,
 and there can be an electric field outside the metal.

Falling Balls 153
Outside a sharp or narrow metal at high voltage,
the voltage varies rapidly with position,
so that the electric field is very strong
 and
nd it can
n push
p h charges
h r onto
nt passing
p in air
ir p
particles.
rti l

This phenomenon is a corona discharge


in which the narrow metal sprays charges
and can easily deposit or dissipate static electricity.
Falling Balls 154
Question 3

Xerographic Process
How does a copier make its copies permanent?
Falling Balls 155
Falling Balls 156
Copier Structure






Summary about
Xerographic Copiers
It sprays charge from a corona discharge
That charge precoats a photoconductor
It projects a light onto the photoconductor
The charge escapes from illuminated regions
The remaining charge attract toner particles
Those particles are fused to the paper as a copy
26
Falling Balls 157
Falling Balls 158
Observations about Flashlights

Flashlights



Falling Balls 159
You turn them on and off with switches
Brighter flashlights usually have more batteries
Flashlights grow dimmer as their batteries age
Sometimes smacking a flashlight brightens it
Falling Balls 160
6 Questions about Flashlights






Why do flashlights need batteries and bulbs?
How does power flow from batteries to bulbs?
How does a flashlight’s switch turn it on or off?
How can a battery be recharged?
Why does a shortshort-circuited flashlight get hot?
What distinguishes differentdifferent-voltage lightbulbs?
lightbulbs?
Falling Balls 161
Question 1

Why do flashlights need batteries and bulbs?
Falling Balls 162
What Batteries Do


Batteries provide flashlights with electric power
A battery “pumps” charges from – to +





Battery’s chemical potential energy decreases
charges
charges’ electrostatic potential energy increases
Voltage rise from the – end to + end:
1.5 volts in a typical alkaline cell,
 3.0 volts or more in a lithium cell,
 and of even more in a chain of cells.


What Lightbulbs Do
Lightbulbs turn electric power into light power
A bulb lets charges flow through its filament




Decreases the charges’ electrostatic potential energy
P d
Produces
thermal
h
l energy, including
i l di light.
li h
Voltage drop from entry end to exit end
In a two
two--cell alkaline flashlight, the drop is 3.0 V
In a two
two--cell alkaline flashlight, the rise is 3.0 V
27
Falling Balls 163
Falling Balls 164
Question 2

How does power flow from batteries to bulbs?
Electric Power

Electric power is the rate of energy transfer,




Falling Balls 165
Electric current is the rate of charge transfer,
Electric Current in a Flashlight

electric charge passing a point per unit of time,
 measured in amperes (i.e., coulombs/second).

B
Batteries
i provide
id power to electric
l i currents
Lightbulbs consume power from electric currents
In a flashlight, an electric current carries power
from batteries (the energy source)
through a wire (the outgoing current path)
 to
t a lightbulb
li htb lb filament
fil m nt (the
(th energy
n r destination),
d tin ti n)


B
Batteries
i provide
id electric
l i power
Lightbulbs consume electric power
Falling Balls 166
Electric Current




The current then returns



Falling Balls 167
Falling Balls 168
Current
arrives at – end of battery at low voltage
 is pumped by battery from – end to + end
 exits
it fr
from
m + end
nd off battery
b tt r att high
hi h voltage
lt
 experiences an overall voltage rise
About Metal Conductors

Battery provides electric power to current:
Metals are imperfect conductors



through another wire (the returning current path)
to batteries, for reuse.
The current’s job is to deliver power, not charge!
How a Battery Works

electric energy transferred per unit of time,
measured in watts (i.e., joules/second).


electric currents don’t coast through them
electric fields are needed to keep currents moving.
For a current to flow through a filament,


the filament must have an electric field in it
caused by a voltage drop and an associate gradient.
power provided = current · voltage rise
28
Falling Balls 169
Falling Balls 170
How a Lightbulb Filament Works

Current
Question 3

How does a flashlight’s switch turn it on or off?
arrives at filament at high voltage
 struggles to get through filament
 exits
it fr
from
m filament
fil m nt att low
l voltage
lt
 experiences an overall voltage drop


Filament consumes electric power from current:
power consumed = current · voltage drop
Falling Balls 171
Falling Balls 172
Circuits and Flashlights

Steady current requires a circuit or loop path
Question 4

How can a battery be recharged?
charge mustn’t accumulate anywhere
 a closed conducting loop avoids accumulation


I a flashlight,
In
fl hli h the
h electric
l i circuit
i i iis


closed (complete) when you turn the switch on
open (incomplete) when you turn the switch off
Falling Balls 173
Falling Balls 174
Recharging a Battery (Part 1)

While a battery discharges:
Current flows from – end to + end (forward)
 Current experiences a voltage rise
 Charges’
Ch r ’ electrostatic
l tr t ti potential
p t nti l energy
n r increases
in r
 Battery’s chemical potential energy decreases

Recharging a Battery (Part 2)

While a battery recharges:
Current flows from + end to – end (backward)
Current experiences a voltage drop
 Charges’
Ch r ’ electrostatic
l tr t ti potential
p t nti l energy
n r ddecreases
r
 Battery’s chemical potential energy increases


29
Falling Balls 175
Falling Balls 176
The Direction of Current

Current is defined as the flow of positive charge

but negative charges (electrons) carry most currents.

Batteries typically establish the current direction
Current direction doesn’t affect

Current direction is critically important to


It’s difficult to distinguish between:
N
Negative
i charges
h
fl
flowing
i to the
h right
i h
 Positive charges flowing to the left.


Effects of Current Direction


We pretend that current is flow of + charges,


wires, heating elements, or lightbulb filaments,
electronic components such as transistors and LEDs
and some electromagnetic devices such as motors.
but it’s really – charges flowing the other way.
Falling Balls 177
Falling Balls 178
Question 5

Why does a shortshort-circuited flashlight get hot?
Short Circuits

If a conducting path bridges the filament,



Th is
There
i no appropriate
i energy destination,
d i i

Such a short circuit is a recipe for fires!

Falling Balls 179
so energy loss and heating occurs in the wires.
Falling Balls 180
Question 6

current bypasses the filament
circuit is abbreviated or “short.”
What distinguishes differentdifferent-voltage lightbulbs?
Ohm’s Law

Currents undergo voltage drops while passing
through wires, filaments, and other conductors.
In ordinary electrical conductors, the voltage
drop is proportional to the current:
voltage drop = resistance · current

That relationship is known as Ohm’s law.

where resistance is a characteristic of the conductor.
30
Falling Balls 181
Falling Balls 182
Resistance and Filaments

The smaller a filament’s resistance,
the more current it carries for a given voltage drop
 the more electrical power it consumes


To
T avoid
id overheating,
h i fil
filaments in
i highhigh
hi h-voltage
l
flashlights must have
larger resistances (to limit power consumption)
 or larger surfaces (to dissipate more thermal power)
Summary about Flashlights






Falling Balls 183
Falling Balls 184

Household Magnets




Falling Balls 185





Current carries power from batteries to bulb
The switch controls the flashlight’s circuit
Current flows only when the circuit is closed
The batteries raise the current’s voltage
The lightbulb lower the current’s voltage
5 Questions about
Household Magnets
Why do any two magnets attract and repel?
Why must magnets be close to attract or repel?
Why do magnets stick only to some metals?
Why does a magnetic compass point north?
Why do some magnets use electricity?
Observations about
Household Magnets
They attract or repel, depending on orientation
Magnets stick only to certain metals
Magnets affect compasses
The earth seems to be magnetic
Some magnets use electricity to operate
Falling Balls 186
Question 1

Why do any two magnets attract and repel?
31
Falling Balls 187
Falling Balls 188
Magnetic Pole (Part 1)


Objects that attract or repel magnetically carry
portions of a physical quantity called magnetic
pole or simply “pole”
Pole comes in two types:
Magnetic Pole (Part 2)

Magnetic pole



Poles of the same type repel
 Poles of different types attract
 The two types are named “north” and “south”

is a conserved quantity
is analogous to electric charge
Th is,
There
i however,
h
one big
bi diff
difference:


no isolated magnetic pole has ever been found!
the net pole on any object is always exactly zero!
north pole  south pole
net pole  north pole  south pole
Falling Balls 189
Falling Balls 190
Magnetic Pole (Part 3)


Every magnet has equal north and south poles
They have magnetic polarizations, not net poles



Question 2

Why must magnets be close to attract or repel?
A typical bar or button magnet is a magnetic dipole
A di
dipole
l h
has one north
h pole
l and
d one south
h pole
l
A fragment of a magnet
has a net pole of zero
 retains its original magnetic polarization
 is typically a magnetic dipole

Falling Balls 191
Falling Balls 192
Magnetic Forces (Part 1)

Two poles push or pull on one another
with forces that are exactly equal in magnitude
 but exactly opposite in direction.


Th magnetostatic
These
i forces
f
are


proportional to the amount of each pole
inversely proportional to (distance between poles)2
Magnetic Forces (Part 2)

Since a magnet is a dipole (or more complicated)
it has both north and south poles
it simultaneously attracts and repels a second magnet
 their
th ir n
nett fforces
r ddepend
p nd on
n di
distance
t n and
nd orientation
ri nt ti n
 their net forces decrease precipitously with distance
 they may also experience net torques


The forces increase as the separation decreases
permeability of free space  pole1  pole 2
force =
4π  (distance between poles)2

32
Falling Balls 193
Falling Balls 194
Question 3

Why do magnets stick only to some metals?
Magnetism in Atoms

Magnetism is due primarily to electrons



Electrons are intrinsically magnetic—
magnetic—they’re dipoles
Atoms contain electrons, so atoms can be magnetic
Wh electrons
When
l
assemble
bl iinto atoms,
their magnetic dipoles often cancel one another
but this cancellation is usually incomplete
 so most atoms are magnetic.


Falling Balls 195
Falling Balls 196
Magnetism in Materials

When atoms assemble into materials,
the electron magnetic dipoles can cancel still further
 and that cancellation is complete in most materials.
 Most
M tm
materials
t ri l are
r essentially
nti ll n
non
nonn-magnetic
m n ti
Refrigerators and Magnets






have small domains that are magnetic dipoles
 Those domains ordinarily cancel on another
 An external magnet, however, can alter the domains
Falling Balls 197
Soft magnetic materials
When a magnetic pole is brought near the steel
iit causes some domains
d
i to grow and
d others
h to shrink
hi k
and the steel develops a net magnetic polarization
 so that it attracts the magnetic pole.


Magnets thus stick to steel refrigerators
Falling Balls 198
Soft & Hard Magnetic Materials

but they normally cancel so it appears nonmagnetic.

Some materials don’t experience full cancellation
Ferromagnetic materials

A refrigerator’s steel has magnetic domains,
Question 4

Why does a magnetic compass point north?
have domains the grow or shrink easily,
 so they are easy to polarize or depolarize.
 They
Th qquickly
i kl fforget
r t th
their
ir pr
previous
i
m
magnetizations.
n tiz ti n


Hard magnetic materials
have domains that don’t grow or shrink easily,
so they are hard to polarize or depolarize.
 They can be magnetized permanently.


33
Falling Balls 199
Falling Balls 200
Magnetic Fields

A magnetic field
is a structure in space that pushes on magnetic pole
 is vector in character: it has magnitude and direction
 may
m ddepend
p nd on
np
position
iti n and
nd tim
time
The Earth’s Magnetic Field






The magnetic field at a given position and time

experiences a magnetic torque
that aligns it so that its north
pole points northward.
Falling Balls 202
Question 5

so it is surrounded by a magnetic field
and that field pushes north poles northward.
A magnetic
i compass iimmersed
d iin earth’s
h’ fi
field
ld

is proportional to the force on a north test pole
 is often represented graphically by an arrow
 but is actually located at just one point on that arrow

Falling Balls 201
The earth is magnetic,
Why do some magnets use electricity?
Electromagnetism (Version 1)

Magnetic fields are produced by
magnetic poles (but free poles don’t seem to exist),
moving electric charges,
 and
nd changing
h n in electric
l tri fi
fields
ld [for
[f r llater…].
t r ]



Electric fields are produced by
electric charges,
moving magnetic poles [for later…],
 and changing magnetic fields [for later…].


Falling Balls 203
Falling Balls 204
Electromagnets

Electric currents are magnetic
A current
current--carrying wire has a magnetic field
 A coil of wire carrying current mimics a bar magnet.


A electromagnet
An
l
uses an electric
l i current to
produce its magnetic field, although that field is
often enhanced by ferromagnetic materials.




Summary about
Household Magnets
They all have equal north and south poles
They polarize soft magnetic materials and stick
They are surrounded by magnetic fields
Can be made magnetic by electric currents
34
Falling Balls 205
Falling Balls 206
Observations about
Electric Power Distribution
Electric Power
Distribution





Falling Balls 207
4 Questions about
Electric Power Distribution




Why isn’t power transmitted at low voltages?
Why isn’t power delivered at high voltages?
What is “alternating current” and why use it?
How does a transformer transfer power?
Falling Balls 209
Household electricity is alternating current (AC)
Household voltages are typically 120V or 240V
Power is distributed at much higher voltages
Power transformers are common around us
Power substations are there, but harder to find
Falling Balls 208
Question 1

Why isn’t power transmitted at low voltages?
Falling Balls 210
Electric Power and a Wire

An electric current passing through a wire
converts electrical power in thermal power

Si
Since
th
the wire
i obeys
b Oh
Ohms llaw,
Large Currents are Wasteful

The goal of a power distribution system is to
transmit lots of electric power to a city,

while
hil wasting
ti littl
little electric
l t i power in
i the
th wires,
i
power wasted = current · voltage drop in wire.
power transmitted = current · voltage drop at city,
city,
power wasted = resistance · current2.
voltage drop in wire = resistance · current,
current,

the power that wire wastes is
power wasted = resistance · current2.

Doubling current quadruples wasted power!

That energy efficiency can be achieved by using
a small current,
a huge voltage drop,
 and low
low--resistance wires.


35
Falling Balls 211
Falling Balls 212
Question 2

Why isn’t power delivered at high voltages?
High Voltages are Dangerous

When large voltage drops are available,
strong electric fields are present,
charges experience enormous forces,
 and
nd currents
rr nt ttend
nd tto fl
flow through
thr h unexpected
n p t dp
paths.
th



High--voltage electrical power in a home is
High
a spark hazard,
a fire hazard,
 and a shock hazard.


Falling Balls 213
Falling Balls 214
The Voltage Hierarchy



Large currents are too wasteful for transmission
High voltages are too dangerous for delivery
So electric power distribution uses a hierarchy:
Question 3

What is “alternating current” and why use it?
high-voltage circuits in the countryside
highmedium--voltage circuits in cities
medium
 low
low--voltage circuits in neighborhoods and homes



Transformers transfer power between circuits!
Falling Balls 215
Falling Balls 216
Alternating Current (AC)

In alternating current,
the voltages of the power delivery wires alternate
 and the resulting currents normally alternate, too.
AC and Transformers




Alternating
Al
i voltage
l
iin the
h US


completes 60 cycles per second,
reversing every 1/120 second.

AC has little effect on simple electric devices
(e.g., lightbulbs,
lightbulbs, space heaters, toasters)
AC is a nuisance for electronic devices
(e g computers,
(e.g.,
comp ters televisions,
televisions sound
so nd systems)
AC permits the easy use of transformers,
which can move power between circuits:
from a low
low--voltage circuit to a highhigh-voltage circuit
 from a highhigh-voltage circuit to a lowlow-voltage circuit


36
Falling Balls 217
Falling Balls 218
Question 4

How does a transformer transfer power?
Electromagnetism (Version 2)

Magnetic fields are produced by
magnetic poles (but free poles don’t seem to exist),
moving electric charges,
 and
nd changing
h n in electric
l tri fi
fields
ld [more
[m r llater…].
later…]
t r ].



Electric fields are produced by
electric charges,
moving magnetic poles,
poles,
 and changing magnetic fields.
fields.


Falling Balls 219
Falling Balls 220
Electromagnetic Induction

Moving poles or changing magnetic fields
Lenz’s Law

produce electric fields,
 which propel currents through conductors,
 which p
produce magnetic
g
fields.



“When a changing
g g magnetic
g
field induces a current in a
conductor, the magnetic field from that current
opposes the change that induced it.”
Changing magnetic effects induce currents
Induced currents produce magnetic fields
Falling Balls 221
Lenz’s law predicts the nature of the induced
magnetic fields:
Falling Balls 222
Transformers


Alternating current in one circuit can induce an
alternating current in a second circuit
A transformer
uses induction
i d i
 to transfer power
between its circuits
 but doesn’t
transfer any charges
between its circuits

Current and Voltage



A transformer must obey energy conservation
Power arriving in its primary circuit must equal
power leaving in its secondary circuit
Si
Since
power iis the
h product
d off voltage
l
· current,
current,


a transformer can exchanging voltage for current
or current for voltage!
37
Falling Balls 223
Falling Balls 224
Step--Down Transformer
Step

A step
step--down transformer
Step--Up Transformer
Step

has relatively few turns in its secondary coil
 so charge is pushed a shorter distance
 and
nd experiences
p ri n a smaller
m ll r voltage
lt
ri
rise

A larger current
at smaller voltage
flows in the
secondary circuit
Falling Balls 225




A step
step--up transformer increases the voltage
for efficient longlong-distance transmission
A step
step--down transformer decreases the voltage
for safe delivery to communities
comm nities and homes
Summary about
Electric Power Distribution





Falling Balls 227
Electric power is transmitted at high voltages
Electric power is delivered at low voltages
Transformers transfer power between circuits
Transformers require AC power to operate
The power distribution system is AC
Falling Balls 228
Observations about Hybrid
Automobiles

Hybrid Automobiles
A smaller current
at larger voltage
flows in the
secondary circuit
Falling Balls 226
Power Distribution System

A step
step--up transformer
has relatively many turns in its secondary coil
so charge is pushed a longer distance
 and
nd experiences
p ri n a llarger
r r voltage
lt
ri
rise






A hybrid car propels itself on fuel or batteries
It combines electrical and mechanical power
It switches easily between fuel, batteries, or both
It can recharge its batteries during braking
It can turn its engine off when not needed
It can restart its engine quickly and easily
38
Falling Balls 229





5 Questions about Hybrid
Automobiles
How does a hybrid car power its wheels?
How does a hybrid car generate electric power?
How does a hybrid car use that electric power?
How does a hybrid car manage that power?
If magnets don’t move, can they affect charge?
Falling Balls 231
Falling Balls 230
Question 1

How does a hybrid car power its wheels?
Falling Balls 232
Combining Mechanical Power

A hybrid automobile uses a machine that blends
The Transaxle

rotary mechanical power from its fuelfuel-burning engine
 rotary mechanical power from its electric motors
 rotary
r t r m
mechanical
h ni l p
powerr fr
from
m it
its wheels
h l



That “transaxle” can transfer mechanical power
between any of those devices in either direction!
Falling Balls 233
Falling Balls 234
Rotary Power

A hybrid car’s transaxle is a gear assembly that
couples together its engine, motors, and wheels
conveys mechanical power between those devices
 replaces
r pl
th
the tr
transmission
n mi i n off a n
normal
rm l carr

Recall that to provide rotary power to a machine
Question 2

How does a hybrid car generate electric power?
you must exert a torque on that machine
 in the direction of its angular velocity.


Th transaxle
The
l allows
ll
engine,
i motors, and
d wheels
h l
to exert torques on one another
as they turn in various directions at various speeds
 and thereby transfer rotary power to one another.



Power can flow in any direction via the transaxle!
39
Falling Balls 235
Falling Balls 236
Generating Electricity

Recall that changing magnetic fields
An AC Generator



Changing magnetic effects induce currents
Moving magnets have changing magnetic fields
and can induce currents in coils of wire
 with magnetic fields that oppose the moving magnets.


except that it has no primary coil
and instead uses a spinning magnet
 to induce AC current
in its secondary coil.



Mechanical power becomes electrical power!
Falling Balls 237
An AC Generator resembles a transformer

produce electric fields,
 which propel currents through conductors,
 which
hi h produce
pr d
magnetic
m n ti fi
fields.
ld

Magnet rotation speed
sets the AC frequency.
Magnet strength, turns
in the coil, and rotation
speed set voltage rise.
Falling Balls 238
Question 3

How does a hybrid car use that electric power?
An AC Motor

An AC Motor resembles a transformer
except that it has no secondary coil
and instead uses a spinning magnet
 to
t obtain
bt in power
p
r fr
from
m
its primary coil.




Falling Balls 239
Falling Balls 240
Generators = Motors

AC frequency sets the
Magnet rotation speed.
Magnet strength, turns
in the coil, and rotation
speed set voltage drop.
If generators and motors look similar,
Question 4

How does a hybrid car manage that power?
that’s because they’re basically the same device!
 they differ only in the direction of power flow


If you twist
i it
i forward,
f
d it
i acts as a generator



You do work on it and transfer power to it
Lenz’s law: magnetic effects twist you backward
If you twist it backward, it acts as a motor
You do negative work on it and extract power from it
 Lenz’s law: magnetic effects twist you forward

40
Falling Balls 241
Falling Balls 242
Hybrid Propulsion System

Its electronics transfer electrical power between
Meeting Every Requirement

its batteries, which use direct current,
 its motor/generators, which use alternating current,
 with
ith help
h lp off AC↔DC in
invertors
rt r (hi
(hi--tech
t h switches)
it h )

Its transaxle transfers
mechanical power between
its motor/generators
its engine
 its wheels






Falling Balls 243
Each rotary device has its own angular velocity
Engine operates best at a specific angular velocity
Wheels operate best when they roll on the ground
 Motor/generators
M t r/ n r t r can
n operate
p r t att any
n angular
n l r velocity
l it

Flexibility of the motor/generators makes up for
the pickiness of the engine and wheels
The vehicle can drive fast on level ground, climb
hills, and using braking to recharge its batteries.
Falling Balls 244
Question 5

If magnets don’t move, can they affect charge?
A Different Point of View

From rotor’s perspective, the poles don’t move




Falling Balls 245
A charge moving through a magnetic field
experiences the Lorentz force,
 a force that pushes it perpendicular to its velocity
 and
nd p
perpendicular
rp ndi l r to
t the
th magnetic
m n ti field:
fi ld
Lorentz force = charge · velocity · magnetic field ·
sine(angle)
where the “angle” is that between
the velocity and the magnetic field.
Summary about Hybrid Vehicles



F
From
rotor’s
’ perspective,
i the
h charges
h
d move
do
When a charge moves through a magnetic field,
it experience a new force: the Lorentz force
Falling Balls 246
The Lorentz Force

so there is no electric field to push on charge.
How can the motor/generator still work?


It uses its motors to convert electrical power
from its batteries and generators into mechanical
power for its wheels, generators, and engine
A hybrid vehicle uses
ses its generators to convert
mechanical power from its engine and wheels
into electrical power for its batteries and motors
Its generators and motors are the same devices
The Lorentz force resolves the
apparent paradox
41
Falling Balls 247
Falling Balls 248
Observations about Power Adapters

Power Adapters



Falling Balls 249





5 Questions about
Power Adapters
Why isn’t a power adapter simply a transformer?
Why can electrons move in metals not insulators?
How does charge move in a semiconductor?
How does a diode carry current only one way?
How does a capacitor store electric charges?
Falling Balls 251
Power Adapter Components (part 1)

A basic power adapter
converts AC power to lowlow-voltage DC power.
 A transformer performs only one of its three steps.


S 1:
Step
1 household
h
h ld AC to llowlow-voltage
l
AC
Performed by a stepstep-down transformer
Household AC flows into the primary coil
 Low
Low--voltage AC flow out of the secondary coil


They obtain power from AC electrical outlets
They provide DC power to electronic devices
They somehow fix the AC versus DC problem
They come in various voltages and other ratings
Falling Balls 250
Question 1

Why isn’t a power adapter simply a transformer?
Falling Balls 252
Power Adapter Components (part 2)

Step 2: lowlow-voltage AC to lowlow-voltage pulsed DC
Performed by diodes: one
one--way devices for current
Low--voltage AC flows into a network of diodes
Low
 The
Th di
diodes
d steer
t r th
the current
rr nt so it lleaves th
the adapter
d pt r
through one wire and returns through the other
 AC reversals cause that DC current to pulse


42
Falling Balls 253
Falling Balls 254
Power Adapter Components (part 3)

Step 3: lowlow-voltage pulsed DC to lowlow-voltage DC
Question 2

Why can electrons move in metals not insulators?
Performed by a capacitor: a charge storage device
 Low
Low--voltage pulsed DC flows into the capacitor
 Capacitor
C p it r stores
t r charge
h r when
h n voltage
lt
iis in
increasing
r in
 Capacitor releases charge when voltage is decreasing
 The capacitor smoothes out the voltage pulses
 Low
Low--voltage DC flows out of the capacitor

Falling Balls 255
Falling Balls 256
Metals, Insulators, and Diodes

These three have different electrical behaviors:
Quantum Physics (Part 1)

Metals can carry current in any direction
 Insulators can’t carry current
 Diode
Di d carry
rr current
rr nt only
nl in one
n dir
direction
ti n

To understand a diode,



we need to understanding metals and insulators
 so we must take a peek at quantum physics.
Modern physics (post(post-1900) recognizes that
everything in nature is both particle and wave
things are most wave
wave--like as they move unobserved
 things are most particleparticle-like when they interact

Falling Balls 257
Classical physics (pre(pre-1900) thought that
everything in nature is a particle or a wave
electrons, atoms, and billiard balls are particles
 light
li ht and
nd sound
nd are
r waves



Falling Balls 258
Quantum Physics (Part 2)

Example 1: light
travels as waves (electromagnetic waves)
 is emitted and absorbed as particles (photons)


E
Example
l 22: electrons
l
are emitted and detected as particles (electrons)
travel as waves (matter waves)
 reside in atoms and solids as standing waves

Electrons in Solids (Part 1)

In a solid, each electron is a standing wave
Similar to the vibration of a string or a drumhead
 Only certain standing waves fit properly in the solid
 Each allowed standing wave is called a “level”
level
 An electron’s level determines its energy


43
Falling Balls 259
Falling Balls 260
Pauli Exclusion Principle

Pauli exclusion principle:
“No two indistinguishable Fermi particles ever occupy
the same quantum wave”

Electrons
Electrons in Solids (Part 2)



are Fermi particles
obey Pauli exclusion principle
 can be distinguished only by spin
spin--up or spin
spin--down



At most two electrons can occupy a single level.
Falling Balls 261
Electrons settle into a solid’s lowestlowest-energy levels
Fermi level is between last filled and first unfilled
The levels in a solid
are not uniformly
if
l
distributed in energy:
they clump together
in “bands” that are
separated by
“band gaps”
Falling Balls 262
Metals

In a metal,
Insulators

the Fermi level has empty levels just above it
 Like patrons in a partly filled theatre, electrons can
move in response to electric fields
 Currents can flow through a metal in any direction
Falling Balls 263
In an insulator,
The Fermi level has no empty levels nearby
Like patrons in a full theatre, electrons can’t move in
response to electric fields
 Current can’t flow through an insulator



Falling Balls 264
Question 3

How does charge move in a semiconductor?
Semiconductors

Pure semiconductors are “poor insulators”
A narrow band gap separates the full “valence” band
below from the empty “conduction” band above
 Like patrons in a full theatre with a low empty
balcony, electrons can hop to the balcony and move
 Light or heat can allow current in a semiconductor

44
Falling Balls 265
Falling Balls 266
p-Type Semiconductor

Adding impurity atoms to a semiconductor
n-Type Semiconductor

changes the number of electrons it contains
 alters the filling of its valence and conduction bands

Impurities that increase the number of electrons
fill some of the conduction levels
and current can flow via those conduction levels.
 n-type
t p semiconductor
mi nd t r



I
Impurities
i i that
h reduce
d
the
h number
b off electrons
l
leave some of the valence
levels empty
 and current can flow
via those valence levels.
 p-type semiconductor

Falling Balls 267
Falling Balls 268
Question 4

How does a diode carry current only one way?
pn--Junction (before contact)
pn

Before p
p--type semiconductor meets n
n--type,


Falling Balls 269
Falling Balls 270
pn--Junction (after contact)
pn

After p
p--type semiconductor meets n
n--type,
electrons migrate from the nn-type to the pp-type
 an insulating depletion region appears at junction
 and
nd that
th t depletion
d pl ti n region
r i n is
i electrically
l tri ll polarized.
p l riz d

each material can conduct electricity
and each material is electrically neutral everywhere.
Forward Conduction

When electrons are added to the nn-type end and
removed from the p
p--type end,


the depletion region shrinks
and the diode conducts current.
current
45
Falling Balls 271
Falling Balls 272
Reverse Conduction

When electrons are added to the pp-type end and
removed from the n
n--type end,


Question 5

the depletion region grows
and the diode does not conduct current.
current
Falling Balls 273
Falling Balls 274
Capacitors

A capacitor consists of
two conducting plates
 an insulator that separates those plates.


How does a capacitor store electric charges?
Th capacitor
The
i can
Complete Power Adapter



A transformer provides lowlow-voltage AC,
diodes convert that AC to pulsed DC,
and a capacitor smoothes out the pulses.
accumulate equal but opposite charges on its plates
develop a voltage difference between its plates
 store electrostatic potential energy



Charge and voltage difference are proportional:
charge on positive plate = voltage difference · capacitance
Falling Balls 275
Falling Balls 276
Summary about Power Adapters




Use transformers to obtain lowlow-voltage AC
Use diodes to obtain lowlow-voltage pulsed DC
Use a capacitor to obtain lowlow-voltage DC
Semiconductor diodes make them practical
Audio Players
46
Falling Balls 277
Falling Balls 278
Observations about Audio Players




They are part computer, part sound system.
They require electric power, typically batteries.
They reproduce sound nearly perfectly.
They are sensitive to static charge.
Falling Balls 279
4 Questions about Audio Players




How does an audio player “store” sound?
How does it move sound information around?
How does the audio player’s computer work?
How does the audio player’s amplifier work?
Falling Balls 280
Question 1

How does an audio player “store” sound?
Representing Sound


There is no sound inside an audio player
It uses representations of sound information,



sequences of air pressure measurements
that
h contain
i everything
hi needed
d d to recreate the
h sound.
d
It stores and retrieves them in digital form,
prepares them for playback in analog form,
 and finally uses them to reproduce sound itself.

Falling Balls 281
Falling Balls 282
Digital Representation


A group of “symbols” represents a number
A symbol can be any discrete physical quantity:
Analog Representation


a positive or negative charge on a capacitor
an integer
i
value
l off voltage
l
on a wire
i
 a north or south magnetic pole on a magnet

One physical quantity represents one number
Any continuous physical quantity can be used:
the voltage on a wire,
the
h current iin a circuit,
i i
 the strength of a permanent magnet.




The symbols collectively represent one number,
so this symbol approach is insensitive to noise
 and digital representations can be “perfect.”


Each physical quantity represents a number,


so this analog approach is sensitive to noise
and analog representations are “imperfect.”
47
Falling Balls 283
Falling Balls 284
The Player’s Representations

An audio player uses
Question 2

How does it move sound information around?
digital representation for storage and retrieval,
 but analog representation for the actual playback.




S
Storage
and
d retrieval
i l iinvolves
l
a di
digital
i l computer
Playback involves an analog amplifier
Between them is a digital
digital--toto-analog converter
Falling Balls 285
Falling Balls 286
MOSFET Transistors

The electronic components we’ve encountered
so far are all relatively passive:
MOSFET Transistor Off

consists of two backback-toto-back pn
pn--Junctions
normally can’t conduct electric current
 has
h a ““gate”
t ” that
th t can
n attract
ttr t charges
h r int
into its
it “channel”
“ h nn l”

Wires: carry current from place to place
 Capacitors:
p
store charge
g
 Resistors: imperfect conductors that drop voltage
 Diodes: block reverse current flow




To manipulate charge, we need active switches
MOSFET transistors are electronic switches that
allow tiny charges to control large current flows
Falling Balls 287
Falling Balls 288
MOSFET Transistor On

A MOSFET Transistor
Charging the MOSFET’s gate
alters the filling of electron levels in the channel
 so depletion region vanishes
 and
nd the
th device
d i can
n conduct
nd t electric
l tri current.
rr nt

MOSFET Summary




It behaves like a electricallyelectrically-controllable resistor
A tiny amount of charge alters its resistance
It can manipulate digital information by
switching
i hi symbols
b l on or off.
ff
It can manipulate analog information by
controlling charge, current flow, or voltage.
48
Falling Balls 289
Falling Balls 290
Question 3

How does the audio player’s computer work?
Audio Player’s Digital Computer

Computers perform logical operations with bits
A bit is a basebase-two digit
so it can hold one of only two symbols: 0 or 1.
 Bit
Bit--wise
i representation
r pr nt ti n off n
numbers
mb r iis called
ll d binary
bi



Two of the simplest bit logical operations are



Falling Balls 291
inversion (NOT)
not--and (NAND)
not
Any function can be built from these two tools
Falling Balls 292
Inverter (NOT)


Takes one input bit, provides one output bit
Output symbol is inverse of input symbol
Falling Balls 293
Not--AND (NAND)
Not


Falling Balls 294
CMOS Logic

Bits are represented by charge
The symbol 1 is represented by positive charge
 The symbol 0 is represented by negative or no
charge
CMOS Inverter



Takes two input bits, provides one output bit
Output symbol is inverse “and” of input symbols
Logic is built from n
n--channel and p
p--channel
MOSFETS in complementary pairs


Input charge delivered to two complementary
MOSFETs
Positive charge on input
delivers negative charge
to output
Negative charge on input
delivers positive charge
to output
49
Falling Balls 295
Falling Balls 296
CMOS NAND


Positive on both inputs delivers negative charge
to output
Negative on either input
delivers positive charge
to output
Falling Balls 297
Question 4

How does the audio player’s amplifier work?
Falling Balls 298
Audio Player’s Audio Amplifier

Three circuits:

Input circuit: current/voltage represents sound
 Output circuit: amplified “sound” current/voltage
 Power
P
r circuit:
ir it pr
provides
id p
powerr fforr amplification
mplifi ti n


Amplifier Components
Amplifier produces “enlarged” copy of input
Falling Balls 299



Diodes – one
one--way devices for current
Capacitors – store charge, shift voltages
Resistors – provide voltage drops, limit current
Transistors – control current flow
Falling Balls 300
Resistors

A resistor is a simple ohmic device
with a voltage drop that is proportional to current
 and to its characteristic resistance.
 Many
M n values
l
off rresistance
i t n are
r available
il bl


Resistors are useful to
Amplifier (Part 1)

This amplifier is based on one MOSFET
As the MOSFET’s resistance decreases,
the current from +9V to 0V increases,
 the
th voltage
lt
drop
d p off 50
50 resistor
i t increases,
i
 and the voltage at “A” decreases.


reduce the voltage of a current
deliver a current that is proportional to a voltage
 limit a current based on a voltage drop


50
Falling Balls 301
Falling Balls 302
Amplifier (Part 2)

The 100K
100K resistor ensures that MOSFET has
a medium electrical resistance
If the MOSFET is off, + charge flows
onto the gate to turn the MOSFET on.
on
 If the MOSFET is on, – charge flows
onto the gate to turn the MOSFET off.
 Balance is struck with the MOSFET
approximately halfhalf-on
 and the voltage at “A” is about 4.5V.
Amplifier (Part 3)

altering the MOSFET’s
resistance
 so the voltage at “A” changes.

Falling Balls 303
Any charge flowing through the input circuit is
placed on the Gate,


The input capacitor shifts
the input voltage so that,
on average, it matches
the gate voltage.
Falling Balls 304
Amplifier (Part 4)


Changes in voltage “A” cause changes in output
current
The input capacitor shifts
the voltage at “A”
A so that,
that
on average, it matches the
output voltage.
Earpieces


Sound is reproduced by a moving surface
Surface is pushed and pulled electromagnetically
Surface’s wire coil is surrounded by a magnetic field,
so current in
i that
h coilil experiences
i
the
h L
Lorentz fforce
 and the coil accelerates.



Varying currents causes varying accelerations,

Falling Balls 305
and the surface reproduces sound
Falling Balls 306
Summary about Audio Players




Represent sound in digital and analog forms
Use MOSFETs to work with sound information
Digital computer comprised of CMOS logic
Analog amplifier based on MOSFETs.
Radio
51
Falling Balls 307
Falling Balls 308
Observations about Radio






It can transmit sound long distances wirelessly
It involve antennas
It apparently involves electricity and magnetism
Its reception depends on antenna positioning
Its reception weakens with distance
There are two styles of radio: AM and FM
Falling Balls 309
3 Questions about Radio



How can a radio wave exist?
How is a radio wave emitted and received?
How can a radio wave represent sound?
Falling Balls 310
Question 1


How can a radio wave exist?
Related questions:
Electromagnetic Waves


What is an electromagnetic wave anyway?
 How
H can an electric
l i fi
field
ld exist
i without
ih
charge?
h
?
 How can a magnetic field exist without pole?
are structures in space that consist only of electric
fields and magnetic fields.
fields
 They are emitted or received by charge or pole,
 but are selfself-sustaining while traveling in vacuum
 because their electric and magnetic fields endlessly
recreate one another.

Falling Balls 311

Falling Balls 312
Electromagnetism (Version 3)

Magnetic fields are produced by
magnetic poles (but free poles don’t seem to exist),
 moving electric charges,
 and
nd changing
h n in electric
l tri fi
fields
fields.
ld .


Structure of a Radio Wave



Electric fields are produced by
electric charges,
moving magnetic poles,
 and changing magnetic fields.


Radio waves are a class of electromagnetic waves
Electromagnetic waves

Electric field is perpendicular to magnetic field
Changing electric field
creates magnetic field
Ch i magnetic
Changing
i field
fi ld
creates electric field
Polarization of the wave
is associated with the
wave’s electric field
52
Falling Balls 313
Falling Balls 314
Question 2

How is a radio wave emitted and received?
Launching a Radio Wave



Accelerating charge emits electromagnetic waves
The more charge and the more it accelerates, the
stronger the resulting electromagnetic wave
R di stations
Radio
i
need
d to emit
i strong waves


Falling Balls 315
Falling Balls 316
A Tank Circuit

Tank circuit is a harmonic oscillator
It consists of a capacitor and an inductor
 Charge flows rhythmically through the
inductor from one capacitor plate to the
inductor,
other and back again.


Tank’s energy alternates between



An Antenna is a Tank Circuit





magnetic field in its inductor
electric field in its capacitor
Frequency set by capacitor & inductor
Falling Balls 317
An antenna is a straightened tank circuit!
Antenna’s frequency is set by its length
Resonant when it is ½ radio wavelength long
A conducting surface can act as half the antenna
Above a conducting
surface, antenna is
resonant when it is
¼ wavelength long
Falling Balls 318
Emitting Radio Waves (Part 1)




so they move large amounts of charge
using resonant devices: tank circuits and antennas
A transmitter uses a tank circuit to “slosh”
charge up and down its antenna,
which acts as a second tank.
A receiver uses a tank circuit to
detect charge “sloshing” on its
tank--circuit antenna.
tank
Transmitter antenna charge
affects receiver antenna charge
Antenna orientations matter!
Emitting Radio Waves (Part 2)

Accelerating charge emits radio waves
Stationary charge produces an electric field
Steady current produces a magnetic field
 Changing
g g current produces
p
a changing
g g magnetic
g
field, produces a changing electric field, prod…




A radio wave consists only of an electric and
magnetic field
A radio wave travels through empty space at the
speed of light
53
Falling Balls 319
Falling Balls 320
Question 3

How can a radio wave represent sound?
AM Modulation



Falling Balls 321
Information can be encoded as a fluctuating
amplitude of the radio wave
The air pressure variations
that are so
sound
nd ca
cause
se changes
in the amount of charge
moving on the antenna and
thus the intensity of the wave
The receiver detects these
changes in radio wave intensity.
Falling Balls 322
FM Modulation



Information can be encoded as a fluctuating
frequency of the radio wave
The air pressure variations
that are so
sound
nd ca
cause
se slight
shifts in the frequency of
charge motion on the antenna
and the frequency of the wave
The receiver detects these
changes in radio wave frequency.
Falling Balls 323
Summary about Radio




Radio waves are emitted by charge accelerating
on a transmitting antenna
Radio waves are detected when they cause
charge to accelerate on a receiving antenna
Radio waves consist only of selfself-sustaining
electric and magnetic fields
Radio waves can represent sound information as
variations in amplitude or frequency
Falling Balls 324
Observations About Microwaves

Microwave Ovens




Microwave ovens cook food from inside out
They often cook foods unevenly
They don’t defrost foods well
You shouldn’t put metal inside them?!
Do they make food radioactive or toxic?
54
Falling Balls 325



3 Questions about
Microwave Ovens
Why do microwaves cook food?
How does metal respond to microwaves?
How does the oven create its microwaves?
Falling Balls 327
Falling Balls 326
Question 1

Why do microwaves cook food?
Falling Balls 328
Electromagnetic Spectrum

Microwaves are a class of electromagnetic waves
Long-wavelength EM waves: Radio & Microwave
Long Medium
Medium--wavelength: IR, Visible, UV light
 ShortSh rt-wavelength:
Short
l n th X
X--rays
r &G
Gamma
Gammamm -rays
r
Water Molecules




Falling Balls 329
Falling Balls 330
Microwave Heating






Water molecules are
unusually polar
An electric field orients
water molecules
molec les
A fluctuating electric field
causes water molecules to
fluctuate in orientation
Microwaves have alternating electric fields
Water molecules orient back and forth
Liquid water heats due to molecular “friction”
Ice doesn’t heat due to orientational stiffness
Steam doesn’t heat due to lack of “friction”
Food’s liquid water content heats the food
Question 2

How does metal respond to microwaves?
55
Falling Balls 331
Falling Balls 332
Effects of Microwaves

Non--Conductors: Polarization
Non
Mobile polar molecules orient and heat
 Immobile polar molecules do nothing much
 NonN n-polar
Non
p l rm
molecules
l l ddo n
nothing
thin much
m h


Conductors: Current flow
Good, thick conductors reflect microwaves
 Poor conductors experience resistive heating
 Thin conductors experience resistive heating
 Sharp conductors initiate discharges in the air

Falling Balls 333
Interference


Identical waves that overlap can interfere
Interference is when the fields add or cancel





Adding fields are constructive interference
C
Canceling
li fi
fields
ld are destructive
d
i interference
i
f
Reflections lead to interference in a microwave
Interference causes uneven cooking
Most ovens “stir” the waves or move the food
Falling Balls 334
Question 3

How does the oven create its microwaves?
Generating Microwaves




Falling Balls 335




Summary about
Microwave Ovens
They cook food because of its water content
Polar water molecules heat in microwave fields
Thin or sharp metals overheat or spark
The microwaves are produced by a magnetrons
Magnetron tube has tank circuits in it
Streams of electrons amplify tank oscillations
A loop of wire extracts energy from tanks
A short ¼¼-wave antenna emits the microwaves
Falling Balls 336
Sunlight
56
Falling Balls 337
Falling Balls 338
Observations about Sunlight






Sunlight appears whiter than most light
Sunlight makes the sky appear blue
Sunlight becomes redder at sunrise and sunset
It reflects from many surfaces, even nonmetals
It bends and separates into colors in materials
Sunlight a key source of renewable energy
Falling Balls 339
5 Questions about Sunlight





Why does sunlight appear white?
Why does the sky appear blue?
How does a rainbow break sunlight into colors?
Why are soap bubbles and oil films so colorful?
Why do polarizing sunglasses reduce glare?
Falling Balls 340
Question 1

Why does sunlight appear white?
Light

Light is a class of electromagnetic waves
Long-wavelength EM waves: Radio & Microwave
LongMedium--wavelength: IR, Visible, UV light
Medium
 ShortSh rt-wavelength:
Short
l n th X
X--rays
r &G
Gamma
Gammamm -rays
r


Falling Balls 341
Falling Balls 342
Spectrum of Sunlight

Sunlight is thermal radiation—
radiation—heat from the sun
Question 2

Why does the sky appear blue?
Charges in the sun’s hot photosphere jitter thermally
 Accelerating charges emits electromagnetic waves
 The
Th sun
n emits
mit a blackblack
bl k-body
b d spectrum
p tr m att 5800 K


We perceive thermal light at 5800 K as “white”
57
Falling Balls 343
Falling Balls 344
Rayleigh Scattering

Rayleigh scattering occurs when







How does a rainbow break sunlight into colors?
passing sunlight electrically polarizes tiny particles in the air.
That alternating polarization acts as a source of light waves
waves,,
so air particles scatter light—
light—they absorb and then reemit it.
Air particles are too small to be good antennas for light,


Question 3
so longlong-wavelengths (reds) scatter poorly
while shortershorter-wavelengths (violets) scatter better.
Rayleigh scattered sunlight is bluish in appearance
The missing blue light reddens the solar disk itself

particularly at sunrise and sunset
Falling Balls 345
Falling Balls 346
Light and Refraction

Sunlight slows while it passes through matter
Light waves electrically polarize matter
 That polarization delays the light wave’s passage
 Each
E hm
material
t ri l h
has an
n “ind
“index off rrefraction”—
refraction”
fr ti n”—the
th factor
f t r
by which it reduces light’s speed.
Light and Reflection








Falling Balls 348
Light and Dispersion
The different colors of light in sunlight
have different frequencies
 and polarize a material slightly differently,
 so they
th tr
travell att slightly
li htl diff
different
r nt speeds.
p d
 Violet light usually travels slower than red


Sunlight partially reflects from most surfaces
Sunlight reflects almost completely from metals
it bends toward the perpendicular if it slows down
it bends away from the perpendicular if it speeds up
Falling Balls 347

which affects both how fast light travels in them and
relationship between its electric & magnetic fields.
Ch
Changes
in
i how
h light
li h travels
l causes reflections
fl i

When light changes speed at an interface,

Light polarizes different materials differently,
Rainbows

Occur when sunlight encounters water droplets

and undergoes refraction, reflection, and dispersion.
Refraction (bending) depends speed change

so violet light usually bends more than red
58
Falling Balls 349
Falling Balls 350
Question 4

Why are soap bubbles and oil films so colorful?
Light and Interference


Overlapping waves superpose and may interfere
Light following different paths can interfere




Falling Balls 351
The two reflections from
a soap or oil film interfere
Different colors often
interfere differently
Falling Balls 352
Question 5

constructively if fields point in the same direction
or destructively
d
i l if fields
fi ld point
i in
i opposite
i directions.
di i
Why do polarizing sunglasses reduce glare?
Reflection of Polarized Light


Angled reflections depend on polarization
When light’s electric field is parallel to a surface



there is a large fluctuating surface polarization
andd thus
h a strong reflection.
fl i
When electric field is perpendicular to a surface
there is a small fluctuating surface polarization
 and thus a weak reflection.


Falling Balls 353
Falling Balls 354
Polarization and Sunlight

Polarizing sunglasses
block horizontally polarized light
 and thus block glare from horizontal surfaces.


R l i h scattering
Rayleigh
i h
has polarizing
l i i effects,
ff

so much of the blue sky is polarized light, too.
Glare is mostly polarized parallel to the surface
Summary about Sunlight





Sunlight is thermal light at about 5800 K
It undergoes Rayleigh scattering in the air
It bends and reflects from raindrops
It interferes colorfully in soap and oil films
It reflects in a polarizing fashion from surfaces
59
Falling Balls 355
Falling Balls 356

Discharge Lamps





Falling Balls 357




4 Questions about
Discharge Lamps
Why phase out incandescent lamps?
How can colored lights mix so we see white?
How can white light be produced without heat?
How do gas discharge lamps produce their light?
Falling Balls 359

Incandescent lamps are reddish and inefficient
Filament temperature is too low, thus too red



They often take a few moments to turn on
They come in a variety of colors, including white
They are often whiter than incandescent bulbs
They last longer than incandescent bulbs
They sometimes hum loudly
They flicker before they fail completely
Falling Balls 358
Question 1

Why phase out incandescent lamps?
Falling Balls 360
Shortcomings of Thermal Light

Observations about
Discharge Lamps
Question 2

How can colored lights mix so we see white?
The temperature of sunlight is 5800 K
Th temperature off an incandescent
The
i
d
lamp
l
is
i 2700 K
An incandescent lamp


emits mostly invisible infrared light,
so less than 10% of its thermal power is visible light.
60
Falling Balls 361
Falling Balls 362
Seeing in Color

We have three groups of lightlight-sensing cone cells
Question 3

How can white light be produced without heat?
Their peak responses are to red, green, and blue light
 Those are therefore the primary colors of light



Wh the
When
h primaries
i
i mix,
i we see others
h colors
l
When the primaries mix evenly, we see white
Falling Balls 363
Falling Balls 364
Fluorescent Lamps (Part 1)

Fluorescent tubes
contain low density gas and metal electrodes,
 which inject free electric charges into the gas
 to
t form
f rm a plasma—
plasma
pl m —a gas off charged
h r dp
particles
rti l
 and electric fields cause current to flow in the plasma.
Fluorescent Lamps (Part 2)





Falling Balls 365
Collisions in the plasma cause
electronic excitation in the gas atoms
and occasionally ionize the gas atoms,
 which
hi h helps
h lp tto sustain
t in th
the pl
plasma.
m

Excited atoms emit light through fluorescence
Fluorescence is part of quantum physics
Falling Balls 366
Quantum Physics of Atoms

In an atom,



An electron in a specific orbital has a total energy,

An atom’s electrons



the negative electrons “orbit” the positive nucleus
and form standing waves known as orbitals
orbitals..
Each orbital can have at most two electrons in it


Atoms and Light
that is the sum of its kinetic and potential energies.
are normally in lowest energy orbitals – the ground state
but can shift to higher energy orbitals – excited states.
Electron orbitals are standing waves:
they do not change with time
they involve no charge motion
 they
th ddo n
nott emit
mit ((orr absorb)
b rb) lilight.
ht



While an electron is changing orbitals,
orbitals,



there is charge motion and acceleration,
so the electron can emit (or absorb) light.
Such orbital changes are call radiative transitions
61
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Falling Balls 368
Light from Atoms

The wave/particle duality applies to light:
Light travels as a wave (diffuse rippling fields)
 but is emitted or absorbed as a particle (a photon).
Photons, Energy, and Color



A atom’s
An
’ orbitals
bi l differ
diff b
by specific
ifi energies
i


These energy differences set the photon energies,
 so an atom has a specific spectrum of photons.

Falling Balls 369
Photon’s frequency is proportional to its energy
Photon energy = Planck constant · frequency
and its frequency · wavelength = speed of light.
light.
Each photon emitted by an atom has
a specific energy,
a specific frequency,
 a specific wavelength (in vacuum),
 and a specific color when we see it with our eyes.


Falling Balls 370
Atomic Fluorescence



Excited atoms lose energy via radiative transitions
During a transition, electrons shift to lower orbitals
Photon energy is the difference in orbital energies






Small energy differences  infrared (IR) photons
Moderate energy differences  red photons
Big energy differences  blue photons
Even bigger energy differences  ultraviolet (UV) photons
Each atom typically has a bright “resonance line”
Mercury’s resonance line is at 254 nm, in the UV
Falling Balls 371
Phosphors


A mercury discharge emits mostly UV light
A phosphor can convert UV light to visible
by absorbing a UV photon
and emitting a less
less--energetic visible photon
photon.
 The missing energy usually becomes thermal energy.



Fluorescent lamps use whitewhite-emitting phosphors

Specialty lamps use colored light
light--emitters



Starting a discharge requires electrons in the gas
Those electrons can be injected into the gas by




Atoms are sputtered off the electrodes
 Damage limits the number of times a lamp can start

Fluorescent Lamps (Part 4)

Gas discharges are electrically unstable
Gas is initially insulating
Once discharge is started, gas become a conductor
 The
Th m
more
r current
rr nt it carries,
rri th
the b
better
tt r it conducts
nd t
 Current tends to skyrocket out of control

heated filaments with special coatings
or by
b hi
high
h voltages
l
Once discharge starts, it can sustain the plasma
Starting the discharge damages the electrodes
Blue, green, yellow, orange, red, violet, etc.
Falling Balls 372
Fluorescent Lamps (Part 3)

They imitate thermal whites at 2700 K, 5800 K, etc.


Stabilizing discharge requires ballast


Inductor ballast (old, 60 Hz, tend to hum)
Electronic ballast (new, highhigh-frequency, silent)
62
Falling Balls 373
Falling Balls 374
Question 4

How do gas discharge lamps produce their light?
Low--Pressure Discharge Lamps
Low

Mercury gas has its resonance line in the UV



Low--pressure mercury lamps emit mostly UV light
Low
Some gases have resonance lines in the visible
Low--pressure sodium vapor discharge lamps
Low
emit sodium’s yellowyellow-orange resonance light,
so they are highly energy efficient
 but extremely monochromatic and hard on the eyes.


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Falling Balls 376
Pressure Broadening

High pressures broaden each spectral line
Radiation Trapping

Collisions occur during photon emissions,
 so frequency and wavelength become smeared out.
 Collision
C lli i n energy
n r shifts
hift th
the ph
photon
t n energy
n r
Falling Balls 377


Falling Balls 378
High--Pressure Discharge Lamps
High


At higher pressures, new spectral lines appear
High--pressure sodium vapor discharge lamps
High
emit a richer spectrum of yellowyellow-orange colors,
are still quite energy efficient
efficient,
 but are less monochromatic and easier on the eyes.



High--pressure mercury discharge lamps
High
Radiation trapping occurs at high atom densities
Atoms emit resonance radiation very efficiently
Atoms also absorb resonance radiation efficiently
 Resonance
R n n rradiation
di ti n ph
photons
t n are
r tr
trapped
pp d in the
th gas
 Energy must escape discharge via other transitions






Summary about
Discharge Lamps
Thermal light sources are energy inefficient
Discharge lamps produce more light, less heat
They carefully assemble their visible spectra
They use atomic fluorescence to create light
Some include phosphors to alter colors
emit a rich, bluishbluish-white spectrum,
 with good energy efficiency.
 Adding metalmetal-halides adds red to improve whiteness.

63
Falling Balls 379
Falling Balls 380

Lasers and LEDs



Falling Balls 381



3 Questions about
Lasers and LEDs
How does laser light differ from regular light?
How does a laser produce coherent light?
How does an LED produce its light?
Falling Balls 383
Electrons obey the Pauli exclusion principle
Each wave mode can have only one unique electron.
 That result gives structure to atoms and materials


Ph
Photons
don’t
d ’ obey
b the
h Pauli
P li exclusion
l i principle
i i l
Each wave mode can have many photons
 A radio wave has many photons in a single wave
Lasers and LEDs often have pure colors
Lasers produce narrow beams of intense light
Lasers are dangerous to eyes
Reflected laser light has a funny speckled look
Falling Balls 382
Question 1

How does laser light differ from regular light?
Falling Balls 384
Light: Photons and Waves

Observations about Lasers
and LEDs
Spontaneous Emission




Excited atoms normally emit light spontaneously
These photons are uncorrelated and independent
Each photons has its own wave mode
These independent waves are incoherent light


Most light sources produce photons randomly
Each photon usually has its own wave mode
 But laser light is an exception!

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Falling Balls 386
Stimulated Emission




Excited atoms can be stimulated into duplicating
passing light
These photons are correlated and identical
Th photons
The
h
allll h
have the
h same wave mode
d
This single, giant wave is
coherent light
Falling Balls 387
Question 2

How does a laser produce coherent light?
Falling Balls 388
Laser Amplification

Light can be amplified using stimulated emission
Excited atom
atom--like systems can act as a laser medium
 That medium will duplicate any photons that have the
right wavelength,
wavelength polarization,
polarization and orientation
 This duplication is perfect: the photons are true clones
Laser Oscillation





This light amplification is the basis for lasers
Falling Balls 389
A laser medium can amplify its own light
A laser medium in a resonator acts as an oscillator
It duplicates its one of its own spontaneous photons
 Duplicated
D pli t d ph
photons
t n leak
l k from
fr m semitransparent
mitr n p r nt mirr
mirrorr

The photons from this oscillator are identical
Falling Balls 390
Properties of Laser Light







Coherent – identical photons
Controllable wavelength/frequency – colors
Controllable spatial structure – narrow beams
Controllable temporal structure – short pulses
Energy storage and retrieval – intense pulses
Giant interference effects
But apart from all this, laser light is still just light
Examples of Lasers

Gas lasers (powered by discharges)



Helium-neon lasers (red, green, yellow)
HeliumCarbon dioxide lasers (infrared)
S lid state llasers ((poweredd by
Solid
b current or light)
li h )
Diode lasers (red, blue, infrared)
Ruby lasers (red)
 Nd:YAG lasers (infrared), but green when “doubled”
 Ti:Sapphire lasers (infrared)


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Question 3

How does an LED produce its light?
Light--Emitting Diodes
Light

LEDs are Light
Light--Emitting Diodes
They conduct current only in one direction
Each charge releases energy on crossing pn
pn--junction
 That
Th t energy
n r iis often
ft n emitted
mitt d as a ph
photon
t n off lilight
ht



For LEDs to emit higher
higher--energy photons,



Falling Balls 393
they must be designed to have larger band gaps
they must be supplied with larger voltage drops
Laser diodes are LEDs that can amplify light.
Falling Balls 394
Summary about Lasers and LEDs




Lasers produce coherent light by amplification
Coherent light contains many identical photons
Laser amplifiers and oscillators are common
LEDs are incoherent, lightlight-emitting diodes
Falling Balls 395
Cameras
Falling Balls 396
Observations about Cameras





They record a scene on an image sensor
Good cameras need focusing, cheap ones don’t
Many cameras have zoom lenses
Some cameras have bigger lenses than others
They have ratings like focal length and ff-number
6 Questions about Cameras






Why does a camera need a lens?
Why do most camera lenses need focusing?
Why are lenses telephoto or widewide-angle?
Why do fancy lens’s have internal apertures?
Why is a good camera lens so complex inside?
How does the image sensor respond to light?
66
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Falling Balls 398
Question 1

Why does a camera need a lens?
Light from an Object

An illuminated object reflects or scatters light
You see the object via reflected or scattered light
The object’s light produces diffuse illumination
 You
Y can’t
n’t tell
t ll what
h t the
th object
bj t looks
l k like
lik fr
from
m thi
this
diffuse illumination


Falling Balls 399
Falling Balls 400
Converging Lenses

A converging lens bends light rays via refraction
Real Images

Light rays that were spreading now converge
 Rays from a common point on an object converge
to a common point on the far side of the lens
Falling Balls 401

Falling Balls 402
Question 2

An image forms in space on far side of the lens
The image is a pattern of light in space that exactly
resembles the object, except for size and orientation
 The image is “real”
real – you can put your hand in it

Why do most camera lenses need focusing?
Lenses and Image Sensor



The sensor records the pattern of light it receives
If you put the sensor in a real image, it will record
a pattern of light that looks just like the object
F a goodd photograph,
For
h
h the
h reall iimage should
h ld b
be
sharply focused on the image sensor and its size
should match
the image sensor.
67
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Falling Balls 404
Focusing

The farther the object,
Lens Diameter and Focusing

the less diverging its light as that light enters the lens
 the more converging that light after it leaves the lens
 and
nd the
th nearer
n r r to
t the
th lens
l n the
th real
r l im
image fforms.
rm


Different objects form real
images at different distances
from the lens.
Lens--toLens
to-sensor distance must
match lenslens-toto-image distance.
Falling Balls 405
Larger lens gathers more light
so the image is brighter
but focus is more critical
 and
nd there
th r iis lless ddepth
pth off ffocus.




Smaller lens gathers less light
so the image is dimmer
but focus is less critical
 and there is more depth of focus.


Falling Balls 406
Question 3

Why are lenses telephoto or widewide-angle?
Focal Length

Focal length measures lens’s converging ability
Long focal length: weak lens, long image distance
Short focal length: strong lens, short image distance
 Behavior
B h i r accurately
r t l ddescribed
rib d b
by th
the llens
n equation:
q ti n


1
1
1


Object distance Image distance Focal length

Larger image distance, then bigger image


Falling Balls 407
Falling Balls 408
Wide Angle vs Telephoto

Wide--angle lens converges rays strongly,
Wide
Long focal length: big dim image
Short focal length: small bright image
Question 4

Why do fancy lenses have internal apertures?
so they focus close to the lens
 and form a bright, small image near the lens.
 Small
Sm ll diameter
di m t r lenses
l n are
r usually
ll adequate.
d q t


Telephoto lens converges rays weakly,
so they focus far from the lens
and form a dim, large image far from lens.
 Large diameter lenses are usually necessary.


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Falling Balls 410
Aperture or ff-number

f-number is focal length over lens diameter

A large ff--number lens produces a dim image

A small ff-number lens produces a bright image

Fancy lenses have adjustable ff-numbers,



Why is a good camera lens so complex inside?
and characterizes the brightness of the image.


Question 5
with
i h a llarge ddepth
h off fi
field/focus
ld/f
(focus
(f
iis fforgiving).
i i )
with a small depth of field/focus (focus is critical).
to control both image brightness and depth of focus.
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Falling Balls 412
Lens Flaws

Dispersion  different colors focus differently



Reflections  fogg in photographic
p
g p images
g




Use low
low--dispersion glass (fluoride glasses)
Use multi
multi--piece lenses or “achromats”
Zoom Lenses



Use antireflection coatings
Spherical aberration  imperfect focus
Poor focusing off axis  coma distortions
Spherical focus projected on flat film  Astigmatism

A zoom lens typically has three images overall
Its first lens group produces the first image
Its second and third lens
groups project
j a resized
i d
real image onto the
image sensor.
Use aspheric lenses
Falling Balls 413
Falling Balls 414
Question 6

How does the image sensor respond to light?
Black and White Film

Light exposure creates a latent image
Silver bromide grains absorb photons (a silver salt)
Photon energy separates salt into silver and bromine
 If a 4 atom
t
silver
il cluster
l t forms
f
 grain
i will
ill develop
d l p
 Gold sensitization lowers threshold to 2 silver atoms





Development turns exposed salt grains to silver
Silver particle is misshapen and appears black
Film forms a negative image of exposing object
69
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Falling Balls 416
Color Film

Sensitizers and filters yield three latent images
Sensitizers and filters are built into the film
 Latent images are sandwiched together in the film
 Layers
L r rrecord
rd rred,
d green,
r n and
nd bl
blue lilight
ht rrespectively
p ti l


During development, colored dyes are produced
Spent developer causes dye molecules to form
 Red : cyan, blue : yellow, green : magenta


Digital Cameras






Instead of film, use CCD imaging chip
Chip is divided into tiny squares or pixels
Each photon causes a charge transfer in its pixel
After exposure, the pixels retain a charge image
Charge is shifted out of pixels using MOSFETs
Camera obtains and saves image
Dyes form a negative image of exposing object
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Falling Balls 418
Summary about Cameras




They use converging lenses to form real images
Lens focal length sets image size
Lens ff-number sets image brightness
The image sensor records the pattern of light
Falling Balls 419
Observations about Optical
Recording and Communications





Optical disks can store lots of audio or video
That audio or video is of the highest quality
Optical disks continue to play perfectly for years
Playback of optical disks involves lasers
Lasers and fibers are used in communication
Optical Recording and
Communications
Falling Balls 420
5 Questions about Optical Recording
and Communication





How is information represented digitally?
How is information recorded on an optical disk?
How is information read from an optical disk?
How can light carry information long distances?
Why does light follow an optical fiber’s bends?
70
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Falling Balls 422
Question 1

How is information represented digitally?
Review of Digital Representation


Audio or video info is a sequence of numbers
Each number can be represented digitally
by putting specific symbols in a set of digits.
Digital representations often involve binary digits,
digits
 which can each hold only two symbols: 0 and 1.
 Each symbol is a discrete value of a physical quantity



Digital representations have


Falling Balls 423
good noisenoise-immunity
and permit error correction (elimination of noise).
Falling Balls 424
Digital Audio


The air pressure in sound
is measured thousands of
times per second
Each meas
measurement
rement is
represented digitally using
about 16 binary digits,
each a 0 or a 1.
Falling Balls 425
Question 2

Falling Balls 426
Structure of CDs and DVDs




These disks have spiral tracks in reflective layers
Each track contains pits and flats
Digital symbols consist of the
l
lengths
h off the
h pits
i and
d fl
flats
The track structure is made as
small as can be detected by the
playback system, so as to maximize
the density of information.
How is information recorded on an optical disk?
Question 3

How is information read from an optical disk?
71
Falling Balls 427
Falling Balls 428
Playback Techniques




Laser light is focused on the shiny layer
Reflection is weaker from a pit than from a flat
Reflected light is directed to photodiodes
Reflected light intensity
indicates pits or flats
Playback Issues

Light must hit pits perfectly


Light must hit only one pit



Feedback optimizes the position of the light spot
U llaser lilight—
Use
light
h —a single
i l wave
Use a converging lens to focus that wave to a spot
The wave forms a “waist”—
“waist”—its minimum width
Wave limits on focusing are known as diffraction
Waist can’t be much smaller than a wavelength
 so pit size can’t be much smaller than a wavelength.


Falling Balls 429
Falling Balls 430
Advantages of Digital Recording

Freedom from noise and media damage issues
Question 4

How can light carry information long distances?
Digital representation avoids information loss
 Error correction ensures clean information
 Surface
S rf contamination
nt min ti n ddoesn’t
n’t matter
m tt r (much)
(m h)




High information density
Data compression is possible
Perfect, loss
loss--less copies are possible
Falling Balls 431
Falling Balls 432
Optical Communication


Both analog and digital representations possible
Analog representation



often involves AM modulation of the light
andd is
i often
f usedd for
f remote process monitoring.
i i
Digital representation
Transmission Techniques

Light in air: direct lineline-ofof-sight



Infrared remote controls
Infrared computer links
Li h in
Light
i optical
i l fibers:
fib
arbitrary
bi
paths
h

Optical cables and networks
often uses pulses with discrete amplitudes as symbols
 and provides noisenoise-immunity, error correction,
compression, and channelchannel-sharing.

72
Falling Balls 433
The Components of Optical
Communications

Transmitters




Question 5

Why does light follow an optical fiber’s bends?
Incandescent lamps (poor performance)
Light Emitting Diodes (adequate performance)
Laser Diodes (high performance)
Receivers



Falling Balls 434
Photoresistive cells (poor performance)
Photodiodes (high performance)
Conduits

Optical Fibers (ranging from poor to high performance)
Falling Balls 435
Falling Balls 436
Total Internal Reflection



As light enters a material with a lower index of
refraction, it bends away from the perpendicular
If that bend exceeds 90°
90°,
the light reflects instead
That reflection is perfect:
total internal reflection
Optical Fibers




Falling Balls 437
Falling Balls 438
Communication Issues




Those symbols are usually pulses of light
If pulses spread out and overlap, information is lost
T keep
To
k
pulses
l from
f
spreading
di in
i time
i


Optical Fiber Types
Information is sent as a stream of digital symbols


An optical fiber consists of a high
high--index glass
core in a lowlow-index glass sheath
When light tries to leave the core at a shallow
angle it experiences total internal reflection
angle,
Light bounces endlessly through the core and
emerges from the end of the fiber
If the glass is pure and perfect enough, the light
may travel for many kilometers through the fiber
all the light must follow a single path through fiber
all frequencies of light must travel at the same speed
The fiber’s structure and materials are critical
To limit possible paths, use a “single mode” fiber
73
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Falling Balls 440
Summary about Optical Recording
and Communication
Communication Issues

To limit frequencyfrequency-related spreading of pulses
minimize dispersion with monochromatic laser light
 in low
low--dispersion glass at its optimal wavelength.


Si
Since
lilight
h attenuates as iit passes through
h
h fib
fiber




use lowlow-loss glass
 and amplify the light periodically,
 using fiber laser amplifiers.
Optical disks store information as pits and flats
Focused laser light reads that information
Digital representations allow perfect playback
Optical fibers carry information as light


Systems using different colors can share a fiber!
Falling Balls 441
Falling Balls 442

Nuclear Weapons




Falling Balls 443



3 Questions about
Nuclear Weapons
Where is nuclear energy stored in atoms?
Why are some atomic nuclei unstable?
How does a nuclear chain reaction work?
Observations about
Nuclear Weapons
They release enormous amounts of energy
They produce incredible temperatures
They produce radioactive fallout
They are relatively difficult to make
They use chain reactions
Falling Balls 444
Question 1

Where is nuclear energy stored in atoms?
74
Falling Balls 445
Falling Balls 446
Atomic Nuclei

Atoms are usually electrically neutral
Structure of Nucleus

They must have as many + charges as – charges
 Each electron must be matched by a + charge


A the
At
h center off an atom iis iits nucleus
l
Extremely small (1/100,000th of atom’s diameter)
 Contains most of the atom’s mass
 Also contains most of the atom’s potential energy





Evidence is related to: E=mc2
Falling Balls 447
Nucleus contains two kinds of nucleons
T forces
Two
f
are active
i in
i a nucleus
l




Protons are positively charged
Neutrons are electrically neutral
Electrostatic repulsion between protons
Nuclear force attraction between touching nucleons
At short distances, the nuclear force dominates
At long distances, the electric force dominates
Falling Balls 448
Question 2

Why are some atomic nuclei unstable?
Nuclear Stability





Falling Balls 449
Falling Balls 450
Radioactivity

The nucleons in a nucleus are in equilibrium
To be classically stable, that equilibrium must be stable
To be quantumquantum-mechanically stable, that equilibrium
must
ust also
a so be the
t e overall
ove a potential
pote t a energy
e e gy minimum
u
Quantum mechanics and the Heisenberg uncertainty
principle allow the nucleons to “try out” arrangements
that are quite different from their equilibrium positions
If they find a path to a new, lowerlower-potential
potential--energy
equilibrium, the nucleus may fall apart
Large nuclei have two possible problems:
Question 3

How does a nuclear chain reaction work?
Too many protons: too much electrostatic potential
 Too many neutrons: isolated neutrons are unstable




Balance
B
l
between
b
protons and
d neutrons iis tricky
i k
Large nuclei tend to fall apart spontaneously
These breakups are known as radioactive decay

and can include a splitting process called fission
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Falling Balls 452
Induced Fission

A large nucleus can break when struck
Collision knocks its nucleons
out of stable equilibrium
 Collision
Collision--altered nucleus
may undergo induced fission
 Since a neutron isn’t repelled
by nucleus, it makes an ideal
projectile for inducing fission
Chain Reaction


Falling Balls 453
Since neutrons can induce fission



and induced fission releases neutrons,
this cycle can repeat,
a chain reaction!
Each fission releases energy
Many fissions release
prodigious amounts of energy
 Sudden energy release
produces immense explosion

Falling Balls 454
Requirement for a Bomb

A fission bomb requires 4 things:
An initial neutron source
a fissionable material (undergoes induced fission)
 each
h fi
fission
i nm
mustt release
r l
additional
dditi n l n
neutrons
tr n
 material must use fissions efficiently (critical mass)
The Gadget & Fat Man



 235U


Each of these fission bombs started as a 239Pu
sphere below critical mass (6 kg)
It was crushed explosively to supercritical mass
and
d promptly
l underwent
d
an explosive chain reaction.
and 239Pu are both fissionable materials,
but 235U is rare and must be separated from 238U
 and 239Pu is made by exposing 238U to neutrons.

Falling Balls 455
Falling Balls 456
Little Boy



This bomb started as a 235U hollow sphere
below critical mass (60 kg)
A cannon fired a 235U plug through that sphere
so that it exceeded critical mass
and it promptly
underwent an
explosive chain
reaction.





Summary about
Nuclear Weapons
Nuclear energy is stored in atomic nuclei
Nuclear fission released electrostatic potential
Each fission releases an astonishing energy
Induced fission permits a chain reaction
Fission bombs explode via a chain reaction
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Falling Balls 458

Nuclear Reactors




Falling Balls 459




4 Questions about
Nuclear Reactors
How can a nuclear reactor use natural uranium?
How do thermal fission reactors work?
How can a fission chain reaction be controlled?
How can a nuclear reactor be made safe?
Falling Balls 461
Question 1

Uranium--235 (235U) is
Uranium
radioactive – fissions and emits neutrons
 fissionable – breaks when hit by neutrons
 a rare
r r fr
fraction
ti n off n
natural
t r l uranium
r ni m (0
(0.72%)
72%)
Uranium--238 (238U) is
Uranium
radioactive – emits helium nuclei, some fissions
nonfissionable – absorbs fast neutrons without fission
 a common fraction of natural uranium (99.27%)

How can a nuclear reactor use natural uranium?
Falling Balls 462
Problem with Natural Uranium

Fissioning uranium nuclei emit fast neutrons
Fast neutrons can fission 235U,
 but fast neutrons are strongly absorbed by 238U.


They provide enormous amounts of energy
They consume nuclear fuel
They produce radioactive waste
Their nuclear fuel can be reprocessed
They have safety issues
Falling Balls 460
About Uranium

Observations about
Nuclear Reactors


N
Natural
l uranium
i
contains mostly 238U, with some 235U,
 so chain reactions won’t work in natural uranium


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Falling Balls 464
Thermal Neutrons

Fission neutrons can be slowed to thermal speeds
Question 2

How do thermal fission reactors work?
Slow neutrons can fission 235U,
 but slow neutrons don’t interact with 238U.



A 235U chain
h i reaction
i can occur iin naturall
uranium if its neutrons are slowed by a moderator
Moderator nuclei


are small nuclei that don’t absorb colliding neutrons
but extract energy and momentum from the neutrons
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Falling Balls 466
Thermal Fission Reactors





Reactor core contains large amount of uranium
Uranium is natural or slightly enriched
Moderator is interspersed throughout core
Moderator slows neutrons to thermal speeds
Nuclear chain reaction occurs only among 235U
Choosing Moderators

Hydrogen nuclei (protons)
Good mass match with neutrons
Excellent energy and momentum transfer
 Slight
Sli ht possibility
p ibilit off absorbing
b rbin neutron
n tr n



Deuterium nuclei (heavy hydrogen isotope)
Decent mass match with neutron
Good energy and momentum transfer
 No absorption of neutrons


Falling Balls 467
Falling Balls 468
More about Moderators

Carbon
Question 3

How can a fission chain reaction be controlled?
Adequate mass match with neutron
 Adequate energy and momentum transfer
 Little
Littl absorption
b rpti n off neutrons
n tr n


Choosing a moderator
Deuterium is best, but it’s rare (used as water)
Hydrogen is next best (used as heavy water)
 Carbon is acceptable and a convenient solid


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Falling Balls 470
Thermal Fission Chain Reaction

Critical mass is governed by
Controlling Chain Reactions (Part 1)

size and structure of reactor core
 type of nuclear fuel (extent of 235U enrichment)
 location
l ti n and
nd quality
q lit off moderator
m d r t r
 positions of neutronneutron-absorbing control rods
Critical mass governs chain reaction rate
Below it, fission rate diminish with each generation
Above it, fission rate increases with each generation
 Generation
G n r ti n rrate
t off pr
prompt
mpt n
neutrons
tr n iis very
r short
h rt
 Controlling prompt
prompt--neutron fission is difficult!




Delayed neutrons make reaction controllable
Some fissions produce short
short--lived radioactive nuclei
These radioactive nuclei emit neutrons after a while
 Delayed neutrons contribute to the chain reactions


Falling Balls 471
Falling Balls 472
Controlling Chain Reactions (Part 2)

There are two different critical masses
Using Nuclear Reactors

Prompt critical: prompt neutrons sustain chain reaction
 Delayed critical: prompt and delayed neutrons required





R
Reactors
operate

Nuclear reactor releases thermal power
Fissions release thermal energy in the reactor core
That thermal energy is extracted by a coolant
 The
Th coolant
l nt is
i usedd to
t power
p
r a heat
h t engine
n in
 That heat engine produces electrical power

Below prompt critical mass
Above delayed critical mass
Control rods govern the fission rate
Falling Balls 473
Falling Balls 474
Question 4

How can a nuclear reactor be made safe?
Long Term Safety Issues

Fission reactors produce


radioactive nuclei (from fissions)
plutonium (from neutron capture by 238U)

R di
Radioactive
i nuclei
l i are a radiation
di i h
hazard
d

Plutonium is a nuclear proliferation hazard



They must be sequestered securely for eons
It can be used as a nuclear fuel in reactors
but it can also be used in weapons.
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Falling Balls 476
Short Term Safety Issues

To avoid catastrophes,
chain reactions must never get out of control
 reactors must never overheat
Nuclear Accidents




stable—chain reaction stops if overheating occurs
stable—
 redundant
redundant—
—no single failure can cause a disaster
 easy to quench—
quench—chain reaction stops immediately
Three Mile Island (US)

Chernobyl Reactor 4 (USSR)




Cooling
C li pump ffailed
il d and
d core overheated
h
d ((while
hil off)
ff)
Coolant boiled in overmoderated graphite reactor
Exceeded prompt critical and partially vaporized
Tokia--mura Accident (Japan)
Tokia

Falling Balls 477
Carbon moderator burned while being annealed

R
Reactors
must b
be ddesigned
i d so that
h they
h are

Windscale Pile 1 (Britain)
Critical mass was reached while processing uranium
Falling Balls 478
Summary about Nuclear Reactors




They can use natural or slightly enriched uranium
They slow fission neutrons using a moderator
They control the chain reaction carefully
They produce radioactive waste and plutonium
Falling Balls 479
Observations About
Medical Imaging and Radiation






They manage to work right through your skin
Imaging involves radiation of various sorts
Some imaging radiation is itself hazardous
Radiation can make you well, sick, or neither
Some radiation involves radioactivity
Some radiation involves accelerators
Medical Imaging and
Radiation
Falling Balls 480
5 Questions about Medical Imaging
and Radiation





How are XX-rays produced?
Why do XX-rays image bones rather than tissue?
How does CT scanning create a 3D image?
How do gammagamma-rays kill cancerous tissue?
Why does MRI image tissue, not bone?
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Falling Balls 482
Question 1

How are XX-rays produced?
X-rays


Are short
short--wavelength electromagnetic waves
Each XX-ray photon has a large amount of energy,



X-rays are produced by very energetic events,


Falling Balls 483
enough to do severe chemical damage to molecules
or to knock
k k particles
i l out off atoms.
such as rapid electron acceleration near a nucleus
or a radiative transition in a highly excited atom.
Falling Balls 484
Bremsstrahlung XX-rays

When a fast
fast--moving electron whips around a
massive nucleus,


Characteristic XX-rays

that electron accelerates rapidly
and may emit much of its energy as an XX-ray photon
photon.
Falling Balls 485
it may knock an electron out of a
tightly bound orbital
 and leave the atom (now an ion) in
a highhigh-energy state.
 That atom then undergoes
a radiative transition to a
lower--energy state
lower
 and emits an XX-ray photon.

Falling Balls 486
Producing XX-rays




When a fast
fast--moving electron hits a massive
nucleus,
Accelerate electrons to 10kV - 100kV
Let electrons hit heavy atoms
Some XX-rays emitted via bremsstrahlung and
some as characteristic
h
i i X
X--rays
An XX-ray tube filters away
the lowest energy photons,
because they’re useless
and cause skin burns.
Question 2

Why do XX-rays image bones rather than tissue?
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Falling Balls 488
X-rays and Matter

X-rays interact with atoms via
Photoelectric Effect

Rayleigh scattering
 Photoelectric effect


R l i h scattering
Rayleigh
i iis what
h makes
k the
h sky
k bl
blue
An atom temporarily
absorbs a photon and
then reemits it
 This “scattered” photon
travels in a new direction


Falling Balls 489

In this effect, an XX-ray causes
a radiative transition that ejects
an electron from an atom
The ejected electron
electron’ss energy
is the difference between the
X-ray photon’s energy and the energy needed to
remove the electron from the atom
Effect is strongest when ejected electron energy
is low, so it requires atoms with manymany-electrons
Falling Balls 490
X-ray Imaging

An atom that blocks XX-rays casts a shadow
Question 3

How does CT scanning create a 3D image?
Many-electron atoms produce strong shadows
Many Few
Few--electron atoms cast essentially no shadows



X-ray imaging
i
i observes
b
shadows
h d
off llarge atoms
Unfortunately, all atoms Rayleigh scatter XX-rays,
causing a distracting haze
 that can be filtered away by collimating structures.

Falling Balls 491
Falling Balls 492
CT Scanning

Many separate XX-ray images
are used to produce CT database



Question 4

How do gammagamma-rays kill cancerous tissue?
X-rays from different angles mix
shadows differently
Computer can recreate original
3-D by analyzing database
Computer typically plots
cross sections of the body
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Falling Balls 494
Gamma Rays


Gamma-rays are extremely high energy photons
GammaThey are produced by


radiative transitions within atomic nuclei and
particle
i l accelerators
l
(high
(high(hi h-energy bremsstrahlung
b
bremsstrahlung).
hl ).
)
Falling Balls 495
Gamma--rays and Matter
Gamma

Gamma rays interact with individual charges



via Compton scattering (electron(electron-photon collisions)
and electronelectron-positron pair production.
“P i production”
“Pair
d i ” is
i the
h
conversion of energy
(a photon) into matter
(an electron and
an anti
anti--electron).
Falling Balls 496
Radiation Therapy

Gamma rays are highly penetrating in tissue



Why does MRI image tissue, not bone?
Little Rayleigh scattering and photoelectric effect
Gamma ray events are Compton or Pair Prod,



Question 5
each
h off which
hi h ddamages many molecules
l l
and often kills cells.
Approaching tumors from many angles
minimizes collateral damage to healthy tissue
Falling Balls 497
Falling Balls 498
MRI Imaging (Part 1)

Nuclear Magnetic Resonance (NMR)
Hydrogen nuclei are protons
 Protons are magnetic—
magnetic—they are tiny dipole magnets
 Because of q
quantum physics,
p y , protons
p
have onlyy two
observable orientations: “spin“spin-up” and “spin“spin-down.”
 In a magnetic field, spinspin-up and spinspin-down protons
have different energies
 A radioradio-wave photon with the correct frequency (and
thus the correct energy) can flip a proton’s spin.
MRI Imaging (Part 2)

Magnetic resonance imaging is based on NMR
The person enters a carefully designed magnetic field
That magnetic field varies slightly with location
 The radioradio-wave frequency
q
y needed to flip
p a proton
p
depends on that proton’s exact location (and field).
 Using complicated magnetic fields and radioradio-wave
pulses, you can image a person’s hydrogen atoms.




MRI images hydrogen and its tissue environment.
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Falling Balls 499
Summary about Medical Imaging
and Radiation




X-rays and gammagamma-rays are high energy photons
X-rays scatter from heavy atoms, for imaging.
Gamma--rays disrupt cells, for therapy.
Gamma
MRI detects and locates hydrogen nuclei.
84