Skating 1
Skating 2
Observations about Skating

Skating
When you’re at rest on a level surface,



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
Skating 3
1.
2.
3.
4.
Skating 4
4 Questions about Skating
Question 1
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?
Q: Why does a stationary skater remain stationary?
A: A body at rest tends to remain at rest
Skating 5
This observed behavior is known as inertia
Skating 6
Question 2
Q: Why does a moving skater continue moving?
A: A body in motion tends to remain in motion
This behavior is the second half of inertia
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.
Note that a motionless object obeys this law!
1
Skating 7
Skating 8
Question 3
Q: Why does a skater need ice or wheels to skate?
A: RealReal-world complications usually mask inertia
Physical Quantities
1. Position – an object’s location
2. Velocity – its change in position with time
Solution: minimize or overwhelm complications
p


To observe inertia, therefore,

work on level ground (minimize gravity’s effects)
 use wheels, ice, or air support (minimize friction)
 work fast (overwhelm friction and air resistance)

Skating 9
Both are vector quantities:

Position is distance and direction from a reference
Velocity is speed and direction of motion
Skating 10
Newton’s First Law (Version 2)
An object that is free of external influences moves
at a constant velocity.
Physical Quantities
3. Force – a push or a pull

N that
Note
h a motionless
i l object
bj iis ““moving”
i ” at
a constant velocity of zero!
Skating 11
Force is another vector quantity:


the amount and direction of the push or pull
Net force is the vector sum of all forces on an object
Skating 12
Newton’s First Law
An object that is not subject to any outside forces
moves at a constant velocity.
Question 4
Q: How does a skater start or stop moving?
A: A net force causes the skater to accelerate
accelerate!!
4. Acceleration – change in velocity with time
5. Mass – measure of object’s inertia

Acceleration is yet another vector quantity:

the rate and direction of the change in velocity
2
Skating 13
Skating 14
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 
Traditional form:
About Units

Position → m (meters)
Velocity → m/s (meters
(meters--perper-second)
2
 Acceleration
A l r ti n → m/
m/s (meters
(
(meters-perper-secondd2)
 Force → N (newtons)
 Mass → kg (kilograms)


net force
mass
net force = mass  acceleration
F = ma
Skating 15
SI or “metric” units:

Newton’s second law relates the units:
1 N (net force)
1 m/s 2 (acceleration) 
1 kg (mass)
Skating 16
Summary about Skating


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


When you experience external forces


You accelerate – you move at a changing velocity
Acceleration depends on force and mass
Turn off all electronic devices
Skating 17
Skating 18
Observations about Falling Balls

When you drop a ball, it
begins at rest, but acquires downward speed
 covers more and more distance each second


Wh you tossed
When
d a ball
b ll straight
i h up, iit
rises to a certain height
 comes momentarily to a stop
 and then descends, much like a dropped ball


5 Questions about Falling Balls
1.
2.
3.
4.
5.
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?
A thrown ball travels in an arc
3
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Skating 20
Question 1
Q: Why does a dropped ball fall downward?
A: Earth’s gravity exerts a force on the ball



That force is the ball’s weight
That weight points toward earth’s center
Its weight causes the falling ball to accelerate
downward—
downward
—toward earth’s center
Skating 21
Question 2
Q: Do different balls fall at different rates?
A: No, they all fall together!
A ball’s weight is proportional to its mass:
weight of ball
newtons
 9.8
mass of ball
kilogram
Their ratio is called “the acceleration due to gravity”
Skating 22
Acceleration Due to Gravity



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
kilogram
second 2
On earth’s surface, all falling balls accelerate
downward at 9.8 meter/second2
Skating 23
Question 3
Q: Would a ball fall differently on the moon?
A: Yes!
Moon’s acceleration due to gravity is 1.6
Skating 24
Question 4
Q: Can a ball move upward and still be falling?
A: Yes!
A falling ball experiences only its weight


meters
second 2
Its acceleration is constant and downward
Its velocity increases in the downward direction
Falling Downward

When dropped from rest,
ball’s velocity starts at zero
and increases downward
 ball
ball’ss altitude decreases at
an ever faster rate

Ball’s initial velocity can be anything, even upward!
4
Skating 25
Skating 26
Falling Upward First

When thrown upward,
ball’s velocity starts upward
but increases downward
 ball
ball’ss altitude increases at an
ever slower rate until…
 velocity is momentarily zero
 then ball falls downward…

Question 5
Q: Does a ball’s horizontal motion affect its fall?
A: No. Ball falls vertically, but coasts horizontally.




Skating 27
Ball’s acceleration is
purely vertical (downward)
It falls vertically
It coasts horizontally
Its path is a parabolic arc
Skating 28
Summary About Falling Balls


Without gravity, an isolated ball would coast
With gravity, an isolated ball
Ramps
experiences its weight,
 accelerates
l
d
downward,
d
 and its velocity becomes increasingly downward



Whether going up or down, it’s still falling
It can coast horizontally while falling vertically
Turn off all electronic devices
Skating 29
Skating 30
Observations About Ramps




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
4 Questions about Ramps
1.
2.
3.
4.
Why doesn’t a cart fall through a sidewalk?
How does the sidewalk know how hard to push?
Why is it easy to push the cart up the ramp?
What physical quantity is the same for any ramp?
5
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Skating 32
Question 1
Question 2
Q: Why doesn’t a cart fall through a sidewalk?
A: The sidewalk pushes up on it and supports it
Q: How does the sidewalk know how hard to push?
A: The sidewalk and cart negotiate
Sidewalk and cart cannot occupy the same space
Sidewalk exerts a support force on cart that
The cart and sidewalk dent one another slightly
prevents cart from penetrating sidewalk’s surface
acts perpendicular to sidewalk’s surface → upward
 balances cart’s downward weight


Skating 33
the more they dent, the harder they push apart
cart accelerates up or down in response to net force
 cart bounces up and down during this negotiation


Cart comes to rest at equilibrium—
equilibrium—zero net force
Skating 34
Newton’s Third Law
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.
Skating 35
Misconception Alert
The forces two objects exert on one another must
be equal and opposite, but each force of that
Newton’s third law pair is exerted on a different
object so those forces do not cancel one another
object,
another.
Skating 36
The Cart and Sidewalk Negotiate
If the cart and sidewalk dent one another too much,
each one pushes the other away strongly
 they accelerate away from one another

Question 3
Q: Why is it easy to push the cart up the ramp?
A: The ramp supports most of the cart’s weight
support force
If the
h cart andd sidewalk
id lk dent
d one another
h too little,
li l


each one pushes the other away weakly (or not at all)
they accelerate toward one another
If the cart and sidewalk dent one another just right,

cart is in equilibrium (zero net force)
ramp force (vector sum)
weight
Net force on cart is the ramp force, which is small
6
Skating 37
Skating 38
Pushing the Cart up the Ramp
To start the cart moving uphill
push cart uphill more than the downhill ramp force
 net force is uphill, so cart accelerates uphill

Question 4
Q: What physical quantity is the same for any ramp?
A: The work you do lifting the cart a certain height
T keep
To
k
the
h cart moving
i uphill
hill
work = force · distance
push cart uphill just enough to balance ramp force
 cart continues uphill at constant velocity

To stop the cart moving uphill,
push cart uphill less than the downhill ramp force
 net force is downhill, so cart accelerates downhill

Skating 39
(where force and distance are in same direction)
For a steep ramp:
work = Force · Distance
For a shallow ramp:
work = Force · Distance
Skating 40
Energy and Work

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
Transfers of Energy



Energy has two principal forms



Work – mechanical means of transferring energy
work = force · distance
Kinetic energy – energy of motion
Potential energy – energy stored in forces
Y
Your
workk transfers
f energy from
f
you to the
h cart


Your chemical potential energy decreases
Cart’s gravitational potential energy increases
(where force and distance are in same direction)
Skating 41
Skating 42
Mechanical Advantage


Mechanical advantage is doing the same work,
using a different balance of force and distance
A ramp provides mechanical advantage
Y lif
You
lift cart with
i h less
l force
f
b more distance
but
di
 Your work is independent of the ramp’s steepness

Summary about Ramps



Ramp supports most of the cart’s weight
You do work pushing the cart up the ramp
The ramp provides mechanical advantage
It allows you to push less hard
but you must push for a longer distance
 Your work is independent of ramp’s steepness


7
Skating 43
Skating 44
Observations about Seesaws

Seesaws




A balanced seesaw rocks back and forth easily
Equal--weight children balance a seesaw
Equal
Unequal--weight children don’t normally balance
Unequal
Moving heavier child inward restores balance
Sitting closer to the pivot speeds up the motion
Turn off all electronic devices
Skating 45
Skating 46
5 Questions about Seesaws
1.
2.
3.
4.
5.
6.
How does a balanced seesaw move?
Why does a seesaw need a pivot?
Why does a lone rider plummet to the ground?
Why do the riders’ weights and positions matter?
Why does distance from the pivot affect speed?
How do the riders twist each other?
Skating 47
Question 1
Q: How does a balanced seesaw move?
A: It moves at constant angular velocity
…because the seesaw has rotational inertia!
Newton’s first law of rotational motion
A rigid object that’s not wobbling and that is free of
outside torques rotates at constant angular velocity.
Skating 48
Physical Quantities
1. Angular Position – an object’s orientation
2. Angular Velocity – change in angular position with time
3. Torque – a twist or spin
Question 2
Q: Why does a seesaw need a pivot?
A: To prevent translational motion (i.e., falling)


All three are vector quantities

Pivot is placed at natural pivot—
pivot—center of mass
Pivot allows rotation,
rotation, but not translation
Ang. Pos. is angle and rotation axis from reference
 Ang. Vel. is angular speed and rotation axis
 Torque is amount and rotation axis of twist or spin

8
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Skating 50
Question 3
Physical Quantities
Q: Why does a lone rider plummet to the ground?
A: Torque on seesaw causes angular acceleration
4. Angular Acceleration – change in angular velocity with time
5. Rotational Mass – measure of rotational inertia

The weight of a lone rider produces a torque
torque = lever arm · forceperp

Angular acceleration is another vector quantity:

The rate and rotation axis of change in ang
ang.. velocity
(where the lever arm is a vector from pivot to location of force)


That torque would cause angular acceleration
Seesaw’s angular velocity would change with time
Skating 51
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.
net torque
angular acceleration =
rotational mass
Skating 52
Question 4
Q: Why do the riders’ weights and positions matter?
A: Must balance seesaw—
seesaw—zero net torque

Addingg a second rider adds a second torque
q



A rider’s torque is their weight times lever arm


Skating 53
Q: Why does distance from the pivot affect speed?
A: Moving toward the pivot reduces rotational mass
Lever arm is a vector from p
pivot to rider
Gravitation torque is proportional to lever arm
 Rotational mass is proportional to lever arm2
 Angular acceleration is proportional to 1/lever arm
Question 6
Q: What twists does each rider experience?
A: A gravitational torque and one from other rider
 Each seesaw rider experiences torques about pivot



A heavier rider should sit closer to the pivot
A lighter rider should sit farther from the pivot
Skating 54
Question 5

The two torques act in opposite directions
If net torque due to gravity is zero, seesaw is balanced
Move toward pivot → faster angular accelerations



A gravitational torque produced by rider’s weight
A torque exert by the other rider
When seesaw balances, those torques sum to zero
Riders exert equal but opposite torques
on one another
9
Skating 55
Newton’s Third Law of
Rotational Motion
For every torque that one object exerts on a second,
there is an equal but oppositely directed torque that
the second object exerts on the first.
Skating 56
Summary about Seesaws





Skating 57
Balanced seesaw: zero gravitational torque
Balanced seesaw has constant angular velocity
Net torque causes angular acceleration of seesaw
Heavier riders need smaller lever arms
Lighter riders need larger lever arms
Skating 58
Observations about Wheels

Wheels



Friction makes wheel
wheel--less objects skid to a stop
Friction can waste energy and cause wear
Wheels mitigate the effects of friction
Wheels can also propel vehicles
Turn off all electronic devices
Skating 59
Skating 60
5 Questions about Wheels
1.
2.
3.
4.
5.
Why does a wagon need wheels?
Why is sliding a box hardest at the beginning?
What happens to energy as a box skids to rest?
How do wheels help a wagon coast?
What energy does a wheel have?
Question 1
Q: Why does a wagon need wheels?
A: Friction opposes a wheel
wheel--less wagon’s motion

Frictional forces
oppose relative sliding motion of two surfaces
act along the surfaces to bring them to one velocity
 come in Newton’s third law pairs


10
Skating 61
Skating 62
Question 2
Question 3
Q: Why is sliding a box hardest at the beginning?
A: Static friction is stronger than sliding friction.
Q: What happens to energy as a box skids to rest?
A: That energy becomes thermal energy.
Static friction opposes the start of sliding
Only sliding friction wastes energy

varies in amount from zero to a maximum value
The two surfaces travel different distances
The missing work becomes thermal energy
 The surfaces also experience wear

Sliding friction opposes ongoing sliding


has a constant value proportional to support force
Static friction’s maximum exceeds sliding friction
Skating 63
Skating 64
The Many Forms of Energy


Kinetic: energy of motion
Potential: stored in forces between objects
Gravitational
M
Magnetic
i
 Electrochemical
 Nuclear

Elastic
El i
Electric
 Chemical




Question 4
Q: How do wheels help a wagon coast?
A: Wheels can eliminate sliding friction.

rollers eliminate sliding friction, but don’t recycle
simple wheels have sliding friction at their hub/axle
 combining roller bearings with wheels is ideal


Thermal energy: disorder into tiny fragments

Skating 65
Wheels & roller bearings eliminate sliding friction
Reassembling thermal energy is statistical impossible
Skating 66
Practical Wheels


Free wheels are turned
by the vehicle’s motion
Powered wheels propel
the vehicle as they turn.
turn
11
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Skating 68
Question 5
Q: What energy does a wheel have?
A: Kinetic energy, both translation and rotational.
Summary about Wheels

Sliding friction wastes energy


For a translating wheel:
1
kinetic energy   mass  speed 2
2
For a rotating wheel:
1
kinetic energy   rotational mass  angular speed 2
2
The wheel of a moving vehicle has both!
Skating 69


Wheels eliminate sliding friction
A vehicle with wheels coasts well
F wheels
Free
h l are turned
d by
b static
i friction
fi i
Powered wheels use static friction to propel car
Skating 70
Observations about Bumper Cars

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
Turn off all electronic devices
Skating 71
Skating 72
3 Questions about Bumper Cars
1.
2.
3.
Does a moving bumper car carry a force?
Does a spinning bumper car carry a torque?
How does a car accelerate on an uneven floor?
Question 1
Q: Does a moving bumper car carry a force?
A: No, the bumper car carries momentum
momentum..
Momentum is a conserved vector quantity


can’t be created or destroyed, but can be transferred
combines bumper car’s inertia and velocity
momentum = mass · velocity
12
Skating 73
Skating 74
Exchanging Momentum


Bumper cars exchange momentum via impulses
impulse = force · time
When car1 gives an impulse to car2, car2 gives an
equall but
b oppositely
i l di
directed
d iimpulse
l to car1.
Question 2
Q: Does a spinning bumper car carry a torque?
A: No, the bumper car carries angular momentum
Angular momentum is a conserved vector quantity
The total momentum doesn’t change
 Car with least mass changes velocity most,
 so the littlest riders get creamed

Skating 75
can’t be created or destroyed, but can be transferred
combines bumper car’s rotational inertia and velocity
angular momentum = rotational mass· angular velocity


Skating 76
Exchanging Angular Momentum


Bumper cars exchange angular momentum
via angular impulses
angular impulse = torque · time
When car1 gives an angular impulse to car2, car2
gives an equal but oppositely directed angular
impulse to car1.
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
The total angular momentum doesn’t change
Car with least rot. mass changes ang.
ang. velocity most.
 so the littlest riders get spun wildly


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Skating 78
Question 3
Q: How does a car accelerate on an uneven floor?
A: It reduces potential energy as quickly as possible
Summary about Bumper Cars

During collisions, bumper cars exchange



Forces and potential energies are related!
A bumper car accelerates in the direction that reduces
its total potential energy as quickly as possible
 On an uneven floor, that is down the steepest slope


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
13
Skating 79
Skating 80
Observations about Spring Scales

Spring Scales


They move downward during weighing
They take a little time to settle
They’re only accurate when everything is at rest
Turn off all electronic devices
Skating 81
Skating 82
4 Questions about Spring Scales
1.
2.
3.
4.
What exactly is a spring scale measuring?
How does a spring scale measure weight?
What is scale’s dial or meter actually reporting?
Why must you stand still on a spring scale?
Question 1
Q: What exactly is a spring scale measuring?
A: The weight of the object being weighed


The object has both a mass and a weight
On the earth’s surface, they are proportional


Skating 83
Skating 84
Mass as a Measure


An object’s mass doesn’t depend on location
Measuring an object’s mass can be done directly:
Exert a known force on the object
M
Measure
the
h object’s
bj ’ acceleration
l i
 Divide the force by the acceleration to find the mass

Object’s mass is the same everywhere
Object’s weight changes with changes in gravity
Weight as a Measure


An object’s weight depends on location (gravity)
Measuring an object’s weight is done indirectly:




Measuring acceleration accurately is difficult


The object’s weight is a force that acts on the object
Th iis no direct
There
di
way to measure that
h weight
i h
Fortunately, measuring weight indirectly is easy
Spring scales measure weight, not mass
14
Skating 85
Skating 86
Question 2
Q: How does a spring scale measure weight?
A: Measures upward force needed for equilibrium
Using a Spring to Measure Weight


Springs provide adjustable, measurable forces
Recall that when an object is at equilibrium,



Spring scale measures weight using equilibrium
Exert an upward force on the object
 Adjust that force until the object is in equilibrium
 Measure the amount of that upward force
 Report that amount as the object’s weight

Skating 87

individual forces sum to zero—
zero—they cancel perfectly.
object
bj iis iinertial—
inertial
i l—it
i remains
i motionless
i l or it
i coasts.
A spring scale
uses a spring to support the object
allows the spring and object to reach equilibrium
 reports the spring’s force as the object’s weight


Skating 88
Question 3
Hooke’s Law
Q: What is scale’s dial or meter actually reporting?
A: It’s reporting how far the spring has distorted
The restoring force on the end of a spring is equal
to a spring constant times the distance the spring
is distorted. That force is directed opposite the
distortion.
distortion


A free spring adopts its equilibrium length
When distorted, its ends experience forces that
restoring force = – spring constant · distortion
act to restore the spring to its equilibrium length
 make the equilibrium length a stable equilibrium
 are proportional to the distortion

Skating 89
Skating 90
A Spring Scale

To weigh an object with a spring scale,
support the object with a spring,
 let the object become motionless at equilibrium,
 and
nd measure
m
r the
th distortion
di t rti n off the
th spring.
prin



The spring constant relates distortion to force
Once the spring constant is calibrated,
calibrated, reporting
the spring’s distortion is equivalent to reporting
the restoring force that is supporting the object
Question 4
Q: Why must you stand still on a spring scale?
A: Scale is only accurate if you are in equilibrium

If you are not in equilibrium,

Since an accelerating object is not at equilibrium,



the spring force is unrelated to your weight
you mustn’t bounce on a scale!
you must wait for the scale to settle before reading!
15
Skating 91
Skating 92
Oscillation

When you first load a scale, it bounces
It accelerates toward a new equilibrium
 It then coasts through that equilibrium
 It then
th n accelerates
l r t b
backk ttoward
rd th
the new
n equilibrium
q ilibri m
 It returns and overshoots many times


Summary about Spring Scales




The spring stretches during weighing
This stretch is proportional to object’s weight
The scale measures the spring’s stretch
The scale reports that stretch as object’s weight
It oscillates around its stable equilibrium


To settle at equilibrium, it must get rid of energy
Friction and air resistance help it settle
Skating 93
Skating 94

Ball Sports: Bouncing



Observations about
Bouncing Balls
Some balls bounce better than others
Dropped balls don’t rebound to their full height
Balls bounce differently from different surfaces
Ball bounce differently from moving objects
Turn off all electronic devices
Skating 95
Skating 96
Question 1
4 Questions about Bouncing Balls
1.
2.
3.
4.
Why doesn’t a ball rebound to its original height?
Why does the floor’s surface affect the bounce?
How does a moving bat drive a ball forward?
What happens to the bat when a ball hits it?
Q: Why doesn’t a ball rebound to its original height?
A: It wastes some of its energy during the bounce

While slowing as it hits a rigid floor, a ball’s



While rebounding from the floor, the ball’s



kinetic energy decreases by the collision energy
elastic potential energy increases as it dents
elastic potential energy decreases as it undents
kinetic energy increases by the rebound energy
Not all collision energy becomes rebound energy
16
Skating 97
Skating 98
Measuring a Ball’s Liveliness


Two common measures of a ball’s liveliness:
rebound speed
coefficient of restitution 
collision speed
rebound
b
d energy
energy ratio 
collision energy
Question 2
Q: Why does the floor’s surface affect the bounce?
A: If the floor dents, it also receives collision energy



Since kinetic energy is proportional to speed2,
energy ratio  coefficient to frestitution


Floor also has an energy ratio that affects the bounce
Impact forces on ball & floor: equal but opposite,

2
Skating 99
The dentingg floor stores and returns energy
gy
so work done on each is proportional to its dent
fraction of collision energy is proportional to its dent
A soft, lively floor can help the ball bounce!
Skating 100
Question 3
Q: How does a moving bat drive a ball forward?
A: Ball bounces off bat, in bat’s frame of reference
 When bat and ball are moving toward one another
Ball and Bat (Part 1)



Ball heads toward home plate at 100 km/h
Bat heads toward pitcher at 100 km/h
Collision speed is 200 km/h
Collision speed is their speed of approach
 Rebound speed is their speed of separation


In the bat’s inertial frame of reference
reference,,


perspective in which bat’s center of mass is motionless,
the ball simply bounces off the bat
Skating 101
Skating 102
Ball and Bat (Part 2)



Collision speed is 200 km/h
Baseball’s coefficient of restitution: 0.55
Rebound speed is 110 km/h
Ball and Bat (Part 3)



Rebound speed is 110 km/h
Bat heads toward pitcher at 100 km/h
Ball heads toward pitcher at 210 km/h
17
Skating 103
Skating 104
Question 4
Q: What happens to the bat when a ball hits it?
A: It accelerates, angular accelerates, and vibrates
Summary about Bouncing Balls




The ball’s impact force on the bat

Each ball has a coefficient of restitution
Energy lost in a bounce becomes thermal
The bouncing surface can affect a ball’s bounce
Surfaces bounce, too
transfers momentum and angular mom to the bat
 can deform the bat, causing it to vibrate
 increases with the stiffnesses of the bat and ball
 lasts longer when the bat and ball are livelier

Skating 105
Skating 106
Observations about
Carousels and Roller Coasters
Carousels and Roller
Coasters




You can feel your motion with your eyes closed
You feel pulled in unusual directions
You sometimes feel weightless
You can become inverted without feeling it
Turn off all electronic devices
Skating 107
5 Questions about Carousels and
Roller Coasters
1.
2.
3.
4.
5.
What aspects of motion do you feel?
Why do you feel flung outward on a carousel?
Why do you feel light as a roller coaster dives?
Why do you feel heavy as a roller coaster turns?
How do you stay seated on a looploop-thethe-loop?
Skating 108
Question 1
Q: What aspects of motion do you feel?
A: You feel acceleration,
acceleration, but not velocity

This feelingg of acceleration is not a real force
It’s just a sensation caused by your body’s inertia
It’s directed opposite your acceleration
 It’s proportional to that acceleration



You feel an overall apparent weight:
weight:

feeling of real weight plus feeling of acceleration
18
Skating 109
Skating 110
The Feeling of Weight

When you are at equilibrium,
The Feeling of Acceleration

a support force balances your weight
 and that support force acts on your lower surface,
 while
hil yourr weight
i ht iis spread
pr d thr
throughout
h t yourr b
body
d


You feel internal supporting stresses
You identify these stresses as weight
Skating 111
When you are accelerating,
a support force causes your acceleration
and that support force acts on your surface,
 while
hil yourr m
mass iis spread
pr d thr
throughout
h t yourr b
body
d





You feel internal supporting stresses
You misidentify these stresses as weight
Skating 112
Question 2
Q: Why do you feel flung outward on a carousel?
A: You are accelerating inward on the carousel

Riders undergo
g uniform circular motion
They follow a circular path at constant speed
 They are accelerating toward the circle’s center
 This acceleration depends on speed and circle size

acceleration 
velocity 2
radius
Skating 113
Carousels (Part 2)

The acceleration of uniform circular motion is



A centripetal
i
l acceleration
l i
gives rise to a feeling of acceleration
that points away from the center of motion
 and is a sensation due to inertia, not a real force



This feeling is often called “centrifugal force”
Skating 114
Question 3
Q: Why do you feel light as a roller coaster dives?
A: Your feeling of acceleration is upward

a centercenter-directed or centripetal acceleration
caused by a centercenter-directed or centripetal force
As you dive down a hill,
your acceleration is downhill
your feeling of acceleration is uphill
 your apparent weight is weak and points down & back
Question 4
Q: Why do you feel heavy as a roller coaster turns?
A: Your feeling of acceleration is outward

As you turn at high speed,
your acceleration is inward
your feeling of acceleration is outward
 your apparent weight is strong and points out & down




19
Skating 115
Skating 116
Question 5
Q: How do you stay seated on a loop
loop--thethe-loop?
A: You are accelerating downward very rapidly
Choosing a Seat

As you go over cliffcliff-shaped hills,



At you arc through the top of the looploop-thethe-loop,
your acceleration is strongly downward
 your feeling of acceleration is strongly upward
 your apparent weight points upward!




Skating 117
Summary about
Carousels and Roller Coasters




Th faster
The
f
you dive
di over the
h first
fi hill,
hill


acceleration is downward
feeling of acceleration is upward
the greater the downward acceleration
the stronger the upward feeling of acceleration
First car dives slowly – weak weightlessness
Last car dives quickly – strong weightlessness!
Skating 118
You are often accelerating on these rides
You experience feelings of acceleration
Those feelings point opposite your acceleration
Your apparent weight can
Bicycles
become larger or smaller than your real weight
point at any angle
 can even point upward!


Turn off all electronic devices
Skating 119
Skating 120
Observations about Bicycles




They are hard to keep upright while stationary
They stay upright easily while moving forward
They require leaning during turns
They can usually be ridden without hands
5 Questions about Bicycles
1.
2.
3.
4.
5.
Why is a stationary tricycle so stable?
Why is stationary bicycle so unstable?
Why does a moving tricycle flip during turns?
Why must you lean a bicycle during turns?
Why can you ride a bicycle without hands?
20
Skating 121
Skating 122
Question 1
Q: Why is a stationary tricycle so stable?
A: The tricycle is in a stable equilibrium

Stable equilibrium has restoring influences


Question 2
Q: Why is stationary bicycle so unstable?
A: The bicycle is in an unstable equilibrium

Unstable equilibrium has destabilizing influences

If center of gravity is above line of support,
that tend to return tricycle to equilibrium
If center of gravity is above base of support,

its gravitational potential energy increases as it tips,
it accelerates in the direction opposite that tip,
 and it tends to return to the stable equilibrium.
its gravitational potential energy decreases as it tips,
it accelerates in the direction of that tip,
 and it tends to tip away from the unstable equilibrium.




Skating 123
that tend to tip bicycle away from equilibrium
Skating 124
Question 3
Q: Why does a moving tricycle flip during turns?
A: Inertial effects overwhelm its static stability

Duringg a turn, wheels accelerate to the inside
but upright rider is almost inertial (coasts forward),
 so tricycle and rider begin to tip.
 Restoring influences arise but they’re too weak,
 so tricycle and rider tip over.
Question 4
Q: Why must you lean a bicycle during turns?
A: To balance inertial effects with static instability








Tricycle drives out from under center of gravity
Tricycle is dynamically unstable
Skating 125
Duringg a turn, the wheels accelerate to the inside
Bicycle drives under rider’s center of gravity
Bicycle is dynamically stable
Skating 126
Question 5
Q: Why can you ride a bicycle without hands?
A: It automatically steers under center of gravity
Summary about Bicycles

Tricycles



When bicycle begins to lean, it steers because
the fork pivots to reduce total potential energy
 ground’s torque on front wheel causes precession


A forwardforward-moving bicycle that begins to tip


and leaning rider accelerates to the inside
so the rider and bicycle turn together safely.
automatically returns to its unstable equilibrium,
and thus exhibits wonderful dynamic stability

have static stability
but inertial effects can flip tricycles during turns
Bi l
Bicycles
are statically unstable
can lean during turns to avoid flipping
 automatically steer back to unstable equilibrium
 have remarkable dynamic stability


21
Skating 127
Skating 128
Observations about Rockets

Rockets





Rockets seem to ride torchtorch-like flames
Rockets can accelerate straight up
Rockets can go very fast
The flame only touches the ground initially
Rockets can apparently operate in empty space
Rockets usually fly nosenose-first
Turn off all electronic devices
Skating 129
Skating 130
6 Questions about Rockets
1.
2.
3.
4.
5.
6.
What pushes a rocket forward?
How does the rocket use gas to obtain thrust?
What keeps a rocket pointing forward?
What limits a spaceship’s speed, if anything?
Once in space, does a spaceship have a weight?
What makes a spaceship orbit the earth?
Question 1
Q: What pushes a rocket forward?
A: It’s gaseous exhaust pushes it forward


A rocket’s momentum is initiallyy zero
That momentum is redistributed during thrust
Ship pushes on fuel; fuel pushes on ship
Fuel (now exhaust) acquires backward momentum
 Ship acquires forward momentum



Rocket’s total momentum remains zero
momentum fuel  momentum ship  0
Skating 131


Skating 132
Rocket Propulsion
Question 2
The ship and fuel have opposite momentums
The ship’s final momentum is
Q: How does the rocket use gas to obtain thrust?
A: Redirects gas’s thermal motion into a directed jet
momentum ship  momentum fuel
 massfuel  velocity fuel

The greater the fuel mass and backward velocity,
the greater the ship’s forward momentum




Combustion p
produces hot, highhigh
g -p
pressure ggas
This gas speeds up in a de Laval nozzle
Gas reaches sonic speed in the nozzle’s throat
Beyond the throat, supersonic
gas expands to speed up further
22
Skating 133
Skating 134
Question 3
Q: What keeps a rocket pointing forward?
A: That depends on where the rocket is located


On the gground, a rocket needs static stabilityy
In the air, a rocket needs aerodynamic stability


Question 4
Q: What limits a spaceship’s speed, if anything?
A: The rocket’s fuel to spaceship ratio


Center of aerodynamic forces behind center of mass
In space, a spaceship is a freely rotating object
Spaceship’s
p
p ultimate speed
p
increases as


the ratio of fuel mass to ship mass increases
the fuel exhaust speed increases
If fuel were released with the rocket at rest,
Orientation governed by angular momentum
Small rockets are used to exert torques on spaceship
 Spaceship’s orientation doesn’t affect its travel

velocityship  

Skating 135
Skating 136
Ship’s Ultimate Speed

mass fuel
 velocityfuel
massship
But because rocket accelerates during thrust,
 massship  mass fuel 
velocityship   log e 
  velocityfuel

massship


Question 5
Q: Once in space, does a spaceship have a weight?
A: Yes, but less than at ground level

Earth’s acceleration due to gravity


constant for small changes in height at ground level
decreases at large altitudes
Actual weight of a spaceship at any altitude is
gravitational constant  massship  massearth
weight =
(distance between centers of ship and earth)2

Skating 137
Skating 138
Law of University Gravitation
Question 6
Two masses attract one another with gravitational
forces equal in amount to the gravitational
constant times the product of their masses, divided
by the square of their separation.
separation
Q: What makes a spaceship orbit the earth?
A: An orbiting spaceship falls, but misses the earth
force =
gravitational constant  mass1  mass 2
(distance between masses)2
23
Skating 139
Skating 140
Orbits

An object that starts with a sideways velocity
can miss the earth as it falls
 follows a trajectory called an orbit


O bi can b
Orbits
be
Minimum speed for lowlow-earth orbit





closed loops: circles and ellipses
 open arcs: parabolas and hyperbolas


Summary About Rockets


A rocket’s fuel (as exhaust) pushes it forward
Total rocket impulse is basically the product of
exhaust speed times exhaust mass
Rockets
R k can be
b stabilized
bili d aerodynamically
d
i ll
Rockets can be stabilized by thrust alone
After engine burnburn-out, spaceships can orbit
is about 28,000 km/h (17,400 mph)
requires far more thrust than merely reaching space
Skating 141
Skating 142
Observations about Balloons

Balloons



Balloons are held taut by the gases inside
Some balloon float in air while others don’t
Hot--air balloons don’t have to be sealed
Hot
Helium balloons leak even when sealed
Turn off all electronic devices
Skating 143
Skating 144
5 Questions about Balloons
1.
2.
3.
4.
5.
How does air inflate a rubber balloon?
Why doesn’t the atmosphere fall or collapse?
Why does the atmosphere push up on a balloon?
Why does a hot air balloon float in cold air?
Why does a helium balloon float in air?
Question 1
Q: How does air inflate a rubber balloon?
A: Its pressure pushes the balloon’s skin outward



Air is a ggas
gas:: individual atoms and molecules
Air has pressure
pressure:: it exerts a force on a surface
Pressure inside a balloon is greater than outside


Total pressure forces on balloon skin are outward
Balloon is held taut by those outward pressure forces
24
Skating 145
Skating 146
Air and Pressure

Air consists of individual atoms and molecules
Pressure Imbalances

Thermal energy keeps them separate and in motion
 Air particles bounce around in free fall, like tiny balls


Ai
Air particles
i l transfer
f momentum as they
h b
bounce
Each momentum transfer involves tiny forces
 A surface exposed to air experiences a force
 The force on a surface is proportional to its area
 The force per area is the air’s pressure
Balanced pressures exert no overall force



U b l
Unbalanced
d pressures exert an overallll fforce
Pressure forces on two sides of a surface don’t balance
Overall pressure force on that surface is nonnon-zero
 Imbalance pushes surface toward the lower pressure




Unbalanced pressures affect the air itself

Skating 147
Pressure forces on two sides of a surface are balanced
Overall pressure force on that surface is zero
The air is pushed toward lower pressure
Skating 148
Question 2
Q: Why doesn’t the atmosphere fall or collapse?
A: A gradient in its pressure supports its weight






Squeezing air particles more closely together
increases the air’s density:
density: its mass per volume
increases the air’s pressure:
pressure: its force per area
 increases
in r
th
the air’s
ir’ weight
i ht p
perr volume
l m


Air has a density
density:
y: it has mass p
per volume
Air’s pressure is proportional to its density
Air’s density gives it a weight per volume
The atmosphere is in equilibrium

Its density and pressure decrease with altitude
The resulting pressure imbalances support its weight
Skating 150
Skating 149

Air and Density
The Atmosphere
Question 3
Supporting its weight structures the atmosphere
Q: Why does the atmosphere push up on a balloon?
A: Its pressure gradient pushes the balloon upward
A pressure imbalance supports each layer’s weight
 Air pressure decreases with altitude, a pressure gradient
 Each
E h llayerr supports
pp rt allll off th
the air
ir above
b
it
 Net force on each layer is zero
 The atmosphere is in stable equilibrium


Because of atmospheric
p
structure, air p
pressure is
stronger near the bottom of a balloon,
weaker near the top of the balloon,
 so the air pushes up harder than it pushes down,
 and this imbalance yields an upward buoyant force



The atmosphere pushes upward on the balloon!
25
Skating 151
Skating 152
Archimedes’ Principle
A balloon immersed in a fluid experience an
upward buoyant force equal to the weight of the
fluid it displaces
Question 4
Q: Why does a hot air balloon float in cold air?
A: It weighs less than the air it displaces

As the temperature
p
of air increases, its p
particles



move faster, bounce harder, and bounce more often
contribute more to air’s pressure
A balloon filled with hot air at ordinary pressure
contains fewer particles than the air it displaces
weighs less than the air it displaces
 experiences a buoyant force that exceeds its weight


Skating 153
Skating 154
An Aside About Temperature

Air’s temperature on a conventional scale is


Air’s temperature on an absolute scale is


related to average thermal kinetic energy per particle
proportional
i l to average thermal
h
l ki
kinetic
i energy per part.
Question 5
Q: Why does a helium balloon float in air?
A: It weighs less than the air it displaces


SI unit of absolute temperature: kelvins or K
0 K is absolute zero: no thermal energy available
 Step size: 1 K step same as 1 °C step
 Room temperature is approximately 300 K

Skating 155
Compared
p
with air, the p
particles in helium ggas


A balloon filled with helium at ordinary pressure
contains as many particles as the air it displaces
weighs less than the air it displaces
 experiences a buoyant force that exceeds its weight


Skating 156
Pressure and Particle Density


Particle density:
density: particles per volume
Particles in a gas contribute equally to pressure



lower-mass particles move faster and bounce more,
lowerso allll the
h effects
ff
off particle
i l mass cancell out
Gases with equal particle densities and equal
temperatures have equal pressures
are lighter, but move faster and bounce more often
contribute just as much to pressure
The Ideal Gas Law
is a summary relationship for gases:
pressure  Boltzmann constant  particle density
 absolute temperature
It assumes perfectly independent particles
 While real gas particles aren’t perfectly independent,
this law is a good approximation for real gases.

26
Skating 157
Skating 158
Summary about Balloons



A balloon will float if its average density is less
than that of the surrounding air
A hothot-air balloon has a lower particle density
and a lower density than the surrounding
s rro nding air
A helium balloon has the same particle density
but a lower density than the surrounding air
Water Distribution
Turn off all electronic devices
Skating 159




Observations about
Water Distribution
Water is pressurized in the pipes
Higher pressure water can spray harder
Higher pressure water can spray higher
Water is often stored in tall water towers
Skating 161
Skating 160
4 Questions about Water Distr.
1.
2.
3.
4.
Why does water move through level pipes?
How can you produce pressurized water?
Where does the work you do pumping water go?
As water flows, what happens to its energy?
Skating 162
Question 1
Q: Why does water move through level pipes?
A: It accelerates toward lower pressure

Water, like all fluids, obeys
y Newton’s laws
Question 2
Q: How can you produce pressurized water?
A: Push inward on the water, using a surface

When water experiences zero net force, it coasts
 When water experiences a net force, it accelerates
 Pressure imbalances exert net forces on water
 Water accelerates toward lower pressure
To p
pressurize water, confine it and squeeze
q
As you push inward on the water,
it pushes outward on you (Newton’s third law).
 Water’s outward push is produced by its pressure,
 so the water’s pressure rises as you squeeze it harder.




Water (a liquid) is incompressible

Its volume remains constant as its pressure increases
27
Skating 163
Skating 164
Pumping Water (no gravity)

To deliver pressurized water to a pipe,
Pumping Requires Work

squeeze water to increase its pressure
 until that pressure exceeds the pressure in the pipe.
 Th
The water
t r will
ill th
then
n accelerate
l r t ttoward
rd th
the pip
pipe
 and pressurized water will flow into the pipe!




Skating 165
You do work as you pump water into the pipe
You squeeze the water inward – the force,
and the water moves inward – the distance.
 The
Th work
rk you ddo p
pumping
mpin water
t r iis:

work = pressure · volume
The pressurized water carries your work with it
We’ll call this work pressure potential energy
Skating 166
Question 3
Question 4
Q: Where does the work you do pumping water go?
A: To the water at the deliverydelivery-end of the pipe
Q: As water flows, what happens to its energy?
A: That energy is converted between several forms

Pressure p
potential energy
gy is unusual because
it’s not really stored in the pressurized water,
 it’s promised by the water’s pressure source.




In SSF, water flows alongg streamlines
Water flowing along a single streamline in SSF
has both PPE and kinetic energy (KE),
must have a constant total energy per volume,
 and obeys Bernoulli’s equation (no gravity):

In steady state flow (SSF),

which is steady flow in motionless surroundings,
surroundings,
promised energy is as good as stored energy,
 so pressure potential energy (PPE) is meaningful.

PPE
KE
Constant


Volume Volume Volume

Skating 167
Skating 168
Gravity Causes Pressure Gradients

Like air in the atmosphere, water in a pipe
has a density and a weight per volume
 has a pressure gradient when it is at equilibrium
 Its
It pressure
pr
r decreases
d r
with
ith altitude
ltit d
 That pressure gradient supports its weight


Water has gravitational potential energy (GPE)

Its GPE increases with altitude
Energy and Bernoulli (with gravity)

Water flowing along a single streamline in SSF
has PPE, KE, and GPE,
must have a constant total energy per volume,
 and
nd obeys
b Bernoulli’s
B rn lli’ equation
q ti n (with
( ith gravity)
r it )


PPE
KE
GPE
Constant



Volume Volume Volume Volume
28
Skating 169
Skating 170
Energy Transformations (part 1)

As water flows upward in a uniform pipe,
Energy Transformations (part 2)

its speed can’t change (a jam or a gap would form),
 so its gravitational potential energy increases
 and
nd its
it pressure
pr
r potential
p t nti l energy
n r ddecreases.
r

As water flows downward in a uniform pipe,



its speed can’t change,
 so its gravitational potential energy decreases
 and its pressure potential energy increases.
As water falls downward from a spout,
its pressure stays constant (atmospheric),
so its gravitational potential energy decreases
 and its kinetic energy increases.

Skating 171
As water rises upward from a fountain nozzle,
its pressure stays constant (atmospheric),
so its gravitational potential energy increases
 and
nd its
it kinetic
kin ti energy
n r decreases.
d r



Skating 172
Energy Transformations (part 3)

As water sprays horizontally from a nozzle,
its height is constant,
 so its kinetic energy increases
 and
nd its
it pressure
pr
r potential
p t nti l energy
n r ddecreases.
r


As a horizontal stream of water hits a wall,
its height is constant,
 so its kinetic energy decreases
 and its pressure potential energy increases.

Skating 173


Water’s energy remains constant during SSF
Water’s energy changes form as it
flows upward or downward inside pipes,
rises or falls in open sprays
sprays,
 and shoots out of nozzles or collides with objects.



Water distribution can driven by
pressurized water (PPE)
elevated water (GPE)
 fast
fast--moving water (KE)


Skating 174

Garden Watering
Summary about
Water Distribution





Observations about
Garden Watering
Faucets let you to control water flow
Faucets can make noise when open
Longer, thinner hoses deliver less water
Water sprays at high speed from a nozzle
Water only sprays so high
A jet of water can push things over
Turn off all electronic devices
29
Skating 175
Skating 176
Question 1
6 Questions about Garden Watering
1.
2.
3.
4.
5.
6.
How does a faucet control flow?
How much does the diameter of a hose matter?
Why does water pour gently from an open hose?
Why does water spray fast from a nozzle?
What causes hissing in a faucet, hose, or nozzle?
Why do pipes rattle when you close the faucet?
Q: How does a faucet control flow?
A: Water’s energy and viscosity limit the flow


Water traverses a narrow passage in the faucet
Total energy limits flow speed through passage



Motion near surfaces slows water in the passage


Skating 177
The water turns its total energy into kinetic energy,
but its peak speed is limited by its initial pressure
Because water at the passage walls is stationary,
viscous forces within the water slow all of it
Skating 178
Viscous Forces and Viscosity

Viscous forces
oppose relative motion within a fluid
 and are similar to sliding friction: they waste energy


Fl id are characterized
Fluids
h
i db
by their
h i viscosities
i
ii
the measure of the strength of the viscous forces
 and caused by chemical interactions within the fluids

Question 2
Q: How much does the diameter of a hose matter?
A: It matters a surprisingly large amount

Water flow through
g a hose is proportional
p p
to
pressure difference between hose ends
1/viscosity
 1/hose length
 (hose diameter)4


flow rate 
Skating 179
Q: Why does water pour gently from an open hose?
A: The free
free--flowing water wastes most of its energy
 Viscous effects in the hose


waste water’s total energy as thermal energy
and become stronger with increased flow speed
Increasing the speed of the flow in the hose


128  hose length  viscosity
Skating 180
Question 3

  pressure difference  hose diameter 4
Question 4
Q: Why does water spray fast from a nozzle?
A: The nozzle causes water to turn PPE into KE
 As water flow necks down in a nozzle, it must
speed up to avoid a “traffic jam”
have a pressure imbalance pushing it forward
 be flowing from higher pressure to lower pressure


increases the energy wasted by each portion of water
makes the loss of pressure more rapid
30
Skating 181
Skating 182
Making Water Accelerate

Even in steadysteady-state, water can accelerate
but forward acceleration would leave gaps
 and backward acceleration would cause jams,
 so the
th acceleration
l r ti n m
mustt in
involve
l tturning.
rnin
Bending the Flow in a Hose





requires obstacles,
and involves pressure imbalances
 and changes in speed.

Skating 184
Speeding the Flow in a Nozzle
Question 5
Speeding the flow requires a pressure imbalance
Q: What causes hissing in a faucet, hose, or nozzle?
A: Water can become turbulent and produce noise.


Flow in bent hose develops a pressure gradient
hi h pressure & llower speed
higher
d
on the outside of the bend
 lower pressure & higher speed
on the inside of the bend
 and water accelerates from
high pressure to lower pressure


The water accelerates toward lower pressure

Acceleration toward the side (turning)
Skating 183
Bending the flow requires a pressure imbalance
The water accelerates toward lower pressure
Flow in nozzle develops a pressure gradient
hi h pressure & llower speed
higher
d
at start of nozzle
 lower pressure & higher speed
as the nozzle narrows
 and water accelerates from
high pressure to lower pressure





in which viscosity dominates the flow’s behavior
and nearby regions of water remain nearby
Now we’ll also consider turbulent flow



Skating 185
We’ve been examiningg laminar flow
in which inertia dominates the flow’s behavior
and nearby regions of water become separated
Turbulent flow produces thermal energy
Skating 186
Reynolds Number
Question 6
The flow type depends on the Reynolds number
inertial influences
Reynolds number 
viscous influences
 obstacle
d
density
b
length  speed
d

viscosity
Q: Why do pipes rattle when you close the faucet?
A: Moving water carries momentum.



Below ~2300 viscosity wins, so flow is laminar
Above ~2300 inertia wins, so flow is turbulent


Water transfers its momentum via impulses:
p
impulse = pressure · surface area · time
Large momentum transfers require


large pressures, large surface areas, or long times.
Moving water can be surprisingly hard to stop

Sudden stops can result in enormous pressures
31
Skating 187
Skating 188
Summary about Garden Watering







Total energy limits speed, height, and pressure
Bending water flows develop pressure gradients
Nozzles exchange pressure for speed
Viscosity wastes flowing water’s total energy
Turbulence wastes flowing water’s total energy
Wasted total energy because thermal energy
Moving water has momentum, too
Balls and Air
Turn off all electronic devices
Skating 189
Skating 190
Observations about Balls and Air




Air resistance slows a ball down
The faster a ball moves, the quicker it slows
Some balls have textured surfaces to affect the air
Spinning balls curve in flight
Skating 191
4 Questions about Balls and Air
1.
2.
3.
4.
Skating 192
Question 1
Types of Aerodynamic Forces
Q: Why do balls experience air resistance?
A: Balls interact with and transfer momentum to air

When a ball moves through
g air, dragg forces arise


Air pushes ball downstream, ball pushes air upstream
 Air transfers downstream momentum to ball


Why do balls experience air resistance?
How do air flow around a ball?
Why do some balls have dimples?
Why do spinning balls curve in flight?


Surface friction causes viscous drag
Turbulence causes pressure drag
Deflected flow causes lift
Deflected flow also leads to induced drag
When a ball deflects passing air, lift forces arise


Air pushes ball to one side, ball pushes air to other side
Air transfers sideways momentum to ball
32
Skating 193
Skating 194
Question 2
Q: How does air flow around a ball?
A: That depends on Reynolds number

At low Reynolds
y
number, the flow is laminar
Only viscous forces transfer momentum to the ball
 The ball experiences only viscous drag
Laminar Flow around a Ball


At high Reynolds number, the flow is turbulent


Pressure forces also transfer momentum to the ball
The ball also experiences pressure drag
Skating 195
Air bends toward ball’s sides

Air bends away from ball’s back

Pressures on opposite sides balance perfectly
Ball experiences only viscous drag



Air flowing into the rising pressure behind ball

accelerates backward (decelerates)
 and converts kinetic energy into pressure potential.
Ai flowing
Air
fl i nearest the
h ball’s
b ll’ surface
f
also experiences viscous drag forces
 and converts kinetic energy into thermal energy.
 If it runs out of total energy, it stops or “stalls”


Q: Why do some balls have dimples?
A: To produce a turbulent boundary layer
Air affected byy ball’s surface is the boundaryy layer
y
Reynolds # <100,000: laminar boundary layer



Since wake pressure is ambient,
ball experiences unbalanced pressures.
Ball experiences a large pressure drag force
Skating 198
Question 3

Big
Bi wake
k forms
f
behind
b hi d ball
b ll


stalls beyond ball’s sides
and peels main air flow off of ball.
If air nearest the ball stalls, turbulence ensues
Skating 197

Air flowing near ball’s surface



At back: high pressure, slow flow
Turbulent Flow around Slow Ball


A side:
At
id llow pressure, ffast fl
flow
Skating 196
The Onset of Turbulence

At front: high pressure, slow flow



Air bends away from ball’s front

Sublayers tumble and interchange; they help each other
 Boundary layer penetrates deeper into rising pressure
Air flowing near ball’s surface






stalls beyond ball’s sides
and peels main air flow off of ball.
B
Boundary
d layer
l
is
i turbulent
b l

Nearest sublayer is slowed relentlessly by viscous drag
Reynolds # >100,000: turbulent boundary layer

Turbulent Flow Around Fast Ball
and retains total energy farther,
so it resists peeling better.
Small wake forms behind ball
Ball experiences a small pressure drag force
33
Skating 199
Skating 200
Tripping the Boundary Layer

To reduce pressure drag, some balls have dimples
Dimples “trips” the boundary layer
 Cause boundary layer to become turbulent.
 Turbulent
T rb l nt boundary
b nd r layer
l r resists
r i t peeling
p lin b
better
tt r
 Ball’s main airflow forms smaller turbulent wake.


Example: Golf balls
Question 4
Q: Why do spinning balls curve in flight?
A: They experience two aerodynamic lift forces

Laminar effect: Magnus
g
force



Turbulent effect: Wake deflection force


Skating 201
Turning surface pushes/pulls on the air flow
Spinning Balls, Wake Force

Air on one side makes long bend toward ball
 Air on other side makes shorter bend away from ball
 Pressures
Pr
r are
r unbalanced
nb l n d
The overall air flow is deflected



Ball pushes air to one side
 Air pushes ball to other side


Ball feels Magnus force
Skating 203
Turning surface alters point of flow separation
Flow separation is delayed on one side
and hastened on the other side,
 so wake
k is
i asymmetric
mm tri


Turning surface alters point of flow separation
Flow separation and wake are asymmetric
Skating 202
Spinning Balls, Magnus Force

Turning surface pushes/pulls on the air flow
Air on one side makes longer bend toward the ball
The overall air flow is deflected



Ball pushes air to one side
Air pushes ball to other side
Ball feels wake deflection force
Skating 204
Summary about Balls and Air






Balls in air experience aerodynamic forces
Downstream forces are drag forces
Sideways pressure forces are lift forces
Moving particles experience viscous drag forces
Moving balls experience pressure drag forces
Spinning balls experience Magnus and wake
deflection lift forces
Airplanes
Turn off all electronic devices
34
Skating 205
Skating 206
Observations about Airplanes






Airplanes use the air to support themselves
Airplanes need airspeed to stay aloft
Airplanes seem to follow their nose, up or down
Airplanes can rise only so quickly
Airplane wings often change shape in flight
Airplanes have various propulsion systems
Skating 207
6 Questions about Airplanes
1.
2.
3.
4.
5.
6.
How does an airplane support itself in the air?
How does the airplane “lift off” the runway?
Why does plane tilt up to rise; down to descend?
Why are there different wing shapes?
How does a plane turn?
How does a plane propel itself through the air?
Skating 208
Question 1
Q: How does an airplane support itself in the air?
A: It deflects air downward; air pushes it upward

Air bends awayy from wingg bottom

Air bends toward wing top

There is an upward pressure force on the wing
Wing transfers downward momentum to the air

Q: How does the airplane “lift off” the runway?
A: The airplane sheds a vortex and is lifted upward

Air pressure rises, speed drops


Question 2
Air pressure drops, speed rises
Skating 209
As wingg starts movingg in air



Trailing edge kink is unstable

After the vortex leaves, the wing experiences lift

Q: Why does plane tilt up to rise; down to descend?
A: The wing’s angle of attack affects its lift
 A wing’s lift depends on




Limits to Lift: Stalling

At too great an angle of attack,
the upper boundary layer stalls,
the airstream detaches from wing,
 the
th lift decreases
d r
dramatically,
dr m ti ll
 and severe pressure drag appears


the shape of its airfoil
its angle of attack
attack—
—its tilt relative to approaching air
Tilting an airplane’s wings affects lift

and the wing sheds a vortex
Skating 210
Question 3

the airflow is symmetric
and the wing experiences no lift

Plane plummets abruptly
Can make the airplane accelerate up or down
Usually requires tilting the airplane’s fuselage
Plane’s tilt controls lift, not direction of travel
35
Skating 212
Skating 211
Question 4
Q: Why are there different wing shapes?
A: Airspeed and performance influence wing design

Asymmetric
y
airfoils produce
p
large
g lifts


Q: How does a plane turn?
A: It uses lift to accelerate in the direction of turn

Are well suited to lowlow-speed flight

Are well suited to highhigh-speed flight
Allow plane to fly inverted easily
Some planes change wing shape in flight
Skating 213
Airplane
p
has three orientation controls:
Its angle of attack is controlled by elevators
Its left
left--right tilt is controlled by ailerons
 Its left
left--right rotation is controlled by rudder

Symmetric airfoils produce small lifts


Question 5



Steering involves ailerons and rudder
Elevation involves elevators and engine
Skating 214
Question 6
Q: How does a plane propel itself through the air?
A: It pushes air backward with its props or engines

Turbojet Engines

Air entering duct diffusor exchanges speed for pressure
A compressor does work on air, increases its pressure
 Fuel
F l is
i burned
b rn d in th
thatt air,
ir in
increasing
r in air’s
ir’ energy
n r
 A turbine extracts work from air, decreasing its pressure
 Air exiting duct nozzle exchanges pressure for speed


Propellers
p
are spinning
p
g wings
g
They deflect air backward,
do work on air (add energy),
 and pump air toward rear of plane



Jet engines are ducted air pumps

Confine the air and pump it toward rear of plane
Skating 215
Skating 216
Turbofan Engines

Turbojet obtains forward momentum by
moving relatively little air
 and giving that air too much energy


Jet engines pump air toward rear of plane
T
Turbofan
b f obtains
b i fforward
d momentum b
by
moving much more air
 giving that air less energy

Summary about Airplanes






Airplanes use lift to support themselves
Propulsion overcomes induced drag
Speed and angle of attack affect altitude
Extreme angle of attack causes stalling
Propellers do work on passing airstream
Jet engines do work on slowed airstream
36
Skating 217
Skating 218
Observations about Woodstoves

Woodstoves





They burn wood in enclosed fireboxes
They often have long chimney pipes
Their surfaces are usually darkly coated
They’ll burn you if you touch them
Heat rises off their surfaces
They warm you when you stand near them
Turn off all electronic devices
Skating 219
Skating 220
5 Questions about Woodstoves
1.
2.
3.
4.
5.
What are thermal energy and heat?
How does a woodstove produce thermal energy?
Why does heat flow from the stove to the room?
Why is a woodstove better than an open fire?
How does a woodstove heat the room?
Question 1
Q: What are thermal energy and heat?
A: Disordered energy and its transfer mechanism

Thermal energy
gy is
disordered energy within an object’s particles
the kinetic and potential energies of those particles
 responsible for temperature



Heat is energy flowing between objects

Skating 221
Skating 222
Question 2
Q: How does a woodstove produce thermal energy?
A: It converts chemical energy into thermal energy

due to a difference in their temperatures
Chemical Forces and Bonds


attractive at long distances
repulsive
l i at short
h di
distances
 zero at a specific equilibrium separation

Fire releases chemical p
potential energy
gy
Wood and air consist of molecules
Molecules are bound by chemical bonds
 When bonds rearrange, they can release energy
 Burning rearranges bonds and releases energy!
Atoms interact via electromagnetic forces
The chemical forces between two atoms are




Atoms at their equilibrium separation



are in a stable equilibrium
are bound together by an energy deficit
Their energy deficit is a chemical bond
37
Skating 223
Skating 224
A Few Names





Molecule: atoms joined by chemical bonds
Molecule:
Chemical bond:
bond: a chemical
chemical--force linkage
Bond strength:
strength: the work needed to break bond
Reactants:: starting molecules
Reactants
Products:: ending molecules
Products
Chemical Reactions



Breaking old bonds takes work
Forming new bonds does work
If new bonds are stronger than the old bonds,


However, breaking old bonds requires energy

Skating 225
chemical potential energy  thermal energy
reaction requires activation energy to start
Skating 226
When Wood Burns…

When you ignite wood,
the reactants are carbohydrates and oxygen
 the products are water and carbon dioxide
 the
th activation
ti ti n energy
n r comes
m fr
from
m a burning
b rnin match
m t h


Question 3
Q: Why does heat flow from the stove to the room?
A: Because the stove is hotter than the room

Heat naturallyy flows from hotter to colder

This reaction releases energy as thermal energy


At thermal equilibrium, temperatures are equal

Temperature measures the average thermal kinetic
energy per particle (slightly oversimplified)

Skating 227
no heat flows between those objects
Skating 228
Question 4
Q: Why is a woodstove better than an open fire?
A: It releases heat, but not smoke, into the room

Microscopically, thermal energy moves both ways
Statistically, the net flow is from hotter to colder
An open
p fire is energy
gy efficient, but has problems
p
Heat Exchangers

A woodstove is a heat exchanger


It separates air used by the fire from room air
It transfers heat without transferring smoke
Smoke is released into the room
Fire uses up the room’s oxygen
 Can set fire to the room




A fireplace is cleaner, safer, but less efficient
A woodstove can be clean, safe, and efficient
38
Skating 229
Skating 230
Question 5
Q: How does a woodstove heat the room?
A: It uses all three heat transfer mechanisms

Conduction and Woodstoves


adjacent atoms jiggle one another
atoms do work and exchange energies
 on average, heat flows from hot to cold atoms

Those heat transfer mechanisms are
conduction: heat flows through materials
convection: heat flows via moving fluids
 radiation: heat flows via electromagnetic waves





In a conductor,

All three transfer heat from hot to cold


Skating 231
In conduction, heat flows but atoms stay put
In an insulator,
mobile electrons carry heat long distances
heat flows quickly from hot to cold spots
Conduction moves heat through stove’s walls
Skating 232
Convection and Woodstoves

In convection, heat flows with a fluid’s atoms
Fluid warms up near a hot object
 Flowing fluid carries thermal energy with it
 Fluid cools down near a cold object
j
 Overall, heat flows from hot to cold
Radiation and Woodstoves



Buoyancy drives natural convection
Warmed fluid rises away from hot object
 Cooled fluid descends away from cold object


Convection circulates hot air around the room
Skating 233

In radiation, heat flows via electromagnetic
waves (radio waves, microwaves, light, …)
Range of waves depends on temperature





Higher temperature  more radiated heat
Blacker surface  more radiated heat
Black emits and absorbs radiation perfectly
Skating 234
Stefan--Boltzmann Law
Stefan

Emissivity is a surface’s emissionemission-absorption efficiency



cold:
ld radio
di wave, microwaves,
i
iinfrared
f d light
li h
hot: infrared, visible, and ultraviolet light
0  perfect inefficiency: white, shiny, or clear
1  perfect efficiency: black
The amount of heat a surface radiates is
power  emissivity  Stefan-Boltzmann constant
temperature 4  surface area
What About Campfires?



No conduction, unless you touch hot coals
No convection, unless you are above fire
Lots of radiation:


your face feels hot because radiation reaches it
your back feels cold because no radiation reaches it
where temperature is measured on an absolute scale
39
Skating 235
Skating 236
Summary about Wood Stoves




Use all three heat transfer mechanisms
Have tall chimneys for heat exchange
Are darkdark-coated to encourage radiation
Are sealed to keep smoke out of room air
Water, Steam, and Ice
Turn off all electronic devices
Skating 237





Observations about
Water, Steam, and Ice
Water has three forms or phases
Ice is common below 32 °F (0 °C)
Water is common above 32 °F (0 °C)
Steam is common at high temps
The three phases sometimes coexist
Skating 239
Skating 238
4 Questions about Water, Steam, Ice
1.
2.
3.
4.
Skating 240
Question 1
Q: How can water and ice coexist in a glass?
A: At 32 °F (0 °C), both phases are stable


How can water and ice coexist in a glass?
Can steam exist below 212 °F (100 °C)?
Where do ice cubes go in a frostless freezer?
Is salt the only chemical that helps melt ice?
Water has three p
phases: solid, liquid,
q
and gas
g
Ice has a melting temperature of 32 °F (0 °C)
Phases of Matter



Ice is solid:
solid: fixed volume and fixed shape
Water is liquid:
liquid: fixed volume but variable shape
Steam is gas:
gas: variable volume and variable shape
below which solid ice is the stable phase,
above which liquid water is the stable phase,
 at which ice and water can coexist


40
Skating 241
Skating 242
Phase Equilibrium

When two (or more) phases are present
Ice and Water

molecules continually shift between the phases
 one phase may grow at the expense of another phase
 that
th t growth
r th often
ft n takes
t k orr releases
r l
thermal
th rm l energy
n r


At phase equilibrium,
To melt ice at 32 °F (0 °C),
destabilize ice relative to water by



two (or more) phases can coexist indefinitely
 neither phase grows at the expense of the other

To freeze water at 32 °F (0 °C),
stabilize ice relative to water by



Skating 243
adding heat
increasing pressure (ice is very atypical!)
removing heat
decreasing pressure (water is very atypical!)
Melting ice takes latent heat of melting
Skating 244
Question 2
Q: Can steam exist below 212 °F (100 °C)?
A: Yes, but its pressure is less than atmospheric

Water and Steam


Liquid
q water and gaseous
g
steam


can coexist over a broad range of temperatures
but equilibrium steam density rises with temperature
To evaporate water,
destabilize water relative to steam by


To condense steam,
stabilize water relative to steam by



Skating 245
Skating 246
Steam bubbles can form inside water



Pressure in steam bubble depends on steam density


Boiling occurs when bubbles
nucleate—when seed bubbles form
nucleate—
 grow via evaporation
Boiling temperature depends on ambient pressure
Elevated pressure

steam bubbles
b bbl can survive
i and
d grow via
i evaporation
i


Boiling (Part 2)
If steam pressure exceeds ambient pressure,

removing heat
increasing the density of the steam
Evaporating water takes latent heat of evaporation
Boiling (Part 1)

adding heat
reducing the density of the steam


raises water’s boiling temperature
S
Some
foods
f d cookk faster
f
at sea level
l l or below
b l
Diminished pressure


lowers water’s boiling temperature
Some foods cook slower at high altitudes
Need for latent heat stabilizes temperature
41
Skating 247
Skating 248
Question 3
Q: Where do ice cubes go in a frostless freezer?
A: The ice sublimes directly into steam

Solid ice and ggaseous steam
can coexist over a broad range of temperatures
 but equilibrium steam density rises with temperature

Ice and Steam




adding heat
reducing the density of the steam
To
T deposit
d
i steam, stabilize
bili iice relative
l i to steam by
b



Skating 249
To sublime ice, destabilize ice relative to steam by
removing heat
increasing the density of the steam
Subliming ice takes latent heats of melting and
evaporation
Skating 250
Relative Humidity

At 100% relative humidity,


Below 100% relative humidity,




water evaporates and/or ice sublimes




Summary about
Water, Steam, and Ice
Phase transitions reflect relative phase stabilities
Phases in equilibrium are stable and constant
Temperature and pressure affect phase stabilities
Phase transitions usually take or release heat
Dissolved impurities
p
stabilize liquid
q water


steam condenses as liquid water and/or deposits as ice
Below 0 °C, ice and steam are active phases
Above 0 °C, water and steam are active phases
At 0 °C, water, steam, and ice are all active phases
Skating 251

Q: Is salt the only chemical that helps melt ice?
A: No, any chemical that dissolves in water works
Above 100% relative humidity,


steam is in phase equilibrium with water and/or ice
Question 4


reduce ice’s melting temperature
increase water’s boiling temperature
Shifts are proportional to solute particle density
Any soluble material can help ice to melt
Skating 252
Clothing, Insulation,
and Climate
Turn off all electronic devices
42
Skating 253
Observations about Clothing,
Insulation, and Climate






Clothing keeps you warm in cold places
Clothing can keep you cool in very hot places
Insulation controls heat flow in various objects
Insulation can be obvious, as in foam cups
Insulation can be subtle, as in special windows
Greenhouse gases trap heat and warm the earth
Skating 255
Skating 254
4 Questions about Clothing,
Insulation, and Climate
1.
2.
3.
4.
How does clothing control thermal conduction?
How does clothing control thermal convection?
How does insulation control thermal radiation?
Why do greenhouse gases warm the earth?
Skating 256
Question 1

How does clothing control thermal conduction?
Thermal Conductivity


Heat naturally flows from hot to cold
If one end of a material is hotter than the other
it will conduct heat from its hot end to its cold end
at a rate equall to the
h material’s
i l’ area
 times the temperature difference
 times the material’s thermal conductivity
 divided by the material’s thickness.


heat flow 
Skating 257
Skating 258
Limiting Thermal Conduction

Clothing is often intended to reduce heat flow




How does clothing control thermal convection?
electrical insulators, not metals
materials that trap air—
air—air is a very poor thermal conductor
and it should use relatively thick materials


Question 2
so it should use lowlow-thermal conductivity materials


conductivity  temperature diff  area
thickness
wool sweaters, down coats, heavy blankets
Reducing exposed area is helpful when possible
Reducing the temperature difference always helps
43
Skating 259
Skating 260
Natural Convection


Heat naturally flows from hot to cold
If one region of a fluid is hotter than the other



Forced Convection

It fails when the hotter fluid is above the colder fluid
It fails when fluids experience large drag forces
 It fails
f il in certain
rt in awkward
k rd geometries
m tri

those regions will also have different densities
andd buoyancy
b
may cause the
h fl
fluid
id to circulate.
i l
The rate of heat flow depends on


the heat capacity and mobility of the fluid
 how quickly heat flows into or out of the fluid
 how well buoyancy circulates fluid from hot to cold
Stirring the fluid enhances heat flow


Skating 261
Buoyancy isn’t always effective at moving fluids

Wind leads to faster heat transfer (wind chill)
Moving through air or water speeds heat transfer
Skating 262
Limiting Thermal Convection

Clothing can reduce convective heat flow by
Question 3

How does insulation control thermal radiation?
preventing fluids from circulating
 reducing temperature differences in the fluid


The
Th most effective
ff i clothing
l hi is
i thick
hi k andd fluffy
fl ff



The fluffiness traps air so that it can’t convect
The thickness allows the surface temperature to
drop to that of your surroundings so that there is no
external convection
A wind breaker minimizes forced convection
Skating 263
Skating 264
Thermal Radiation

Materials all emit thermal radiation because
Black Body Spectrum (Part 1)

they contain electric charges
 and thermal energy causes those charges accelerate.
 A
Accelerating
l r tin charges
h r emit
mit electromagnetic
l tr m n ti waves


Hotter temperatures yield shorter wavelengths
A surface’s efficiency at absorbing and emitting
thermal radiation is measured by its emissivity



1 for a perfect emitteremitter-absorber (black)
0 for a nonemitter
nonemitter--nonabsorber (white,
(white clear,
clear shiny)
The spectrum and intensity of a black surface’s
thermal radiation depend only on its temperature
44
Skating 266
Skating 265
Black Body Spectrum (Part 2)



The black body spectrum of the sun is white light
Objects hotter than about 500 °C glow visibly
But even your skin emits
i i ibl thermal
invisible
h
l radiation
di i
Radiative Heat Transfer

Your skin radiates heat at a rate given by the
Stefan--Boltzmann law:
Stefan
power  emissivity  Stefan-Boltzmann constant
temperature 4  surface area
where temperature is an absolute temperature.


Skating 267
Skating 268
Limiting Thermal Radiation (Part 1)

Insulation can reduce radiative heat flow by
Limiting Thermal Radiation (Part 2)

having surfaces with low emissivities
 reducing temperature differences between surfaces


Because of the 4th power, thermal radiation is
extremely sensitive to temperature.
Black or gray objects with different temperatures
can exchange heat via thermal radiation
To reduce radiative heat flow


E i i i depends
Emissivity
d
d on temperature

You can see highhigh-temperature emissivity



black surfaces have high
high--temperature emissivities near 1
white, clear, shiny surfaces values near 0
You can’t see lowlow-temperature emissivity


most materials have lowlow-temperature emissivities near 1
conducting (metallic) surfaces can have values near 0
Skating 269
Skating 270
Question 4
Q: Why do greenhouse gases warm the earth?
A: By increasing altitude of earth’s radiating surface


Earth receives thermal radiation from the sun
Earth emits thermal radiation into space
The atmosphere contributes to that thermal radiation
 Effective radiating surface is 5 km above sea level



use conducting, low
low--emissivity surfaces
allow exterior surfaces to reach ambient temperature
Effects of the Atmosphere

Atmosphere has a temperature gradient



air expands and cools is its altitude increases
air temperature decreases 6.6 °C per km of altitude
A
Atmosphere’s
h ’ average temperature


at 5 km is -18 °C
at sea level is 15 °C
Balance requires Earth’s radiating surface is -18 °C
Greenhouse gases increase altitude of that surface
45
Skating 271
Skating 272
Effects of Greenhouse Gases

Greenhouse gases “darken” the atmosphere
Low-temperature emissivity of atmosphere increases
Low Effective radiating surface moves to higher altitude
 Average
A r ttemperature
mp r t r att sea level
l l increases
in r



Increasing greenhouse gases cause global warming
Greenhouse gases include
water, carbon dioxide
water,
dioxide,, nitrogen oxides
oxides,, and methane
 but not nitrogen or oxygen; they’re transparent to IR








Summary about Clothing,
Insulation, and Climate
Clothing and insulation limit heat transfer
They use materials with low thermal conductivities
They introduce drag to impede convection
They use low emissivities to reduce radiation
Greenhouse gases affect Earth’s thermal radiation
Those gases raise Earth’s surface temperature
Limiting greenhouse gases is critical to our future
Skating 273
Skating 274

Air Conditioners




Observations about
Air Conditioners
They cool the air in a room
They emit hot air from their outside vents
They consume lots of electric power
They are less efficient on hotter days
Some can be reversed so that they heat room air
Turn off all electronic devices
Skating 275
Skating 276
Question 1
5 Questions about Air Conditioners
1.
2.
3.
4.
5.
Why doesn’t heat flow naturally from cold to hot?
Why does an air conditioner need electricity?
How does an air conditioner cool room air?
What role does the electricity play?
How does an air conditioner heat outdoor air?
Q: Why doesn’t heat flow naturally from cold to hot?
A: Such heat flow would violate the law of entropy

There are 4 laws of thermodynamics
y
that
govern the flow of thermal energy
relate disordered (thermal) energy and ordered energy
 relate heat and work



We will consider 3 of those laws
46
Skating 277
Skating 278
Law of Thermal Equilibrium
This law observes that there is a consistency about
situations in which heat does not flow:
“If two objects
bj
are in
i thermal
h
l equilibrium
ilib i
with
iha
third object, then they are in thermal equilibrium
with each other.”
Law of Conservation of Energy
This law recognizes that heat is a form of energy:
“The change in the internal energy equals
the heat in minus the work out”
where:
The internal energy is thermal + stored energies
The heat in is the heat transferred into object
 The work out is the external work done by object


Skating 279
Skating 280
Order versus Disorder

Converting ordered energy into thermal energy
Entropy

involves events that are likely to occur
 is easy to accomplish and often happens


Converting
C
i thermal
h
l energy iinto ordered
d d energy



involves events that are unlikely to occur
 is hard to accomplish and effectively never happens
E
Entropy


Statistically, disordered never becomes ordered
Skating 281
is the measure of a system’s disorder
includes every type of disorder: energy and structure
never decreases in a system that is thermally isolated
can be rearranged within a system
 can be transferred between systems
 is NOT a conserved quantity!


Entropy
Skating 282
Law of Entropy
This law observes that entropy guides the time
evolution of isolated systems:
More on the Law of Entropy

According to the Law of Entropy:
Entropy of thermally isolated system can’t decrease
but entropy can be rearranged within that system
 so part
p rt off th
the system
t m can
n become
b m colder
ld r
as another part becomes hotter!
 Entropy is “exported” from cold part to hot part


“Th entropy off a thermally
“The
h
ll isolated
i l d system never
decreases”

Exporting entropy is like throwing out trash!
47
Skating 283
Skating 284
Natural Heat Flow


Hypothetical Energy and Entropy
One unit of thermal energy is more disordering
to a cold object than to a hot object
When heat flows from hot object to cold object,
Thermal Energy
0
1
2
3
4
hot object’s
h
bj ’ entropy: ↓
cold object’s entropy: ↑↑
 so their total entropy: ↑



Law of Entropy is satisfied
Skating 285
Skating 286
Unnatural Heat Flow

When heat flows from cold object to hot object,
cold object’s entropy: ↓↓
 hot object’s entropy: ↑
 so their
th ir ttotal
t l entropy:
ntr p ↓


Question 2
Q: Why does an air conditioner need electricity?
A: Electricity provides the necessary order


unless we create of additional entropy!
unless something ordered becomes disordered!
An air conditioner
moves heat from cold (room air) to hot (outside air)
would cause total entropy of world to decrease
 were it not for the electric power it consumes!

Law of Entropy would be violated,



It turns electric power into thermal power

Skating 287
Air conditioners are heat pumps

Air Conditioner

use work to transfer heat from cold to hot

Automobiles are heat engines

Heat machines are governed by law of entropy

so the total entropy of world does not decrease
Skating 288
Heat Machines

Entropy
0
4
7
9
10
use flow
fl off heat
h from
f
hot
h to cold
ld to do
d workk
An air conditioner uses a working fluid to


absorb heat from cold (room air)
release heat to hot (outside air)

Th evaporator (indoors)
The
(i d
)

The condenser (outdoors)



transfers heat from cold (room air) to working fluid
transfers heat from working fluid to hot (outside air)
The compressor (outdoors)

does work on working fluid and produces entropy.
48
Skating 289
Skating 290
Question 3
Q: How does an air conditioner cool room air?
A: Its evaporator absorbs heat from the room air


Evaporator
p
is wide indoor p
pipe
p
Working fluid
Question 4
Q: What role does the electricity play?
A: It powers the compressor and creates entropy


enters evaporator as cool lowlow-pressure liquid
 absorbs heat from room air and evaporates
 leaves evaporator as a cool lowlow-pressure gas
enters compressor as a cool lowlow-density gas
has work done on it by the compressor
 leaves compressor as hot highhigh-density gas


Heat has been removed from the room!
Skating 291
Compressor
p
increases ggas’s pressure
p
and densityy
Working fluid



Entropy has been created!
Skating 292
Question 5
Q: How does an air conditioner heat outdoor air?
A: Its condenser releases heat to the outdoor air


Condenser is narrow outdoor p
pipe
p at high
g p
pressure
Working fluid
enters condenser as hot highhigh-pressure gas
releases heat to outdoor air and condenses
 leaves condenser as a cool high
high--pressure liquid

Air Conditioner Overview


Heat has been delivered to the outdoors!
Skating 293



Summary about
Air Conditioners
They pump heat from cold to hot
They don’t violate thermodynamics
They convert ordered energy to thermal energy
absorbing heat from room air

Compressor raises pressure

Fluid condenses in condenser




Fluid evaporates in evaporator

releasing heat to outdoor air
Constriction lowers pressure


evaporation
i → condensation
d
i
condensation → evaporation
and the cycle repeats endlessly…
Skating 294
Automobiles
Turn off all electronic devices
49
Skating 295
Skating 296
Observations about Automobiles





They burn gas to obtain their power
They are rated in horsepower and by volume
Their engines contain “cylinders”
They have electrical systems
They are propelled by their wheels
6 Questions about Automobiles
1.
2.
3.
4.
5.
6.
Skating 297
How can an automobile run on thermal energy?
How efficient can an automobile engine be?
How is an automobile engine a heat engine?
Why do cars sometime “knock?”
How is a diesel engine different?
Why does the engine have a catalytic converter?
Skating 298
Question 1
Q: How can an automobile run on thermal energy?
A: An automobile engine is a heat engine

An automobile
allows heat to flow from hot (flame) to cold (air)
 would cause total entropy of world to increase greatly
 were it not for the mechanical power it produces!
Question 2
Q: How efficient can an automobile engine be?
A: Its efficiency is limited by the law of entropy






It turns some thermal power to mechanical power


A heat pump
cannot decrease the world’s overall entropy
 efficiency depends on the temperature difference


heat flowing from hot to cold creates more entropy
so more heat can be converted to work
Skating 300
About Heat Pumps

cannot decrease the world’s overall entropy
efficiency depends on the temperature difference
As that temperature difference increases,

so the total entropy of world increases only modestly
Skating 299
A heat engine
g
A that
As
h temperature diff
difference increases,
i
heat pumped from cold to hot destroys more entropy
 so more work must be converted to heat
Question 3
Q: How is an automobile engine a heat engine?
A: Heat flows from hot (flame) to cold (outside air)

An internal combustion engine
g




burns a fuel
fuel--air mixture in an enclosed space
to produce hot (burned gases).
As heat flows from hot to cold (outside air)


engine converts some heat into useful work
automobile uses that work to propel itself.
50
Skating 301
Skating 302
Four Stroke Engine




Induction Stroke: fill cylinder with fuel & air
Compression Stroke: squeeze mixture
Power Stroke: burn and extract work
Exhaust Stroke: empty cylinder of exhaust
Induction Stroke






Skating 303
Intake valve opens
Engine pulls piston out of cylinder
Engine does work on piston
L pressure produced
Low
d d inside
i id cylinder
li d
Fuel-air mixture flows into cylinder
FuelIntake valve closes
Skating 304
Compression Stroke

Engine pushes piston into cylinder


Engine does work on piston

Spark plug ignites the fuel
fuel--air mixture
Hot gas pushes piston out of cylinder

Burned gas expands

Mixture is compressed
Mi
Mixture
pressure iincreases
 Mixture temperature increases


Power Stroke


Work becomes heat


Heat becomes work
Exhaust Stroke

Exhaust valve opens
Engine pushes piston into cylinder




Gas pressure decreases
Gas temperature decreases
Skating 306
Skating 305

Piston does work on engine
Engine does work on piston
Hi h pressure produced
High
d d inside
i id cylinder
li d
Burned gas flows out of cylinder
Exhaust valve closes
Efficiency Limits

Overall, an internal combustion engine



produces more work than it consumes
converts some heat into work
L off entropy limits
Law
li i heat
h becoming
b
i workk
Some heat must be released into outside air
Efficiency increases with the temperature difference
 Real engines never reach ideal efficiency


51
Skating 307
Skating 308
Question 4
Q: Why do cars sometime “knock?”
A: Compressing a flammable gas can ignite it

Duringg the compression
p
stroke, fuel
fuel--air mixture
Question 5
Q: How is a diesel engine different?
A: It uses compression heating to ignite fuel

becomes extremely hot
 can ignite spontaneously (knocking
(knocking or preignition)
preignition)





To avoid knocking, car can

reduce its compression ratio to lower peak temperature
use fuel that is more resistant to ignition

Diesel engine has higher compression ratio, so

Higher octane fuels are simply harder to ignite
Skating 309
Diesel engine
g
compresses air to very high pressure & temperature
injects fuel between compression and power strokes
 lets fuel ignite upon entry into the superheated air


its fuel burns to a higher final temperature
it has a higher potential efficiency
Skating 310
Question 6
Q: Why does the engine have a catalytic converter?
A: To remove unwanted components form exhaust

Imperfect
p
fuel
fuel--air mixtures p
produce p
pollutants
Too rich: carbon monoxide and fuel in exhaust
 Too lean: nitrogen oxides in exhaust
 Imperfect diesel: carbonized particulates in exhaust



Catalytic Converters

Catalytic converter reduce pollutant molecules



Platinum helps oxidize carbon monoxide and fuel
Rhodium helps remove nitrogen oxides
Using
U i tiny,
i hi
high
highh-surfacesurface
f -area catalyst
l particles
i l


increases the fraction of atoms available for reactions
decreases the amount of precious metals required
Catalytic converter destroys unwanted molecules
Filter removes and burns unwanted particulates
Skating 311
Skating 312
Summary about Automobiles




Heat flows from hot (burned gas) to cold (air)
Some of that heat is converted to work
Energy efficiency is limited by thermodynamics
Higher temperatures increase efficiency
Clocks
Turn off all electronic devices
52
Skating 313
Skating 314
Observations About Clocks






They divide time into uniform intervals
The measure time by counting those intervals
Some clocks use motion to mark their intervals
Others clocks don’t appear to involve motion
They require energy to operate
They have good but not perfect accuracy
Skating 315
5 Questions about Clocks
1.
2.
3.
4.
5.
Why don’t any modern clocks use hourglasses?
Are all repetitive motions equally accurate
accurate??
Why is a harmonic oscillator a good timekeeper?
Why are some clocks particularly accurate?
accurate?
How are harmonic oscillators used in clocks?
Skating 316
Question 1
Q: Why don’t any modern clocks use hourglasses
hourglasses??
A: Hourglasses are best as timers, not clocks


Repetitive Motions: Clocks

pendulums
torsion balances
 tuning
t nin forks
f rk


Hourglasses
g
measure an interval fairlyy accuratelyy
They are poorly suited to subdividing the day
They require frequent operator intervention
 That operator requirement limits their accuracy

Devices that tick off time intervals repetitively,

began appearing in clocks about 500 years ago.
They are well suited to subdividing the day


Skating 317
Skating 318
About Repetitive Motions

Any device with a stable equilibrium
can move repetitively about that equilibrium
 will move repetitively as long as it has excess energy



They require no operator intervention
Their ticks can be counted automatically
Th repetitive
The
i i motion
i sets a clock’s
l k’ accuracy
It mustn’t depend on externals such as
temperature, air pressure, or time of day
temperature,
the clock’s store of energy
 the mechanism that observes the motion
Question 2
Q: Are all repetitive motions equally accurate?
accurate?
A: Insensitivity to the amplitude of motion helps

A little terminology…
gy
Period: interval between two repetitive motion cycles
Period:
Frequency:: cycles completed per unit of time
Frequency
 Amplitude
Amplitude:: peak distance away from motion’s center
 Timekeeper
Timekeeper:: a clock’s repetitive motion device





In a good clock, the period of its timekeeper
shouldn’t depend on amplitude.
amplitude.
53
Skating 319
Skating 320
Question 3
Q: Why is a harmonic oscillator a good timekeeper?
A: Its period is independent of its amplitude

A harmonic oscillator is a system
y
with
a stable equilibrium
 a restoring influence that’s proportional to displacement


Its period is independent of its amplitude!
Harmonic Oscillators

A harmonic oscillator always has



Ah
harmonic
i oscillator’s
ill
’ period
i d ddecreases as



its inertial aspect becomes smaller
its springspring-like restoring aspect becomes stiffer
Common harmonic oscillators include

Skating 321
an inertial aspect (e.g., a mass)
a spring
spring--like restoring aspect (e.g., a spring).
mass on a spring, pendulum, flagpole, tuning fork
Skating 322
Question 4
Q: Why are some clocks particularly accurate?
A: They take good care of their harmonic oscillators

Clocks have p
practical limits to accuracyy
Sustaining motion can influence the period
 Measuring the period can influence the period
 Temperature, pressure, wind… can influence the period
Question 5
Q: How are harmonic oscillators used in clocks?
A: Their motions are gently encouraged and counted






Clocks also have fundamental limits to accuracy

Common harmonic oscillators used in clocks are
pendulums
balance rings
 quartz crystals

Skating 324
Pendulums (Part 1)


supplies energy to keep its harmonic oscillator going
counts cycles of that oscillator and reports the time

Oscillation decay limits preciseness of period
Skating 323
A clock
A pendulum is (almost) a harmonic oscillator
For small displacements
Its restoring force is proportional to displacement
I period
Its
i d iis iindependent
d
d off amplitude
li d
 Its period is proportional to (length/gravity)
(length/gravity)1/2
Pendulums (Part 2)

A pendulum’s springspring-like restoring force
is caused by gravity
is proportional to the pendulum’s weight
 is
i th
therefore
r f r pr
proportional
p rti n l tto th
the p
pendulum’s
nd l m’ m
mass





Increasing a pendulum’s mass
increases its inertial aspect
increases the stiffness of its restoring force aspect
 therefore has no effect on its period!


54
Skating 326
Skating 325
Pendulum Clocks


Pendulum is the clock’s timekeeper
For accuracy, pendulum’s
length is temperature stabilized
 length is adjusted for local gravity
 friction & air resistance are small
 motion is sustained gently
 motion is measured gently
Balance Ring Clocks







Gravity exerts no torque about the ring’s pivot
G i has
Gravity
h no influence
i fl
on the
h period
i d
For accuracy, balance ring’s
friction & air resistance are small
motion is sustained gently
 motion is measured gently


The clock mustn't move or tilt
Skating 327
Coil spring and balance ring form harmonic osc
osc..
Balance ring twists back and forth rhythmically
Skating 328
Quartz Oscillators

A quartz crystal is a harmonic oscillator
Quartz Clocks

Crystal’s mass provides the inertial aspect
 Crystal’s body provides the spring
spring--like restoring aspect





A ah
As
harmonic
i oscillator,
ill
a quartz crystal’s
l’

oscillation decay is extremely slow
fundamental accuracy is extremely high

Quartz is piezoelectric
Its mechanical and electrical changes are coupled
 Its motion can be induced and measured electrically

Skating 329
The quartz tuning fork in a quartz clock is
kept vibrating by giving it energy electronically
observed and its vibrations counted electronically
 insensitive
in n iti to
t gravity,
r it temperature,
t mp r t r pressure,
pr
r and
nd
acceleration


Quartz’s slow oscillation decay
gives it a very precise period
The crystal’s tuningtuning-fork shape
yields a slow, efficient vibration.
Skating 330
Summary about Clocks




Most clocks involve harmonic oscillators
Amplitude independence aids accuracy
Clock sustains and counts oscillations
Oscillators that lose little energy work best
Musical Instruments
Turn off all electronic devices
55
Skating 331




Observations about
Musical Instruments
They can produce different notes
They must be tuned to produce the right notes
They sound different, even on the same note
They require energy to create sound
Skating 332
1.
2.
3.
4.
5.
6.
7.
Skating 333
Why does a taut string have a specific pitch?
Why does a vibrating string sound like a string?
How does bowing cause a string to vibrate?
Why do stringed instruments need surfaces?
What is vibrating in a wind instrument?
Why does a drum sound particularly different?
different?
How does sound travel through air?
Skating 334
Question 1
Q: Why does a taut string have a specific pitch?
A: A taut string is a harmonic oscillator

Fundamental Vibration

string vibrates up and down as a single arc
1 displacement antinode at string’s center
 2 displacement
di pl m nt nodes,
n d 1n
node
d att each
h end
nd off string
trin

A taut stringg
stable equilibrium shape: a straight line
mass provides an inertial aspect
 tension and length provide spring
spring--like restoring aspect



Its fundamental pitch (frequency of vibration) is
proportional to tension1/2
 proportional to 1/length
 proportional to 1/mass1/2

A taut string is a harmonic oscillator

A string has a fundamental vibrational mode



vibrates about its equilibrium shape
pitch is independent of its amplitude/volume!
Skating 336
Skating 335
Question 2
Q: Why does a vibrating string sound like a string?
string?
A: It has specific harmonics that define its sound

A string can vibrate as
2 halfhalf-strings (2 antinodes)
 3 thirdthird-strings (3 antinodes)
 and more higherhigher-order modes
A String’s Harmonics

Higher--order vibrational modes
Higher


produce overtones (over the fundamental pitch)
string’s overtones are harmonics
harmonics:: integer multiples
First overtone involves 2 halfhalf-strings





7 Questions about
Musical Instruments
Second overtone involves 3 third
third--strings



2 × the fundamental pitch: 2nd harmonic
One octave above the fundamental frequency
3 × the fundamental pitch: 3rd harmonic
An octave and a fifth above the fundamental
Bowing or plucking a string excites a mixture of
fundamental and harmonic vibrations, giving the
string its characteristic sound
56
Skating 337
Skating 338
Question 3
Q: How does bowing cause a string to vibrate?
vibrate?
A: Bowing adds a little energy to string each cycle


Pluckingg a stringg transfers energy
gy all at once
Bowing a string transfers energy gradually



bow does a little work on the string every cycle
energy accumulates via resonant energy transfer
A string will exhibit sympathetic vibration when


another object vibrates at string’s resonant frequency
resonant energy transfer goes from object to string
Skating 339
Question 4
Q: Why do stringed instruments need surfaces
surfaces??
A: Surfaces project sound much better than strings

In air, sound consists of density fluctuations


Air has a stable equilibrium: uniform density
Disturbances from uniform density make air vibrate

Vibrating strings don’t project sound well

Surfaces project sound much better



air flows easily around narrow vibrating strings
air can’t flow easily around vibrating surfaces
air is substantially compressed or rarefied: sound
Skating 340
Question 5
Q: What is vibrating in a wind instrument?
instrument?
A: Air in a tube is a harmonic oscillator

a stable equilibrium arrangement: uniform density
mass provides an inertial aspect
 pressure and length provide springspring-like restoring aspect



Fundamental Vibration
Open--Closed Column
Open
Air column has a fundamental vibrational mode
proportional to pressure1/2,
 proportional to 1/length,
 and proportional to 1/density1/2.
Skating 342
Air Column Harmonics

air column vibrates up and down as a single object
 1 pressure antinode at air column’s closed end
 1 pressure
pr
r n
node
d att air
ir column’s
l mn’ open
p n end
nd
The air column in a open
open--closed pipe vibrates
like half the air column in an openopen-open pipe
 at half the frequency of an openopen-open pipe

In an open
open--open pipe, the overtones are at
2 × the fundamental (2 pressure antinodes
antinodes))
3 × the fundamental (3 pressure antinodes)
 and
nd allll int
integerr harmonics
h rm ni


Its fundamental pitch is

vibrates about its equilibrium arrangement
pitch is independent of its amplitude/volume!
Skating 341

air column vibrates up and down as a single object
1 pressure antinode at air column’s center
 2 pressure
pr
r nodes,
n d 1n
node
d att each
h open
p n end
nd off column
l mn

Air in a tube is a harmonic oscillator

Air column has a fundamental vibrational mode

Air in a tube has



Fundamental Vibration
Open--Open Column
Open



In an open
open--closed pipe, the overtones are at
3 × the fundamental (2 antinodes)
5 × the fundamental (3 antinodes)
 and all oddodd-integer harmonics


57
Skating 343
Skating 344
Question 6
Drumhead Vibrations
Q: Why does a drum sound particularly different?
different?
A: Its overtones are not harmonics

Most 11-dimensional instruments



Most 22- or 33- dimensional instruments



can vibrate at half, third, quarter length, etc.
have harmonic overtones
have complicated higherhigher-order vibrations
have nonnon-harmonic overtones.
Examples: drums, cymbals, bells
Skating 345
Skating 346
Question 7
Q: How does sound travel through air?
A: Air exhibits longitudinal traveling waves

Basic modes of finite objects are standing waves

Basic modes of infinite objects are traveling waves



Transverse and Longitudinal Waves

Some objects vibrate sideside-totoside: transverse waves


Finite strings: transverse standing
Open
p string:
g transverse travelingg
Standing wave:
wave: nodes and antinodes don’t move
Traveling wave:
wave: nodes and antinodes travel
Open air is infinite, so it exhibits traveling waves

Some objects vibrate along their
lengths: longitudinal waves


Skating 347
Air column: longitudinal standing
Open air: longitudinal traveling
Skating 348
Summary of Musical Instrument





They use strings, air, etc. as harmonic oscillators
Pitches are independent of amplitude/volume
Tuned by tension/pressure, length, density
Often have harmonic overtones
Project vibrations into the air as sound
The Sea
Turn off all electronic devices
58
Skating 349
Skating 350
Observations about the Sea





The sea is rarely calm; it is covered with waves
The broadest waves travel fastest
Waves seem to get steeper near shore
Waves break or crumble near shore
Waves bend gradually toward the shore
Skating 351
5 Questions about the Sea
1.
2.
3.
4.
5.
Skating 352
Question 1
Q: Why are there tides
tides??
A: The moon’s gravity causes the oceans to bulge
 Moon’s gravity acts nonuniformly on the earth



Why are there tides?
How do giant tides develop?
How does water in a wave move?
How is a tsunami different from normal waves?
Why do waves bend and break near shore?
Tidal distortion of the oceans produces two bulges
Locations of tidal bulges change as the earth rotates
The Sun’s Influence on Tides

Sun’s gravity also acts
nonuniformly on the earth



Moon and Sun bulges compete

High and low tides occur almost twice a day

Question 2
Q: How do giant tides develop
develop??
A: Sympathetic vibration in channels
Water in a confined channel can slosh





Strongest tides are when moon
and sun are aligned
Weakest tides are when moon
and sun are at right angles
Skating 354
Skating 353

Tidal distortion produces bulges
Sun’s tidal bulges are about 1/3
the size of moon’s tidal bulges
It has a stable equilibrium: level
It has springlike restoring forces
It’s a harmonic oscillator
Its period is set by inertia and stiffness
If its sloshing period matches the tidal
period, sympathetic vibration occurs
Standing and Traveling Waves

Sloshing in a channel involves standing waves



Water in a finite channel has standing wave modes
Nodes and antinodes don’t move
W
Waves
on open water are traveling
li waves


Water in an infinite sea has traveling wave modes
Crests and troughs move
59
Skating 355
Skating 356
Question 3
Q: How does water in a wave move?
move?
A: It circles, but remains approximately in place

Sloshingg involves deep
p water waves


The Water’s Circling Motion



Only the wave structure travels across the water
Surface water itself circles as the wave passes
The wave’s crests are formed from local water
All of the water moves back and forth during a cycle
Waves on the open sea are surface water waves

Only the surface water moves during a cycle
Skating 357
Skating 358
Depth of Surface Wave

The circling is strongest at the surface

Becomes weak about 1/2 wavelength deep
Question 4
Q: How is a tsunami different from normal waves?
waves?
A: They have much longer wavelengths

The longer
g the wavelength
g of surface wave,
the faster it travels
the deeper it extends into the water
 the more power it conveys for its amplitude



Tsunamis are


Skating 359
Skating 360
Question 5
Q: Why do waves bend and break near shore?
shore?
A: Shallow water alters the motion of surface waves

A surface wave slows as water ggets shallower
its circling motion is distorted by the rising seabed
 its wavelength decreases
 its crests grow taller and more tightly bunched


Wave breaks when the water can’t form a crest


very long wavelength, deep, and powerful waves
not strictly surface waves
Changing Wave Speeds

Waves experience reflection



Changes in wave speed cause partial reflection
The bigger the speed change, the more reflection
W
Waves
experience
i
refraction
f i
Changes in wave speed
can redirect the wave
 Waves bend toward shore as
they slow in shallowing water

If the seabed slopes gradually, there is rolling surf
If the seabed slopes sharply, plunging breakers occur
60
Skating 361
Summary of the Sea






The moon’s gravity causes the tides
The tides can cause resonant motion in channels
Tidal resonances are standing waves
The open sea exhibits traveling waves
Water moves in circles in those waves
Waves break when the water gets too shallow
61