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# Energy and Forces

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```									Concepts that drive the world
Energy: Physics
 Energy cuts
across all
fields
 Physics
   E = mc2
   How stars
shine
   Electricity
   Heat
   Roller
Coasters
Energy: Climate & Weather…
 Climate/Weather
    Hurricanes
   Several thousand
atomic bombs
   Lightning
   Global warming –
redistribution of
energy across the
globe
Energy: Chemistry
 Energy cuts across
all fields
 Chemistry
   Activation energy
   Energy needed for
a reaction to occur
   Heat and
temperature is
important
   Think of Ozone...
Energy: Food
 Food
   Average American
2700 Calories
(recommended
2200)
 Note the big C!
   kilocalories
   Really means 270,000
calories
Nutrition Labels
 Nutrition labels tell you about the
energy content of food
 Conversions:       Fat:    9 Cal/g
Carbs: 4 Cal/g
Protein: 4 Cal/g
 This product has 72 Cal from fat, 48
Cal from carbohydrates, and 32 Cal
from protein
 sum is 152 Calories: compare to label
 152 Cal = 636 kJ: enough to climb
about 1000 meters (64 kg person)
 1 Cal = 4.134 Jules
Energy and Food…
 Average American
2700 calories
(recommended 2200)
 7 acres to support one
American
 1.5 acres to support
one African
 The world has enough
capacity to support
around 10 billion
people
So what supports me?
How did the science that we used to get to
the Moon evolve?
Natural motion depended on
nature of the object.
Examples:
A rocks falls
Smoke rises
 The falling speed of an object
was supposed to be
proportional to its weight
 So heavier objects fall faster
 Natural motion could be
circular (perfect objects in
perfect motion with no end)
 So planets orbit the Sun in perfect circles
Aristotle: Why do things move?
 Pushing or pulling
forces imposed
motion.
 Some motions were
difficult to understand.
 Example: the flight of
an arrow
   Must be some force that
pulls it forward after it
leaves the bow
   air rushed around
behind the arrow and
pushed it forward.
Other Contributions
 Aristotle also believed:
   Earth was immovable at the
center of the Celestial Sphere,
and -
   All other celestial bodies:
 moved with uniform speed.

 In pure circular motion

 Are "perfect" and
unchangeable
So how do things move anyway: The Greek
perspective
 Earth was special and at
the center
 Series of Crystal Spheres
(Aristotle)
 The prime mover
 Outer sphere

 Just inside the prime-
mover sphere was the
fixed non-moving stars
 Inner spheres were the
planets the Sun and the
Moon
The Greeks: Contributions
 One of the most important
- and infamous -
contributions of the
Greeks was the geocentric
model of the universe.
 The geocentric model
means that the Earth,
"geo," is at the center,
"centric," of the universe,
and that all other bodies
move around it with the
Earth at a fixed location.
Why Earth should be the center?
 This view held so much sway because of many of
the philosophies of the ancient Greeks.
 They believed that the circle is the perfect form, and that
the simplest model that made sense must be the correct
one.
 since the simplest model was that the Earth stood still
and everything moved around it, then that must also be
true.
 After all, we can't feel the Earth moving, so why should
be believe that it does without any extraordinary
evidence?
Aristotle: The man in science!!!!!!!!
 Aristotle was
unquestioned for
2000 years.
 Most thought that the Earth
was the center of everything
for it was in its normal state
 No one could imagine a force
that could move it.
 It was huge!!!!!!!!!!!!!!!

 Sun was center, not
Earth.
 He was hesitant to
publish because he didn't
really believe it either.
 De Revolutionibus
reached him on the day
he died, May 24, 1543.
 Nicolaus Copernicus (1473-1543)
articulated a cosmological theory
discounting the geocentric
Ptolemaic universe.
 did not abandon the Ptolemaic
cosmogony all together.
 his observations resulted in a
universe limited by the sphere of the
fixed stars.
Copernicus not alone…
 Giordano Bruno (1548-1600) criticized
this limited scheme.
 His theories of the infinite universe
 rejected the traditional geocentric (or
Earth-centered) astronomy
   the sphere of the fixed stars is only a trick of
the eye because the fixed stars are too far
away to recognize their movement
Lets see if Bruno was right…
 Parallax, or more accurately
motion parallax (Greek:
παραλλαγή (parallagé) =
alteration)
 apparent shift of an object
against a background due to a
change in observer position
 Easy to test with your finger!!
Earth and parallax
GALILEO: The emergence of a new paradigm
17th Century scientist who
supported Copernicus.
He refuted many of
Aristotle's ideas.
Worked on falling object
problem - used
experimentation!!!.
Galileo and myth
   Although historical
evidence does not appear
to support the contention,
 Galileo is alleged to
have demonstrated by
dropping balls of
different weights from
the Leaning Tower of
Pisa that they fell with
constant acceleration.
Quick Quiz
 Imagine the following situation:
 You have a coffee filter and a lead ball. You drop them at
the same time which one hits first?
 Wad up the coffee filter to the same shape as the lead
ball which one hits first?
Well…. Lets find out….
Do some tests...

Galileo experiment on the Moon
A tennis ball and a golf ball
dropped side-by-side in air. The
tennis ball is affected more by
the air’s resistance than the golf
ball.

The larger the object is, and the
faster it is falling, the greater
the air’s resistance to its motion,
as skydivers all know…
When most of the air is
removed from a
container, feathers and
apples fall almost side-
by-side, their speeds
changing at almost the
same rate.

If all the air was
removed, they would
accelerate downward at
exactly the same rate.
Galileo: Summary
 Knocked down Aristotle's push or pull ideas.
 Rest was not a natural state.
 The concept of inertia was introduced
 Galileo is sometimes referred to as the “father
of experimentation.”
 Objects fall at the same rate, independent of
weight! (acceleration, though Galileo didn’t
know the word yet)
 Important for the navy!!!
Implications: Dropped Ball: Falling
Downward
In free fall objects accelerate
constantly toward Earth at the
rate of g . Objects moving
upward slow down until their
direction is reversed, and then
they accelerate downward.
At the top of their path the
upward speed is zero.
How long?
Only instantaneously.
A constant acceleration means
the speed is changing all the
time, so the speed only passes
through the value of zero at
the top of the path.
Tossed Ball: Falling Upward
Here two heavy balls begin
“free fall” at the same time.

The red one is dropped,
so it moves straight
downward.

The yellow ball is given some
speed in the horizontal
direction as it is released.
The horizontal lines show
that they keep pace with
each other in the vertical
direction.

Why?
They have the same
acceleration, g, downward,
and they both started with
zero speed in the downward
direction.
The yellow ball’s
horizontal speed is not
affected by gravity,
which acts only in the
vertical direction
So they hit the ground
at the same time!
Cannonballs shot horizontally with different
speeds from the ship travel different distances.
But each cannonball drops the same distance in
the same amount of time, since the vertical
acceleration is the same for each.
So no matter how fast you fire the cannonball
they are all in the air the same amount of time!!!!
Sir Isaac Newton (1642 – 1727)
Published the Principia
 Laid out his laws of motion and
universal gravitation laws
 Newton showed that Kepler’s
Laws are specific examples of
general laws of motion and
gravity
 Not a very nice man
 Brilliant, knew it, didn’t
hide it, destroyed rivals
Newton’s Three Laws
1. A body continues at rest or in uniform motion in
a straight line unless acted on by some net
force.
2. The acceleration of a body is inversely
proportional to its mass, directly proportional to
the net force, and in the same direction as the
net force
   F = mass * acceleration
3. To every action, there is an equal and opposite
reaction
Newton’s First Law
A body at rest
tends to remain
at rest

A body in motion
tends to remain
in motion
Newton’s 1st Law: Why you wear a
seatbelt
Newton’s Second Law
The force exerted on an object is equal to the
product of that object’s mass times its
acceleration.
The acceleration is in the same direction as the
force.

Force = mass x acceleration
F=ma
(force and acceleration are vectors)
Newton’s             2nd     Law
 What is Acceleration?
 Acceleration is:

(change in velocity)/(change in
time)
 How fast you change your velocity in a certain amount of
time
   Velocity is a vector – has direction and magnitude
   So change your direction   or speed you experience
acceleration
Where does the bug have:
Constant velocity ?
Acceleration ?
Quiz time again
 Imagine you are driving a car. The car is moving at a
constant velocity of 50 mph. You cover a distance of 50
miles. What is its acceleration?
 1 m/hour2
 50 m/hour2
 2500 m/hour2
 0 m/hour2
Newton’s          3 rd   Law
 The Law of Action and Reaction:
 When any two objects interact, the force exerted by
the first object on the second is equal and opposite to
the force exerted by the second on the first.
 Or, for every action (force), there is an equal and
opposite reaction; that is forces are mutual and act in
pairs.
Quiz Time again: Newton’s 3rd Law
 Sometimes movies get it right
 Watch the fire extinguisher…
 Red Planet
Action-Reaction Pairs
Book pulling on Earth                     Table pushing on book

Physics
Physics is Fun!

Earth pulling on Book                     Book pushing on table
Newton’s Law of Gravitation
G m1m2
F = -
r2
 where G is the “gravitational constant”
 6.67 x 10-11 Nm2/kg2
 m1 is the mass of one body
 m2 is the mass of another body
 r is the separation between them (frequently labeled d)
 Measured from the center of each object
Inverse Square Law
Quiz Time!!
 Imagine you have two objects of equal mass (say 10
kilograms). The two objects are setting 2 meters apart
and you move them till they are 4 meters apart. How
much has the gravitational force changed?
Forces
Initial                After
G m1m2                   G m1m2
Fa = -         2
Fb = -
r                         r2

G m1m2                  G m1m2
Fa = -                  Fb = -
2    2                   42
G m1m2                 G m1m2
Fa = -                 Fb = -
4                       16

Double the distance decrease the force by Four
Newton Gravitation and the Earth
 From the second law of motion (F = ma), we know
that a body of mass m subjected to the Earth's
gravitational force of attraction F undergoes an
acceleration at the Earth's surface of
   g = F/m.
 From the law of gravitation, this force is F =
Gm1m2/r2,
 where m1 is the mass of the Earth, and m2 is your
weight and r is the separation between the centers of
the two bodies, or the Earth's radius.
Figuring out acceleration due to gravity
 Assuming that we know G, we have
 m2g = Gm1m2/r2,
 or
 g = Gm1/r2 = 9.8 m/s2
 where your mass has canceled out.
 The acceleration of the attracted body (you) does not
depend on its own mass
 Mathematical proof that Galileo was
right!!!!
Weight and Mass
   Weight is a type of force:
It is the earth’s gravitational force on an object
   An object’s weight is proportional to its mass
 weight  mass
 weight = constant · mass
   On the Earth’s surface, that constant, g, is
 9.8 Newtons/kilogram = 9.8 meters/second2
(9.8 is approximately 10)
 32 feet/second2
 g is called the acceleration due to gravity
Forces are measured in…
• Force = mass x acceleration, or F=ma
(Newton’s 2nd law)
• Measured in Newtons (unit)
• weight = mass x acceleration, and on
earth, W=mg
• 1 Newton  1 kilogram·meter/second2
(definition)
weight of a medium apple!
So, how does this effect me???
 Helps us in many ways
 Cars, rockets, merry-go-rounds
 Why objects fall down…
 Newton felt that the force of gravity was focused at the
center of an object
 Intuition at first
 Needed to invent calculus to prove it
Center of mass
•Much of physics involves looking
for ways to simplify complicated
interactions.
•An example is the motion of a
baseball bat thrown into the air.
•If one looks carefully, there is
a special point of the bat that
moves in a simple parabolic path.
•That special point is the center
of mass of the bat.

The center of mass of a body or a system of bodies
is the point that moves as though all of the mass were
concentrated there, and all external forces were
applied at that point.
Why things fall over….
 Every object has a special point called the center of
gravity (CG). The CG is usually right smack in the center
of the object.
 if the center of gravity is supported, the object will not
fall over.
 Application !
   You generally want a running back with a low CG then it’s harder
to knock him down.
 The lower the CG the more stable an object is.
Next
 Going to use what we have learned about energy and
forces to get us to the Moon and how roller coasters
work!

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