Download ENERGY - Chapter 3

ENERGY
Chapter 3
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When you have completed this chapter you
should be able to:
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Explain what is meant by work.
Explain what is meant by power.
Distinguish between kinetic energy and potential energy.
Give several examples of potential energy.
State the law of conservation of energy and give several examples of energy
transformations.
Use the principle of conservation of energy to analyze events in which work and different
forms of energy are transformed into one another.
Discuss why heat is today regarded as a form of energy rather than as an actual substance.
Define linear momentum and discuss its significance.
Use the principle of conservation of linear momentum to analyze the motion of objects that
collide with each other or push each other apart, for instance, when a rocket is fired.
State what is meant by angular momentum.
Explain how conservation of angular momentum is used by skaters to spin faster and by
footballs to travel farther.
Describe several relativistic effects and indicate why they are not conspicuous in the
everyday world.
Explain what is meant by rest energy and be able to calculate the rest energy of an object of
given mass.
Describe how gravity is interpreted in Einstein's general theory of relativity.
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Discuss the various factors that are part of the energy problems of the future.
Main Concepts in Ch 3
 Work
 Power
 Energy
 Momentum
 Relativity
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Energy
 In general, energy refers to an ability to
accomplish change
 “Change” is not a very precise notion
 We will start with the simpler concept of
“Work” and use it to relate change and
energy in the orderly way of science
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Work
 Changes that take place in the physical world
are the result of forces
 However, not all forces act to produce
changes
 It is the distinction between forces that
accomplish change and forces that do not
that is central to the idea of work
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Work
 Work done by a force acting on an object is
equal to the magnitude of the force multiplied
by the distance through which the force acts
W=Fxd
W = work
F = applied force
d = distance through which the force acts
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Was Change Accomplished?
Figure 3-1
tam3s6_1
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Work
 The SI unit of work is the joule (J)
 1 joule is the amount of work done by a force
of one Newton when it acts through a
distance of one meter
 1 joule (J) = 1 newton-meter (N . m)
 Joule is named after the English scientist
James Joule
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Work
 The direction of the force F is assumed to be the
same as the direction of displacement d
 If not, we use the magnitude Fd of the projection of
the applied force that act in the direction of motion
 A force that is perpendicular to the direction of motion
of an object can do NO WORK on the object
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Gravity does no work on objects moving horizontally
along the Earth’s surface
However, when we drop an object, work is done on it
as it falls to the ground
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Force and distance
are parallel
Force and distance
are not parallel
Tam3s6_2
Figure 3-3
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Work Done Against Gravity
 Work done in lifting an object against gravity
can be calculated using:
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W = mgh where
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mg = force of gravity on the object is its weight
h = height raised above its original position
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Example 3.1
 Calculate work done when (a) horizontal
force of 100 N is used to push a 20-kg box
across a level floor for 10 m and (b) when
raising the same box over your head by 10 m
W=Fxd=
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(100 N) x (10 m) = 1000 J
 W = mgh =
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(20 kg)(9.8 m/s2)(10 m) = 1960 J
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Power
 The rate at which work is being done
 The more powerful, the faster something can do work
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P = W/t
P = power
 W = Work
 t = time
 The SI unit of power is the watt (W)
 1 watt (W) = 1 joule/second (J/s)
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1 kW = 1000W
 1 hp = 746 W (hp = horsepower)
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Example 3.2
 A 15-kW electric motor
provides power for the
elevator of a building.
What is the minimum
time needed for the
elevator to rise 30 m to
the sixth floor when its
total mass loaded is
900 kg?
W mgh
t 
P
P
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Energy
 Is the property something has that enables it
to do work
 When we say that something has energy, it
means that it is able, directly or indirectly, to
exert a force on something else and perform
work
 When work is done on something, energy is
added to it
 The SI unit of energy is also the joule (J)
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Kinetic Energy
 The energy of a moving object.
 Kinetic energy of moving things depend upon
its mass and speed, such that
= ½ mv2
 The v2 factor means the KE increases
very rapidly with increasing speed
 KE
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Kinetic Energy Example 3.3
The kinetic energy of a 1000-kg car when its speed is 10 m/s is what?
The kinetic energy of a 1000-kg car when its speed is 30 m/s is what?
Figure 3-7
Tam3s6_3
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Potential Energy
 The energy of position
 The amount of work something could do
A raised stone has PE because it can do work on the ground
when dropped.
Figure 3-9
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Kinetic and Potential Energy
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Potential Energy Examples
Figure 3-10
tam3s6_6
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Gravitational Potential Energy
 When an object with mass m is raised a
certain height h above its original position, its
gravitational PE is equal to the work that was
done against gravity to bring it to that height
 PE = mgh
 m = mass
 h = height
 g = gravity
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The increase in PE of a raised object is
equal to the work used to lift it
Tam3s6_7
Figure 3-11
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Energy Transformations
 Nearly all familiar mechanical processes
involve interchanges among KE, PE, and
work
 Kinetic energy can be changed to potential
energy and vice versa
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Energy Transformations
KE is low
PE is high
KE is high
PE is low
Figure 3-13
Tam3s6_8
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Total Energy is constant; Angular momentum is constant
Angular Momentum is
constant
for all points along orbit
Velocity at Aphelion
VA
Minimum KE
Maximum PE
RA
Total Energy
KE + PE
Is also Constant
At Aphelion Angular
Momentum
Is VA x RA
Which is also equal to
Sun
RP
Maximum KE
Minimum PE
VP
x
RP
Velocity at Perihelion
VP
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Energy Transformations in Pendulum Motion
Figure 3-15
Tam3s6_10
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Other Forms of Energy
 Chemical energy
 gasoline is used to propel a car and the
chemical energy of food enables us to perform
work
 Heat energy
 burning coal or oil is used to form the steam
that drives the turbines of power stations
 Radiant energy
 the sun performs work in causing water from
the earth’s surface to rise and form clouds
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The Law of the
Conservation of Energy
 Energy cannot be created or
destroyed, although it can be
changed from one form to
another
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Kinetic, potential, chemical, heat, and
radiant energy can all be changed between
one another
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The Nature of Heat
 What is Heat?
 Heat is a form of
energy
 The heat content of
a body of matter
consists of the KE of
random motion of
the atoms and
molecules of which
the body consists
Vibrating molecules in a solid
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The Nature of Heat
 Less than 2 centuries
ago, heat was thought
of as a substance called
caloric
 Count Rumford (a.k.a.
Benjamin Thompson)
regarded heat as
energy, not as a
substance
 Heat as a substance
could not account for
the unlimited heat
generated by friction
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The Nature of Heat
 James Prescott Joule
(1818-1889) performed
a classic experiment
that proved heat was
energy and not a
substance
 The SI unit of energy,
the Joule, was
subsequently named
after James Prescott
Joule
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Joule’s experimental demonstration that
heat is a form of energy.
Tam3s6_11
Figure 3-20
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Momentum
 Momenta can give us further insights into
the behavior of moving objects
 Linear and angular momenta are vector
quantities and will be described
subsequently
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Linear Momentum
 Linear momentum (p) – Moving objects tend
to continue to move at constant speed along
a straight path
 The linear momentum (or momentum) of
such an object is a measure of this tendency
 p = mv where
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m = mass
v = velocity
 The greater m and v are, the harder it is to
change the object’s speed or direction
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Linear Momentum of a Moving Object
Observe what happens to various variables (p,m,v) when one is changed
What happens to
p when m is
changed?
What happens to
p when v is changed?
Tam3s6_12
Figure 3-21
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Law of Conservation
of Momentum
 In the absence of
outside forces, the total
momentum of a set of
objects remains the
same no matter how the
objects interact with one
another
 Momentum
considerations are
useful when explosions
and collisions are
involved
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Rocket propulsion
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Law of Conservation of Momentum
tam3s6_13
Figure 3-22
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Angular Momentum
 The rotational quantity that corresponds to linear
momentum is called angular momentum
 The conservation of angular momentum is the formal
way to describe the tendency of a spinning body to
continue to spin
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Spinning earth
 Precise definition is complicated because it depends
not only on:
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mass and velocity but
 how
the mass is arranged in the body
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Angular Momentum
The farther away from the axis of rotation the mass is
distributed, the more angular momentum
Also demonstrates
conservation of
angular momentum.
Tam3s6_17
Figure 3-17
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Another Example of
Angular Momentum
 Kepler’s second law of planetary motion is similar to
the changing spin rate of a skater in the previous
slide
 A planet moving around the sun has angular
momentum, which must be the same everywhere in
its orbit
 As a result, the planet’s speed is greatest when it is
close to the sun, least when it is far away
 http://hyperphysics.phy-astr.gsu.edu/HBASE/mechanics/indexv.html
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Table 3-1
Energy, Power, and Momentum
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Einstein
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Einstein’s Relativity
 Albert Einstein (1879-1955)
published three papers in 1905.
 Proposed light has a dual
character (chapter 8)
 Brownian motion
 Theory of Special Relativity
 Theory of Special Relativity
(1905) revolutionized science.
 Relativity links not only time
and space but also energy
and matter
 From this paper came many
remarkable predictions, all of
which have been confirmed
by experiment
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Einstein’s Relativity
 Eleven years later, Einstein
took relativity a step further
by interpreting gravity as a
distortion in the structure of
space and time known as
the Theory of General
Relativity
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Special Relativity
 Einstein’s 1905 theory, which led to the
two postulates is called special
relativity because it is restricted to
constant velocities
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Special Relativity
 First Postulate states the laws of physics are the
same in all frames of reference moving at
constant velocity with respect to one another
 Two observers in motion relative to each other
 Each will disagree on what they observe
 Each viewpoint is equally valid
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Windowless Airplane
 This introduces the first postulate. There is no
experiment you can perform to determine if
you are standing still or moving in a straight
line at a constant speed.
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Bottom Line
 All uniform motion is relative. That is, you can
not determine if you are standing “still” or
moving in a straight line at a constant speed,
and the speed of light in a vacuum is the
same for all observers undergoing
uniform motion.
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Special Relativity
 Second Postulate which comes from the
results of numerous experiments says
 The
speed of light in free space has the
same value for all observers no matter
their motion
 And that value is c = 3 x 108 m/s or
about 186,000 mi/s
 Nothing can travel faster than the speed
of light-it’s the ultimate speed limit
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http://www.davidcolarusso.com/blog/?p=39#more-39
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Key Outcomes of Special Relativity
 Time is not the same as seen by two
observers having relative constant
velocity (know this)
 Events seen as simultaneous by one
observer not seen as simultaneous by
another if there is relative constant velocity
 Time Dilation is seen by stationary observer
relative to a moving “clock”
 The twin Paradox
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Key Outcomes of Special Relativity
 Length is contracted in the direction of
motion as seen by a stationary observer
measuring a moving object. (know this)
 The can be seen as an outcome of time
dilation
 All of this is predicated on speeds
approaching a significant % of the speed of
light
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Key Outcomes of Special Relativity
 Mass of an object increases with velocity
and would become infinite as speed
approaches the speed of light ( know this)
 Matter cannot move at the speed of light
meaning that the speed of light is a speed
limit for everything but light
 As V approaches the speed of light the kinetic
energy can exceed ½ m c2 where m is “rest
mass”
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The Lorenz Factor Gamma
 The Lorenz factor ɣ is a measure of how
much special relativity is kicking in
 ɣ = 1/ [ 1- v2 / c2 ]
v/c
ɣ
10%
1.005
80%
1.67
90%
2.29
99.99%
70.7
v/c = 10% is 18,600 miles / sec
equivalent to 75% around the world/ second
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Velocity Impact on time, length and mass
 Time contracts, length contracts, mass
increases
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T observer = T of mover x ɣ
Length stationary = length moving x ɣ
Rest Mass = Moving Mass / ɣ
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Time Dilation and Length Contraction
 http://www.pbs.org/wgbh/nova/einstein/hotsciencetwin/
 The Time Traveler
 http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/specrel/lc.html
 Length Contraction
 http://www.phys.unsw.edu.au/einsteinlight/
 Univ New S. Whales – Good Stuff on Einstein
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Special Relativity
 The most far-reaching conclusion of special
relativity is that mass and energy are related
to each other so closely that matter can be
converted into energy and energy into matter.
 The rest energy of a body is the energy
equivalent of its mass.
 If a body has the mass m0 when it is as rest,
its rest energy is:
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E0 = m0c2
Rest energy = (rest mass)(speed of light)2
http://www.pbs.org/wgbh/nova/einstein/experts.html
Neil Tyson, Tim Halpin-Healy, Sheldon Glashow
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The Tree of Relativity
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Special Relativity
 Calculate the rest energy and potential
energy of a 1.5 kg book on top of Mt. Everest
(8850 m high)
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Eo = mc2 = (1.5kg)(3x108m/s)2=1.35 x 1017J
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PE = mgh = (1.5kg)(9.8m/s2)(8850m)=1.3 x 105J
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Special Relativity
 Can you think of
examples of matter
converting into energy?
 All energy producing
reactions in chemistry
and physics from the
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Lighting of a match
Nuclear fusion of sun
Sun consumes 28 billion
Tons of its mass per second
Fortunately the sun contains 2 x 1030 Kg
So good for 5B more years
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Special Relativity
 Can you think of examples of energy
converting into matter?
 Particle accelerators convert
energy into subatomic particles, for
example by colliding electrons and
positrons. Some of the kinetic
energy in the collision goes into
creating new particles.
 Pair production – when a particle
and its anti-particle materialize
when a high-energy gamma ray
passes near an atomic nucleus.
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General Relativity
 Einstein’s later theory of general relativity dealt with
gravity, including accelerations
 Einstein’s General Theory of Relativity related
gravitation to the structure of space and time
 The force of gravity arises from a warping of
spacetime around a body of matter so that a nearby
mass tends to move toward the body
 General Relativity does not interpret gravity as a
force
 http://www.pbs.org/wgbh/nova/einstein/relativity/
 http://archive.ncsa.uiuc.edu/Cyberia/NumRel/GravWaves.html
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The Elevator Thought Experiment
 There is no experiment that can allow a
determination of the difference between an
elevator at rest on the ground and one that
accelerates at the rate of gravity
 This is the principle of EQUIVALENCE
 This led to conclusion that gravity can deflect
light reinforcing the warped space hypothesis
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General Relativity
 http://www.pbs.org/wgbh/nova/einstein/relativi
ty/
 General relativity may be the biggest leap of the
scientific imagination in history. Unlike many previous
scientific breakthroughs, such as the principle of
natural selection, or the discovery of the physical
existence of atoms, general relativity had little
foundation upon the theories or experiments of the
time. No one except Einstein was thinking of
gravity as equivalent to acceleration, as a
geometrical phenomenon, as a bending of time
and space.
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Gravity
Tam3s6_21
Figure 3-35
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Mass Warps space
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Light is affected by Gravity
 Possibly the most
spectacular of Einstein’s
results was that light should
be subject to gravity
 To check this prediction,
photos were taken of stars
that appeared in the sky
near the sun during an
eclipse in 1919 (stars could
be seen during an eclipse
because the moon obscured
the sun’s disk)
 Photos were compared with
other photos taken of the
same area when the sun
was far away
1.75 arc-seconds, versus a Newtonian
prediction of 0.87
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Another verification of General Relativiy
 The planet Mercury has
very high orbital
eccentricity
 The major axis of its
orbit is rotating faster
than would be
accounted by
Newtonion mechanics
 It was found that
Einstein’s equations of
General Relativity
accounted for the
discrepancy
 Rotation rate is 42
seconds of Arc per
century
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Time and relativity
 Special relativity
 General Relativity
 Time is affected by
 Time is affected by
the relative speeds
 Time is modified by
the factor ɣ
Mass warping the
space time
dimensionality
 Clocks above the
Earth run faster
The GPS system would not function
without correcting for both of these
effects
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