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Chapter 3 - Energy
Changes in motion and position
-involves forces
leads to changes in energy
ENERGY - ability to do work
position change, motion change:
study, mow lawn, wind mill
MECHANICAL WORK -
transformation of forces into energy
force must move object-displacement
no force
no work
no movement
}
F
does
no work
Fd = 1 N
W = Fdd
Force in direction of motion
d = 1m
W = Fdd = (1 N)(1 m) = 1 N m (kg m2/s2)
= 1 Joule = 1J
EXAMPLE : weight lifting
Work to lift a 100 kg barball a distance of 1 m
( @ constant speed)
Lift w/ no a
d=h=1m
Fnet = 0 = weight-Fup
Fup=W=mg
in direction of motion
m = 100 kg
Fup
W
W = Fdd = Fupd = (mg)h =
(100 kg)(10 m/s2)(1 m)
1000 kg m2/s2 = 1000 J
mechanical work
to change the position of the object
Note: no mechanical work done to hold barbell
d=0 when holding still above head
Another example : car racing
A 1000 kg car goes from 0 to 20 m/s in 5 seconds.
How much work is done (by the engine)?
CONNECT Newton’s 2nd law
F=ma
engine accelerates car
to=0 ax
xo=0
vox =0
t = 5s
x=
vx =20 m/s
W = Fdd = Fxd maxd
Work changes the motion of the car
WORK - forces used to give energy
to an object
}
motional energy
MECHANICAL
positional energy ENERGY
chemical, electrical, heat
Power - rate at which work is done
how fast work is done
Powerful: can do work fast
Power (P) = (Work-Energy)/time = W/t
J/s = Watt = W
SI unit for power
Light bulb: 75 W
How much (work) energy in 1 hour?
P = (W-E)/ t E = W = Pt
HORSEPOWER: compare machines to horses
F=150 lbs
v= 2.5 mph
English unit hp
550 ft-lb/s
P = W/ t= (Fdd)/t = Fd (d/ t) = Fdv
1 hp = 1 horsepower = 746 W
Other Power units:
megawatt = MW = 106 W
POWER COMPANIES
KINETIC ENERGY - energy associated with
the motion of an object
Applied forces cause objects to move - accelerates
motional energy – mass and velocity
velocity influences more
K=1/2 mv2 work increases velocity
Work-Energy Theorem
W = DKE
change in kinetic
= 1/2 mv2 -1/2 mvo2
Work to bring an object to rest:
W=1/2 mv2 just the KE
Car example:W= 200,000 J
W= KE = ½ mv2
What is the velocity?
another way of looking at the problem!
POTENTIAL ENERGY - energy associated
with the position of an object
potential for doing work
drop rock – falls –
gains KE (motional)
Transforms force of gravity into KE of motion
- does work when released
Definition: PE = -W
work to achieve
position
Gravitational Potential Energy –
work required to raise the object to a
particular height
PEgrav = Fdd = (mg)h
=mgh like
barbell
h
zero reference – always be consistent in zero height
h= 3m
h=0
h=-2m
Other types of PE
SPRINGS
PE= ½ kx2
change position by compressing
zero – uncompressed
Electrical – work to move charge
Chemical – work to break bond
MECHANICAL ENERGY
Energy associated with the mechanical
work on an object – motional and positional
E = KE + PE(grav)
sum of both
The mechanical energy is conserved
when friction absent
FRICTION – nonconservative
– heats environment
Law of CONSERVATION OF (MECHANICAL) ENERGY
-energy is neither created or destroyed
-assumption: no friction present
E = KE+PE =constant
energies transformed
not lost
Conservation of energy
E=KE+PE
relates motion and position
Einitial = Efinal can solve for position
or motion (v)
EXAMPLE: ROLLER COASTER
A 100 kg rollercoaster moves along the track
shown starting from rest.
For each position marked, find the:
mechanical energy
potential energy
kinetic energy
velocity
vi=0
NO FRICTION
100 m
50 m
30 m
h=0
PE=0
We will be looking at simpler problems
EXAMPLE: A 1.4 kg PSC book is
dropped out of a 20 m high building.
a) What is the PE at the top?
b) What is the KE at the bottom?
c) What is the velocity of the book at the bottom?
20 m
h=0
PE=0
NOTE: PE at the top is transformed into
KE at the bottom!
0
0
E= (KE+PE)top = (KE+PE) bot
PEtop = KEbot
no energy lost – just transformed
All Energy Is Conserved!!!
Can work problems with friction and other forces
-leave this for more advanced course, but
if whole system considered
Etot = PEgrav + PEother + KE
GENERALIZED WORK-ENERGY THEOREM
Ef - Ei=Wnc
work due to friction
change in
mechanical energy
NOW ALL ENERGY IS CONSERVED – everywhere
the energy goes is taken care of
-heat to environment
-mechanical work
-radiant
-sound
-electrical
-nuclear
-anything else
• Energy Flow.
• Work and Energy.
– Energy is used to do work on an
object, exerting a force through a
distance.
– This force is usually against
something and there are five main
groups of resistance.
• Work against inertia.
–Since inertia is an objects
resistance to change of
motion, it naturally follows
that this would resist forces
acting upon it.
• Work against fundamental
forces.
–Gravitational attraction.
–Electromagnetic forces.
–Nuclear forces.
• Work against friction
–Friction is always present
when two objects are in
contact with each other.
–Friction is always a force in
the opposite direction of the
applied force.
• Work against shape.
–Work is needed to stretch or
compress an object.
–This is what happens when
we work against the shape of
a spring.
• Work against any combination
of inertia, fundamental forces,
friction, or shape.
– Some kind of energy change
has taken place, which may
include one of the following:
• Increased kinetic energy.
–Work against inertia results
in energy of motion for an
object.
• Increased potential energy.
–Work against fundamental
forces and work against
shape result in an increase in
energy of position (potential
energy)
• Increased temperature.
–Work against friction always
results in an increase in
temperature.
• Increased combination of
kinetic energy, potential energy,
and/or temperature.
• Energy Forms. (five forms).
– Mechanical energy.
• Usually associated with the
kinetic energy of everyday
objects and potential energy
that results from the effect of
gravity.
Mechanical energy is the energy
of motion, or the energy of
position, of many familiar
objects. This boat has energy of
motion.
– Chemical energy.
• Chemical energy is the form of
energy associated with
chemical reactions.
• Chemical energy is released
during the process known as
oxidation.
• Chemical energy is potential
energy that is released when
chemical reactions break bonds
in molecules.
Chemical energy is a form of potential
energy that is released during a chemical
reaction. Both (A) wood and (B) coal
have chemical energy that has been
stored through the process of
photosynthesis. The pile of wood may
provide fuel for a small fireplace for
several days. The pile of coal might
provide fuel for a power plant for a
– Radiant energy.
• Radiant energy is the form of
energy that travels through
space.
• Also called electromagnetic
radiation.
• Visible light is one small part of
the electromagnetic radiation.
• Largest form of energy Earth
receives
The electromagnetic
spectrum includes
many forms of radiant
energy. Note that
visible light occupies
only a tiny part of the
entire spectrum.
– Electrical energy.
• Electrical energy is a form of
energy that comes from
electromagnetic interactions.
• Electrical energy that travels
through the wires in our homes
to light or houses is a familiar
form of electrical energy.
The blades of a steam turbine. In a
power plant, chemical or nuclear energy
is used to heat water to steam, which is
directed against the turbine blades. The
mechanical energy of the turbine turns
an electric generator. Thus a power plant
converts chemical or nuclear energy to
mechanical energy, which is then
converted to electrical energy.
– Nuclear energy.
• this is the form of energy
generated in nuclear power
plants.
• Fission-split heavy nucleus
• Fusion-combine light nucleus
• E=mc2
• Energy Conversion.
– Energy can be converted from
one form to another.
– For example, during a fall PE lost
= KE gained
– mgh = 1/2mv2
– Solving for vf
– vf = 2gh
– This allows you to calculate the
final velocity of a falling object
after its potential energy is
converted into kinetic energy.
This pendulum bob loses potential
energy (PE) and gains an equal amount
of kinetic energy (KE) as it falls through
as distance h. The process reverses as
the bob moves up the other side of its
swing.
The
energy
forms and
some
conversion
pathways.
• Energy Conservation.
– Any form of energy can be
converted into another form.
– The total amount of energy
remains constant.
– Law of Conservation of Energy:
• Energy is never created or
destroyed. Energy can be
converted from one form to
another, but the total energy
remains constant.
• Energy Sources Today.
– Petroleum is our most widely
used source of energy.
• Petroleum provides about 40
percent of the energy used by
the US.
– Natural gas provides about 20
percent of our energy needs.
– Coal provides about 25 percent of
our energy needs.
– Alternative energies (solar, wind,
geothermal) provide less than 2
percent of the total.
– Over 99 percent of our energy
needs are supplied by 4 sources:
• Petroleum.
• Coal.
• Hydropower.
• Nuclear.
(A) The sources of
energy and
(B) the uses of
energy during the
1990s.
• Petroleum.
– Petroleum is oil that comes from
oil bearing rocks.
– Petroleum and natural gas come
from organic sediments, material
that have settled out of water.
– Most of the organic material
comes from plankton. The process
of converting organisms into
petroleum and natural gas takes
millions of years.
– Natural gas forms under higher
temperatures than petroleum.
• Coal.
– Coal forms from an accumulation
of plant materials that collected
millions of years ago.
– Carbon rich decayed plant
material is called peat.
– Pressure, compaction, and
heating are brought about by
movement of the Earth's crust
eventually change the water
content and release the carbon in
the materials, it has now begun
the process toward coal
formation.
– Coal is ranked according to how long
it took to form and how hard it is.
• Lignite is the lowest ranked and is
softest, took the least time to form,
and burns quickest so contains the
least amount of usable energy.
• Bituminous is the next highest
raking.
• Anthracite is the hardest and took
the longest to form and so contains
the most usable energy.
• Softer coal also has more impurities
which contribute to increased
pollution levels.
• Water Power.
– Moving water is a source of
renewable energy that has been
used for thousands of years.
– At present in the US we have built
about all of the hydropower
plants that we can as we have no
usable sources of moving water
left.
• Nuclear Power.
– Nuclear power plants use the
energy that is release from the
splitting of uranium atoms and
plutonium atoms to produce
electrical energy.