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Energy Makes it Go!!
Energy? What energy?
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nervous energy?
negative energy? positive energy?
Nuclear ( not nucular!) energy?
energy crisis?
What is Energy?
ENERGY
Motivation: Assume you want to study the
kinematics v(t) or x(t) of the sliding object in the
picture. It is too complicated w/out the exact
knowledge of the path. This, and other, kind of
studies are greatly simplified if one uses the
concept of energy.
ENERGY
Motivation: Assume you want to study the
kinematics v(t) or x(t) of the sliding
object in the picture. It is too
complicated w/out the exact knowledge
of the path. This, and other, kind of
studies are greatly simplified if one uses
the concept of energy.
•  It is hard to define Energy but we can say that it relates to the state, the
condition of the object or the configuration of a system of objects. e.g.
the kinetic condition/state of the object (kinetic energy). Other examples
include a spring in compressed state (potential energy), a piece of metal in hot
condition (thermal energy) etc.
•  Kinetic or Potential energy are referred to as form of Mechanical energy.
Thermal energy is considered to be a different category.
•  Energy is a scalar quantity.
Energy is like $$$
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you can change it
it can do useful things for you
you can save it or spend it
its better to have it than not have it
you can waste it (Chapter Five)
useless by itself: merely a concept
this is one way to think about it
(analogy only!!!)
two kinds of crashes
•  bounce back elastic
•  stick together inelastic
•  What’s the difference?
Vis Viva
•  (living force)
•  for elastic (bounce back) collisions,
vis viva is the same before and
after
•  for inelastic (sticky) collisions, vis
viva is smaller after collisions
•  we call this KINETIC ENERGY energy of motion!
Kinetic Energy
•  Kinetic Energy characterizes the state of motion of an
object
•  If an object moves, then it has kinetic energy. It is clear
that this statement is reference frame dependent. For an
object of mass m and moving with velocity v its kinetic
energy (K) is defined as:
1 2
K = mv
2
•  Kinetic Energy can’t be negative, it is always positive or
zero.
Is rock climbing dangerous?
•  potential to gain large kinetic energy
(by falling down!)
•  Energy due to something’s position is
POTENTIAL ENERGY
Potential Energy characterizes the configuration of a system of
particles.
Potential Energy
•  Two common subcategories of potential energy
are:
•  Gravitational potential energy: state of
separation between objects which attract each
other with gravitational force. It increases
with distance.
•  Elastic potential energy: state of
compression of elastic objects (e.g. spring)
Determining potential energy values
•  The graviational potential energy of
an object (in a system) is equal to the
product of its weight times the
distance (height) of separation
P.E.=(Weight)x(height)
How is energy exchanged?
•  The Pit and the Pendulum (example)
•  What happens to that energy if we
stop at top???
•  stored as potential energy
So what?
•  pendulum: kinetic energy and
potential energy are both always
changing
•  Is anything that is not changing?
–  clue: always comes back to same height
when changes direction
•  kinetic plus potential energy does not
change
•  It is called MECHANICAL ENERGY
CONSERVED
(stays the same)
Mechanical Energy
•  As we mentioned before we call mechanical
energy of a system the sum of its kinetic and
potential energy. E = K.E + P.E.
•  If there are no frictional forces, i.e. losses of
energy into heat mechanical energy is conserved
•  MECHANICAL ENERGY CONSERVED
(stays the same)
Work
•  Objects can exchange energy –
•  via either forces or heat
•  It is called work, which is the process of
transferring energy between two objects via a
force.
• Who is doing work? the force E.g. If you apply a
force to an object it will accelerate, i.e. its
velocity will increase and so does its kinetic
energy; the applied force is transferring energy
from one object to another, it is doing work.
Work
•  Work is energy transferred from (to) an object
by means of a force acting on it
• If it is “To” an object; then we say that the
force is doing positive work
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From an object; then we say that the force is
doing negative work.
•  Note: Transfer of energy doesn’t mean flow of any
material or exchange of mass between the objects
Work done by a Force
We can distinguish the following cases (φ is the angle between the
force and the direction of motion):
•  φ=0
(force along direction of motion) à Work is positive
•  φ<900
W>0 (force is doing positive work, speed is increasing)
•  φ=900
•  φ>900
(force normal to velocity - is not doing work) W=0
W<0 (force is doing negative work, slowing down)
•  φ=180 (force along opposite direction of motion) à Work is negative
Work done by a Force
W=0
W<0
W>0
d
Multiple Forces
In the case of multiple forces we can apply the superposition principle:
So you can either replace all forces by just their sum, or
sum all individual works done.
Example
Work done by Weight
•  For horizontal displacements, Wg = 0
•  For vertical motion if f=1800 (going up) then work is
negative (object slows down)
•  If f=00 (falling down) then work is positive (accelerates).
Power
•  Power is the rate at which work is done, i.e. if work W is
done by a force in time Δt, the average power due to the
force is defined to be:
W
P=
Δt
The SI Unit of power is Watt, but we also use ft.lb/s and horsepower
(hp). 1 Watt = 1 W = 1 J/s = 0.738 ft lb/s, 1hp = 550 ft lb/s =
746 W
But, eventually….
•  pendulum slows down
•  what happens to energy?
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•  Where does it go????
•  What is it?
•  How can we make it?
•  Is it the same as temperature?
The heat is on!!
•  burning match vs. tub-full of hot
water
–  which is hotter??
–  which contains more heat??
•  first question, more precisely: which
has higher temperature?
Temperature vs. Heat
•  Temperature (roughly) describes the
“intensity” of heat
•  Heat content (roughly) describes the
total amount of heat.
•  Match has higher temperature, but
bath tub has greater heat content
•  higher temperature : more molecular
kinetic energy (sort of)
Low fat: only 3,452 Calories!
•  that’s right folks, heat is measured
in calories
•  It takes one calorie of heat to raise
the temperature of one gram of
water one degree Celsius
•  careful: nutritional Calorie = 1000
calories
James Joule (1818-1889)
•  Industrial
Revolution
•  Demonstrated that
mechanical energy
could be directly
converted into heat
Joule’s churn
•  weight falls; gives up
potential energy
•  water temperature
rises!
•  the further the weight
falls, the more the
temperature goes up
•  mechanical equivalent
of heat
what can this mean?
•  potential energy can be converted
directly into heat!
•  heat must be just another form of
energy!!!
•  (we need to be able to convert heat
into other energy: we will come back
later)
Recall...
•  mechanical energy is in some cases
conserved (elastic collisions, ideal
pendula, etc.)
•  in some cases it’s not (inelastic
collisions, imperfect pendula, etc)
•  When we consider heat as a form of
energy, TOTAL ENERGY is
conserved!!
•  Conservation of Energy Principle!!!!
one more detail..
•  how do we most often produce heat?
•  burn gasoline, wood, coal, whatever.
•  These contain “chemical” energy
So…
•  When we account for all the energy:
–  kinetic, potential, heat, chemical
•  The total energy of the universe stays
the same!!!!
•  Energy can be neither created nor
destroyed!
•  A Universe Shaking Idea!!!! (but
Universe itself seems to have escaped
this law!)
Tie it up
•  all different types of things
•  can become one another
•  must all be essentially the same thing:
energy
•  just changes from one form to
another; never destroyed --- never
created