Conceptual Physics

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Conceptual Physics

• Chapter Nine Notes
• Energy

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9.1 Work

• In the past several chapters, we utilized
  Newton's laws to analyze the motion of objects.
  Force and mass information were used to determine
  the acceleration of an object. Acceleration
  information was subsequently used to determine
  information about the velocity or displacement of
  an object after a given period of time. In this
  manner, Newton's laws serve as a useful model for
  analyzing motion and making predictions about the
  final state of an object's motion. In this unit,
  an entirely different model will be used to
  analyze the motion of objects. Motion will be
  approached from the perspective of work and
  energy. The affect that work has upon the energy
  of an object (or system of objects) will be
  investigated the resulting velocity and/or
  height of the object can then be predicted from
  energy information. In order to understand this
  work-energy approach to the analysis of motion,
  it is important to first have a solid
  understanding of a few basic terms. Thus, the
  sections of this unit will focus on the
  definitions and meanings of such terms as work,
  mechanical energy, potential energy, kinetic
  energy, and power.

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• When a force acts upon an object to cause a
  displacement of the object, it is said that work
  was done upon the object. There are three key
  ingredients to work - force, displacement, and
  cause. In order for a force to qualify as having
  done work on an object, there must be a
  displacement and the force must cause the
  displacement. There are several good examples of
  work which can be observed in everyday life - a
  horse pulling a plow through the field, a father
  pushing a grocery cart down the aisle of a
  grocery store, a freshman lifting a backpack full
  of books upon her shoulder, a weightlifter
  lifting a barbell above his head, an Olympian
  launching the shot-put, etc. In each case
  described here there is a force exerted upon an
  object to cause that object to be displaced.
• Mathematically, work can be expressed by the
  following equation.
• where F is the force, d is the displacement, and
  the angle (theta) is defined as the angle between
  the force and the displacement vector. Perhaps
  the most difficult aspect of the above equation
  is the angle "theta." The angle is not just any
  'ole angle, but rather a very specific angle. The
  angle measure is defined as the angle between the
  force and the displacement. To gather an idea of
  its meaning, consider the following three
  scenarios.

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• Scenario A A force acts rightward upon an object
  as it is displaced rightward. In such an
  instance, the force vector and the displacement
  vector are in the same direction. Thus, the angle
  between F and d is 0 degrees.
• Scenario B A force acts leftward upon an object
  which is displaced rightward. In such an
  instance, the force vector and the displacement
  vector are in the opposite direction. Thus, the
  angle between F and d is 180 degrees.
• Scenario C A force acts upward on an object as
  it is displaced rightward. In such an instance,
  the force vector and the displacement vector are
  at right angles to each other. Thus, the angle
  between F and d is 90 degrees.

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• Units of Work
• Whenever a new quantity is introduced in physics,
  the standard metric units associated with that
  quantity are discussed. In the case of work (and
  also energy), the standard metric unit is the
  Joule (abbreviated J). One Joule is equivalent to
  one Newton of force causing a displacement of one
  meter. In other words,
• The Joule is the unit of work.
• 1 Joule 1 Newton 1 meter
• 1 J 1 N m
• In fact, any unit of force times any unit of
  displacement is equivalent to a unit of work.
  Some nonstandard units for work are shown below.
  Notice that when analyzed, each set of units is
  equivalent to a force unit times a displacement
  unit. 
• In summary, work is done when a force acts upon
  an object to cause a displacement. Three
  quantities must be known in order to calculate
  the amount of work. Those three quantities are
  force, displacement and the angle between the
  force and the displacement.

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9.2 Power

• Power
• The quantity work has to do with a force causing
  a displacement. Work has nothing to do with the
  amount of time that this force acts to cause the
  displacement. Sometimes, the work is done very
  quickly and other times the work is done rather
  slowly. For example, a rock climber takes an
  abnormally long time to elevate her body up a few
  meters along the side of a cliff. On the other
  hand, a trail hiker (who selects the easier path
  up the mountain) might elevate her body a few
  meters in a short amount of time. The two people
  might do the same amount of work, yet the hiker
  does the work in considerably less time than the
  rock climber. The quantity which has to do with
  the rate at which a certain amount of work is
  done is known as the power. The hiker has a
  greater power rating than the rock climber.
• Power is the rate at which work is done. It is
  the work/time ratio. Mathematically, it is
  computed using the following equation.
•  

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• The standard metric unit of power is the Watt. As
  is implied by the equation for power, a unit of
  power is equivalent to a unit of work divided by
  a unit of time. Thus, a Watt is equivalent to a
  Joule/second. For historical reasons, the
  horsepower is occasionally used to describe the
  power delivered by a machine. One horsepower is
  equivalent to approximately 750 Watts. 

Most machines are designed and built to do
work on objects. All machines are typically
described by a power rating. The power rating
indicates the rate at which that machine can do
work upon other objects. Thus, the power of a
machine is the work/time ratio for that
particular machine. A car engine is an example of
a machine which is given a power rating. The
power rating relates to how rapidly the car can
accelerate the car. Suppose that a 40-horsepower
engine could accelerate the car from 0 mi/hr to
60 mi/hr in 16 seconds. If this were the case,
then a car with four times the horsepower could
do the same amount of work in one-fourth the
time. That is, a 160-horsepower engine could
accelerate the same car from 0 mi/hr to 60 mi/hr
in 4 seconds. The point is that for the same
amount of work, power and time are inversely
proportional. The power equation suggests that a
more powerful engine can do the same amount of
work in less time.
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• A person is also a machine which has a power
  rating. Some people are more power-full than
  others. That is, some people are capable of doing
  the same amount of work in less time or more work
  in the same amount of time. A common physics lab
  involves quickly climbing a flight of stairs and
  using mass, height and time information to
  determine a student's personal power. Despite the
  diagonal motion along the staircase, it is often
  assumed that the horizontal motion is constant
  and all the force from the steps are used to
  elevate the student upward at a constant speed.
  Thus, the weight of the student is equal to the
  force which does the work on the student and the
  height of the staircase is the upward
  displacement. Suppose that Ben Pumpiniron
  elevates his 80-kg body up the 2.0 meter
  stairwell in 1.8 seconds. If this were the case,
  then we could calculate Ben's power rating. It
  can be assumed that Ben must apply a 800-Newton
  downward force upon the stairs to elevate his
  body. By so doing, the stairs would push upward
  on Ben's body with just enough force to lift his
  body up the stairs. It can also be assumed that
  the angle between the force of the stairs on Ben
  and Ben's displacement is 0 degrees. With these
  two approximations, Ben's power rating could be
  determined as shown below.
•  

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• Ben's power rating is 871 Watts. He is quite a
  horse.
• The expression for power is work/time. And since
  the expression for work is forcedisplacement,
  the expression for power can be rewritten as
  (forcedisplacement)/time. Since the expression
  for velocity is displacement/time, the expression
  for power can be rewritten once more as
  forcevelocity. This is shown below.

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• This new equation for power reveals that a
  powerful machine is both strong (big force) and
  fast (big velocity). A powerful car engine is
  strong and fast. A powerful piece of farm
  equipment is strong and fast. A powerful
  weightlifter is strong and fast. A powerful
  linemen on a football team is strong and fast. A
  machine which is strong enough to apply a big
  force to cause a displacement in a small mount of
  time (i.e., a big velocity) is a powerful
  machine.

Mechanical Energy Previously, it was said that
work is done upon an object whenever a force acts
upon it to cause it to be displaced. Work is a
force acting upon an object to cause a
displacement. In all instances in which work is
done, there is an object which supplies the force
in order to do the work. If a World Civilization
book is lifted to the top shelf of a student
locker, then the student supplies the force to do
the work on the book. If a plow is displaced
across a field, then some form of farm equipment
(usually a tractor or a horse) supplies the force
to do the work on the plow. If a pitcher winds up
and accelerates a baseball towards home plate,
then the pitcher supplies
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• the force to do the work on the baseball. If a
  roller coaster car is displaced from ground level
  to the top of the first drop of a roller coaster
  ride, then a chain driven by a motor supplies the
  force to do the work on the car. If a barbell is
  displaced from ground level to a height above a
  weightlifter's head, then the weightlifter is
  supplying a force to do work on the barbell. In
  all instances, an object which possesses some
  form of energy supplies the force to do the work.
  In the instances described here, the objects
  doing the work (a student, a tractor, a pitcher,
  a motor/chain) possess chemical potential energy
  stored in food or fuel which is transformed into
  work. In the process of doing work, the object
  which is doing the work exchanges energy with the
  object upon which the work is done. When the work
  is done upon the object, that object gains
  energy. The energy acquired by the objects upon
  which work is done is known as mechanical energy.
• Mechanical energy is the energy which is
  possessed by an object due to its motion or due
  to its position. Mechanical energy can be either
  kinetic energy (energy of motion) or potential
  energy (stored energy of position). Objects have
  mechanical energy if they are in motion and/or if
  they are at some position relative to a zero
  potential energy position (for example, a brick
  held at a vertical position above the ground or
  zero height position). A moving car possesses
  mechanical energy due to its motion (kinetic
  energy).

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9.4 Potential Energy

• A moving baseball possesses mechanical energy due
  to both its high speed (kinetic energy) and its
  vertical position above the ground (gravitational
  potential energy). A World Civilization book at
  rest on the top shelf of a locker possesses
  mechanical energy due to its vertical position
  above the ground (gravitational potential
  energy). A barbell lifted high above a
  weightlifter's head possesses mechanical energy
  due to its vertical position above the ground
  (gravitational potential energy). A drawn bow
  possesses mechanical energy due to its stretched
  position (elastic potential energy).

• An object can store energy as the result of its
  position. For example, the heavy heavy ball of a
  demolition machine is storing energy when it is
  held at an elevated position. This stored energy
  of position is referred to as potential energy.
  Similarly, a drawn bow is able to store energy as
  the result of its position. When assuming its
  usual position (i.e., when not drawn), there is
  no energy stored in the bow. Yet when its
  position is altered from its usual equilibrium
  position, the bow is able to store energy by
  virtue of its position. This stored energy of
  position is referred to as potential energy.
  Potential energy is the stored energy of position
  possessed by an object.

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• Elastic Potential Energy
• The first form of potential energy which we will
  discuss is elastic potential energy. Elastic
  potential energy is the energy stored in elastic
  materials as the result of their stretching or
  compressing. Elastic potential energy can be
  stored in rubber bands, bungee chords,
  trampolines, springs, an arrow drawn into a bow,
  etc. The amount of elastic potential energy
  stored in such a device is related to the amount
  of stretch of the device - the more stretch, the
  more stored energy.
• Springs are a special instance of a device which
  can store elastic potential energy due to either
  compression or stretching. A force is required to
  compress a spring the more compression there is,
  the more force which is required to compress it
  further. For certain springs, the amount of force
  is directly proportional to the amount of stretch
  or compression (x) the constant of
  proportionality is known as the spring constant
  (k).

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• Such springs are said to follow Hooke's Law. If a
  spring is not stretched or compressed, then there
  is no elastic potential energy stored in it. The
  spring is said to be at its equilibrium position.
  The equilibrium position is the position that the
  spring naturally assumes when there is no force
  applied to it. In terms of potential energy, the
  equilibrium position could be called the
  zero-potential energy position. There is a
  special equation for springs which relates the
  amount of elastic potential energy to the amount
  of stretch (or compression) and the spring
  constant. The equation is
• To summarize, potential energy is the energy
  which is stored in an object due to its position
  relative to some zero position. An object
  possesses elastic potential energy if it is at a
  position on an elastic medium other than the
  equilibrium position.

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• Chemical Potential Energy
• The chemical energy in fuels is also potential
  energy. Any substance that can do work through
  chemical reactions possesses chemical energy.
  Potential energy is found in fossil fuels,
  electric batteries, and the food we eat.
• Gravitational Potential Energy
• The first form of potential energy which we will
  discuss is gravitational potential energy.
  Gravitational potential energy is the energy
  stored in an object as the result of its vertical
  position or height. The energy is stored as the
  result of the gravitational attraction of the
  Earth for the object. The gravitational potential
  energy of the massive ball of a demolition
  machine is dependent on two variables - the mass
  of the ball and the height to which it is raised.
  There is a direct relation between gravitational
  potential energy and the mass of an object. More
  massive objects have greater gravitational
  potential energy. There is also a direct relation
  between gravitational potential energy and the
  height of an object. The higher that an object is
  elevated, the greater the gravitational potential
  energy. These relationships are expressed by the
  following equation

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• PEgrav mass g height
• PEgrav m g h
• In the above equation, m represents the mass of
  the object, h represents the height of the object
  and g represents the acceleration of gravity (9.8
  m/s/s on Earth).
• To determine the gravitational potential energy
  of an object, a zero height position must first
  be arbitrarily assigned. Typically, the ground is
  considered to be a position of zero height. But
  this is merely an arbitrarily assigned position
  which most people agree upon. Since many of our
  labs are done on tabletops, it is often customary
  to assign the tabletop to be the zero height
  position. Again this is merely arbitrary. If the
  tabletop is the zero position, then the potential
  energy of an object is based upon its height
  relative to the tabletop. For example, a pendulum
  bob swinging to and from above the table top has
  a potential energy which can be measured based on
  its height above the tabletop. By measuring the
  mass of the bob and the height of the bob above
  the tabletop, the potential energy of the bob can
  be determined.

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• Since the gravitational potential energy of an
  object is directly proportional to its height
  above the zero position, a doubling of the height
  will result in a doubling of the gravitational
  potential energy. A tripling of the height will
  result in a tripling of the gravitational
  potential energy.
• Use this principle to determine the blanks in the
  following diagram. Knowing that the potential
  energy at the top of the tall platform is 50 J,
  what is the potential energy at the other
  positions shown on the stair steps and the
  incline?

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9.5 Kinetic Energy

• Kinetic energy is the energy of motion. An object
  which has motion - whether it be vertical or
  horizontal motion - has kinetic energy. There are
  many forms of kinetic energy - vibrational (the
  energy due to vibrational motion), rotational
  (the energy due to rotational motion), and
  translational (the energy due to motion from one
  location to another). To keep matters simple, we
  will focus upon translational kinetic energy. The
  amount of translational kinetic energy (from here
  on, the phrase kinetic energy will refer to
  translational kinetic energy) which an object has
  depends upon two variables the mass (m) of the
  object and the speed (v) of the object. The
  following equation is used to represent the
  kinetic energy (KE) of an object.
• 
  where m mass of object
• v speed of object

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• This equation reveals that the kinetic energy of
  an object is directly proportional to the square
  of its speed. That means that for a twofold
  increase in speed, the kinetic energy will
  increase by a factor of four. For a threefold
  increase in speed, the kinetic energy will
  increase by a factor of nine. And for a fourfold
  increase in speed, the kinetic energy will
  increase by a factor of sixteen. The kinetic
  energy is dependent upon the square of the speed.
  As it is often said, an equation is not merely a
  recipe for algebraic problem-solving, but also a
  guide to thinking about the relationship between
  quantities.
• Kinetic energy is a scalar quantity it does not
  have a direction. Unlike velocity, acceleration,
  force, and momentum, the kinetic energy of an
  object is completely described by magnitude
  alone. Like work and potential energy, the
  standard metric unit of measurement for kinetic
  energy is the Joule. As might be implied by the
  above equation, 1 Joule is equivalent to 1
  kg(m/s)2.

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9.6 Work-Energy Theorem

• Internal vs. External Forces
• There are a variety of ways to categorize all the
  types of forces. Earlier it was mentioned that
  all the types of forces can be categorized as
  contact forces or as action-at-a-distance forces.
  Whether a force was categorized as an
  action-at-a-distance force was dependent upon
  whether or not that type of force could exist
  even when the objects were not physically
  touching. The force of gravity, electrical
  forces, and magnetic forces were examples of
  forces which could exist between two objects even
  when they are not physically touching. In this
  lesson, we will learn how to categorize forces
  based upon whether or not their presence is
  capable of changing an object's total mechanical
  energy. We will learn that there are certain
  types of forces, which when present and when
  involved in doing work on objects will change the
  total mechanical energy of the object. And there
  are other types of forces which can never change
  the total mechanical energy of an object, but
  rather can only transform the energy of an object
  from potential energy to kinetic energy (or vice
  versa). The two categories of forces are referred
  to as internal forces and external forces.

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• Forces can be categorized as internal forces or
  external forces. There are many sophisticated and
  worthy ways of explaining and distinguishing
  between internal and external forces. Many of
  these ways are commonly discussed at great length
  in physics textbooks. For our purposes, we will
  simply say that external forces include the
  applied force, normal force, tension force,
  friction force, and air resistance force. And for
  our purposes, the internal forces include the
  gravity forces, magnetic force, electrical force,
  and spring force.
• The importance of categorizing a force as being
  either internal or external is related to the
  ability of that type of force to change an
  object's total mechanical energy when it does
  work upon an object.

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• When net work is done upon an object by an
  external force, the total mechanical energy (KE
  PE) of that object is changed. If the work is
  positive work, then the object will gain energy.
  If the work is negative work, then the object
  will lose energy. The gain or loss in energy can
  be in the form of potential energy, kinetic
  energy, or both. Under such circumstances, the
  work which is done will be equal to the change in
  mechanical energy of the object. Because external
  forces are capable of changing the total
  mechanical energy of an object, they are
  sometimes referred to as non-conservative forces.
• When the only type of force doing net work upon
  an object is an internal force (for example,
  gravitational and spring forces), the total
  mechanical energy (KE PE) of that object
  remains constant. In such cases, the object's
  energy changes form. For example, as an object is
  "forced" from a high elevation to a lower
  elevation by gravity, some of the potential
  energy of that object is transformed into kinetic
  energy. Yet, the sum of the kinetic and potential
  energies remain constant. This is referred to as
  energy conservation and will be discussed in
  detail later in this lesson.

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9.7 Conservation of Energy

• When the only forces doing work are internal
  forces, energy changes forms - from kinetic to
  potential (or vice versa) yet the total amount
  of mechanical is conserved. Because internal
  forces are capable of changing the form of energy
  without changing the total amount of mechanical
  energy, they are sometimes referred to as
  conservative forces.
• The work-energy theorem describes the
  relationship between work and energy. The
  work-energy theorem states that whenever work is
  done, energy changes. We abbreviate change in
  with the delta symbol, ?, and say
• Work ?KE
• The study of the various forms of energy and the
  transformations from one form to another is the
  law of conservation of energy. The law of
  conservation of energy states that energy cannot
  be created or destroyed. It can be transformed
  from one form into another, but the total amount
  of energy never changes.

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9.8 Machines

• There are six types of simple machine
• A machine is a tool used to make work easier.
  Simple machines are simple tools used to make
  work easier. Compound machines have two or more
  simple machines working together to make work
  easier.

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• Inclined Plane A plane is a flat surface. For
  example, a smooth board is a plane. Now, if the
  plane is lying flat on the ground, it isn't
  likely to help you do work. However, when that
  plane is inclined, or slanted, it can help you
  move objects across distances. And, that's work!
  A common inclined plane is a ramp. Lifting a
  heavy box onto a loading dock is much easier if
  you slide the box up a ramp--a simple machine.
• Wedge Instead of using the smooth side of the
  inclined plane, you can also use the pointed
  edges to do other kinds of work. For example, you
  can use the edge to push things apart. Then, the
  inclined plane is a wedge. So, a wedge is
  actually a kind of inclined plane. An axeblade is
  a wedge. Think of the edge of the blade. It's the
  edge of a smooth slanted surface. That's a wedge!
• Screw Now, take an inclined plane and wrap it
  around a cylinder. Its sharp edge becomes another
  simple tool the screw. Put a metal screw beside
  a ramp and it's kind of hard to see the
  similarities, but the screw is actually just
  another kind of inclined plane. How does the
  screw help you do work? Every turn of a metal
  screw helps you move a piece of metal through a
  wooden space. And, that's how we build things!

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• Lever Try pulling a really stubborn weed out of
  the ground. You know, a deep, persistent weed
  that seems to have taken over your flowerbed.
  Using just your bare hands, it might be difficult
  or even painful. With a tool, like a hand shovel,
  however, you should win the battle. Any tool that
  pries something loose is a lever. A lever is an
  arm that "pivots" (or turns) against a "fulcrum"
  (or point). Think of the claw end of a hammer
  that you use to pry nails loose. It's a lever.
  It's a curved arm that rests against a point on a
  surface. As you rotate the curved arm, it pries
  the nail loose from the surface. And that's hard
  work!
• Wheel and Axle The rotation of the lever
  against a point pries objects loose. That
  rotation motion can also do other kinds of work.
  Another kind of lever, the wheel and axle, moves
  objects across distances. The wheel, the round
  end, turns the axle, the cylindrical post,
  causing movement. On a wagon, for example, the
  bucket rests on top of the axle. As the wheel
  rotates the axle, the wagon moves. Now, place
  your pet dog in the bucket, and you can easily
  move him around the yard. On a truck, for
  example, the cargo hold rests on top of several
  axles. As the wheels rotate the axles, the truck
  moves.

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• Pulley Instead of an axle, the wheel could also
  rotate a rope or cord. This variation of the
  wheel and axle is the pulley. In a pulley, a cord
  wraps around a wheel. As the wheel rotates, the
  cord moves in either direction. Now, attach a
  hook to the cord, and you can use the wheel's
  rotation to raise and lower objects. On a
  flagpole, for example, a rope is attached to a
  pulley. On the rope, there are usually two hooks.
  The cord rotates around the pulley and lowers the
  hooks where you can attach the flag. Then, rotate
  the cord and the flag raises high on the pole.
• A machine transforms energy from one place to
  another or transforms it from one form into
  another.
• In this section we study two specific simple
  machines, the lever and the pulley. Below are
  the three types of lever. We will focus on the
  first class lever.

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• First Class Lever If we push down on effort
  arm, the load is lifted up. We do work on the
  effort arm, and the load arm does work on the
  load.
• If the heat from friction is small enough to
  neglect, the work input will be equal to the work
  output.
• Work input Work output
• Since work equals force times distance, we can
  say
• (Force x distance) input (Force x distance)
  output

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• Moving the fulcrum, allows us to input a small
  force through a large distance, and lift a large
  load through a small distance. However, no
  machine can multiply work or energy!
• The ratio of output force to input force for a
  machine is called mechanical advantage. The MA
  (mechanical advantage) can be found by taking the
  ratio of the output force to the input force. On
  page 155 of our book, the girl pushes down with a
  force of 10N through a distance of 1m. The rock,
  which weighs 80 N is lifted a distance of (1/8)m.
  The MA (mechanical advantage) is (80N)/(10N), or
  8. We can also determine the MA by the ratio of
  the input distance to output distance.
• Pulley A major purpose of a pulley is to change
  the direction of the input force. You can pull
  down one a pulley rope, and the rope will lift
  the object upward.

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• Pulleys can be used several ways.
• A single pulley changes the direction of the
  lifting force. For  example, if you are lifting a
  heavy object with a single pulley anchored to the
  ceiling, you can pull down on the rope to lift
  the object instead  of pushing up. The same
  amount of effort is needed as without a pulley,
  but it feels easier because you are pulling down.
• A fixed pulley is the only pulley that when used
  individually, uses more effort than the  load to
  lift the load from the ground.
• The fixed pulley when attached to an unmovable
  object e.g. a ceiling or wall, acts as a first
  class lever with the fulcrum being located at the
  axis but with a minor change, the bar becomes a
  rope. 
• The advantage of the fixed pulley is that you do
  not
• have to pull or push  the pulley up and down.
  
• The disadvantage is that you have to apply more
• effort than the load you lift (friction).

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• A movable  pulley  is a pulley that moves with
  the load.
• The movable pulley allows the effort to be less
• than the weight of the load. The movable
• pulley also acts as a second class lever.
• The load is between the fulcrum and
• the effort.
• The main advantage of a movable pulley is that
  you
• use less effort to pull the load.
• The main disadvantage of a movable pulley is that
• you have to pull or push the pulley up or
  down.
• If you add a second  pulley, the amount of effort
• to lift the heavy object seems much less .
• For example, to lift a box weighing 150 N, one
• would need to exert 150 N of force without
  the
• help of pulleys.
• However, by using just two pulleys, the person
• would only need to use 75 N of force.

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• A combined pulley makes life easier as the effort
  
• needed to lift the load is less than  half
  the
• weight of the load.
• The main advantage of this pulley is that the
• amount of effort is less than half of the
  load.
• The main disadvantage is it travels a very long
• distance.

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9.9 Efficiency

• A major factor in the usefulness of a machine is
  its efficiency.
• A machine converts the force provided from an
  input energy into motion that changes the
  magnitude or direction of that force. This motion
  against a resistive force is the work done by the
  machine. According to the Law of Conservation of
  Energy, the total input energy must equal the
  total output energy. However, some of the output
  energy does not contribute to the output work and
  is lost to such things as friction and heat.
• The efficiency of a machine is the ratio of the
  input energy to the useful output work.
• Questions you may have include
• What is the work done by a machine?
• What role does the Conservation of Energy play in
  machines?
• What is the efficiency of a machine?

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• The efficiency of a machine is the output work or
  energy divided by the input work or energy.
• Efficiency Wo/Wi
• As an illustration of the losses in all machines,
  a simple lever loses about 2 of the input energy
  to internal friction at its fulcrum, such that
  its efficiency is 98. If 100 joules of work is
  input, 98 joules of work is the output.
• On the other hand, the efficiency of an
  automobile is only around 15. About 75 of the
  energy is lost through wasted heat from the
  engine and another 10 is lost due to internal
  friction, including losses from tire friction.
• The usefulness of a machine is determined by its
  efficiency. A machine converts the force provided
  from an input energy into output work. The Law of
  Conservation of Energy requires that the total
  input energy must equal the total output energy.
  Some output energy does not contribute to the
  output work and is lost to friction or heat. The
  efficiency of a machine is the ratio of the input
  energy to the useful output work (output divided
  by input).

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• In any machine, some energy is transformed into
  atomic or molecular kinetic energy --- making the
  machine warmer. We say this wasted energy is
  dissipated as heat.
• The efficiency of a machine is the ratio of
  useful energy output to total energy input, or
  the percentage of work input that is converted to
  work output.
• useful work output
• Efficiency total work input
• Efficiency can also be expressed as the ratio of
  actual mechanical advantage to theoretical
  mechanical advantage.
• actual mechanical
  advantage
• Efficiency theoretical
  mechanical advantage

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• MECHANICAL ADVANTAGE OF THE INCLINED PLANE

• Complex Machines
• A car jack is a simple example of a complex
  machine that increases the applied force.
• The upward force exerted by the jack is greater
  than the downward force you exert on the handle.
• However, the distance you push the handle down is
  greater than the distance the car is pushed
  upward.
• Because work is the product of force and
  distance, the work done by the jack is equal to
  the work you do on the jack.
• The jack increases the applied force, but it
  doesnt increase the work done.

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9.10 Energy for Life

• As physicists learned in the nineteenth century,
  transforming 100 of thermal energy into
  mechanical energy IS NOT POSSIBLE. Some heat
  must flow from the engine. Friction adds more to
  the energy loss. Even the best designed
  gasoline-powered automobile engines are unlikely
  to be more than 35 efficient!
• On top of these contributors to inefficiency, the
  fuel does not burn completely. A certain amount
  of it goes unused. We can look at inefficiency in
  this way In any transformation there is a
  dilution of the amount of useful energy. Useful
  energy ultimately becomes thermal energy, Energy
  is not destroyed, it is simply degraded. Through
  heat transfer, thermal energy is the graveyard of
  useful energy.

• Every living cell in every organism is a machine.
  Like any machine, living cells need an energy
  supply. Most living organisms on this planet feed
  on various hydrocarbon compounds that release
  energy when they react with oxygen. There is more
  energy stored in gasoline than in the products of
  its combustion. There is more energy stored in
  the molecules in food than there is in the
  reaction products after the food is metabolized.
  This energy difference sustains life.

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9.11 Sources of Energy

• The Sun is the source of practically all our
  energy on Earth!
• Solar Power The sun is the single most
  significant source of energy to the planet Earth,
  and any energy that it provides which isn't used
  to help plants grow or to heat the Earth is
  basically lost. Solar power can be used with
  solarvoltaic power cells to generate electricity.
  Certain regions of the world receive more direct
  sunlight than others, so solar energy is not
  uniformly practical for all areas.
• Hydropower The use of hydropower involves using
  the kinetic motion in water as it flows
  downstream, part of the normal water cycle of the
  Earth, to generate other forms of energy, most
  notably electricity. Dams use this property as a
  means of generating electricity. This form of
  hydropower is called hydroelectricity. Water
  wheels were an ancient technology which also made
  use of this concept to generate kinetic energy to
  run equipment, such as a grain mill.

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• Wind Modern windmills can transfer the kinetic
  energy of the air flowing through them into other
  forms of energy, such as electricity. There are
  some environmental concerns with using wind
  energy, because the windmills often injure birds
  who may be passing through the region.
• Nuclear Certain elements are able to undergo
  powerful nuclear reactions, releasing energy
  which can be harnessed and transformed into
  electricity. Nuclear power is controversial
  because the material used can be dangerous and
  resultant waste products are toxic. Accidents
  that take place at nuclear power plants, such as
  Chernobyl, are devastating to local populations
  and environments. Still, many nations have
  adopted nuclear power as a significant energy
  alternative.
• Biomass Biomass is not really a separate type of
  energy, so much as a specific type of fuel. It is
  generated from organic waste products, such as
  cornhusks, sewage, and grass clippings. This
  material contains residual energy, which can be
  released by burning it in biomass power plants.
  Since these waste products always exist, it is
  considered a renewable resource.

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• Geothermal The Earth generates a lot of heat
  while going about its normal business, in the
  form of subterranean steam and magma among
  others. The energy generated within the Earth's
  crust can be harnessed and transformed into other
  forms of energy, such as electricity.
• Fuel Cells Fuel cells are an important
  enabling technology for the hydrogen economy and
  have the potential to revolutionize the way we
  power our nation, offering cleaner,
  more-efficient alternatives to the combustion of
  gasoline and other fossil fuels. Fuel cells have
  the potential to replace the internal-combustion
  engine in vehicles and provide power in
  stationary and portable power applications
  because they are energy-efficient, clean, and
  fuel-flexible. Hydrogen or any hydrogen-rich fuel
  can be used by this emerging technology.
• THE END!!!!! AT LAST!!!!!!!!!!