Energy

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Chapter 8

• Energy

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Work

• Work a force acting upon an object to cause a
  displacement
• W F?d
• Units Nm J (joule)
• 2 Components of Work
• Application of Force
• Movement of something by that force

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Work

• To do work an object must move in the direction
  that the force is appliedthere must be a
  displacement in the same direction as the force
• Is work being done?
• A student holds a heavy chair for several minutes
  (on the chair)
• A student carries a bucket of water along a
  horizontal path while walking at a constant
  velocity (on the bucket)
• A student lifts a backpack full of books upon her
  shoulder (on the backpack)
• A student pushes a grocery cart down an aisle (on
  the cart)

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Work

• The force used to produce work must be in the
  direction of the displacement
• If you push a crate across the floor and apply
  only a horizontal force, then all of the applied
  force does work on the crate.
• If you push a crate across the floor and apply a
  force at an angle above the horizontal, then only
  the horizontal component of the applied force
  does work on the crate.
• WORK IS ONLY DONE WHEN COMPONENTS OF A FORCE ARE
  PARALLEL TO A DISPLACEMENT!!!

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Work

• Two categories of work
• Work done against a force
• Lifting a barbell over your head
• Work done to change speed
• Stopping a car
• Work is a scalar quantity
• It is positive when the component of the force is
  in the same direction of the displacement
• Lifting a barbell
• It is negative when the component of the force is
  in the opposite direction of the displacement
• stopping a car

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Positive or Negative Work?

• Rusty Nales pounds a nail into a block of wood.
  The hammer head is moving horizontally when it
  applies force to the nail.
• The frictional force between highway and tires
  pushes backwards on the tires of a skidding car.

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Work

• Bud, a very large man of mass 130 kg, stands on a
  pogo stick. How much work is done as Bud
  compresses the spring of the pogo stick 0.50 m?
• After finishing her physics homework, Sherita
  pulls her 50.0 kg body out of a living room chair
  and climbs of the 5.0 m high flight of stairs to
  her room. How much work does Sherita do is
  ascending the stairs?

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Work

• How much work is done on a vacuum cleaner pulled
  3.0 m by a force of 50.0 N at an angle of 30.0
  degrees above the horizontal?
• How much work is done on a 200 N boulder as
• a. you carry is 2 m horizontally across a room?
• b. you lift it 2 m vertically in a room?

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Power

• Suppose a person with a mass of 50.0 kg ascends a
  5.0 m high set of stairs.
• Is more work done if the person is running or
  walking up the stairs?
• The same amount of work is done in either case.
• Then why would the person be more tired if he/she
  ran up the stairs?
• More power is exerted when a person runs up the
  stairs.
• Power the rate at which work is done

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Power

• Power work/time
• P W/?t
• Units of power J/s watt (W)
• A person is more powerful than another if he/she
  can do more work in a given amount of time, or
  can do the same amount of work in less time
• P Fd/t Fv (force x velocity)

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Power

• Two horses pull a car. Each exerts a force of
  250.0 N at a speed of 2.0 m/s for 10.0 minutes.
  a) Find the power delivered by the horses. b)
  How much work is done by the two horses?
• Find the amount of power exerted by a steam
  engine that can do 6.8 x 107 J of work in 1 hour.

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Power

• 3. If little Nellie Newton lifts her 40-kg body a
  distance of 0.25 meters in 2 seconds, then what
  is the power delivered by little Nellie's biceps?
  
• A 193 kg curtain needs to be raised 7.5 m, at a
  constant speed, in as close to 5.0 s as possible.
  The power rating for three motors are listed at
  1.0 kW, 3.5 kW, and 5.5 kW. Which motor is best
  for the job?

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Mechanical Energy

• Energy the ability to do work
• Mechanical Energy the total energy associated
  with an object or group of objects
• There are two common forms of mechanical energy
• Potential Energy
• Kinetic Energy
• Mechanical energy is relative it depends on the
  location you choose for a frame of reference
• A 1 N apple held 1 m above the floor has 1 J of
  potential energy
• The same apple held 10 m above the ground has 10
  J of potential energy

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Potential Energy

• An object stores energy in its position
• Potential Energy energy that is stored and held
• Has the POTENTIAL to do work

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Gravitational Potential Energy

• Work is required to lift an object against
  Earths gravity
• Gravitational PE mgh
• An object gains gravitational PE when it is
  lifted from one level to a higher level
• ?PE mg?h
• There are other forms of stored energy
• When a bow is pulled back and before it is
  released, the energy in the bow is equal to the
  work done to deform it.
• ?PE F?d
• When a spring is compressed there is elastic PE
  stored in the spring
• PEelastic ½ kx2
• (k spring constant, x distance
  compressed/stretched)
• The unit for energy is the joule

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Potential Energy

• Legend has it that Isaac Newton discovered
  gravity when an apple fell from a tree and hit
  him on the head. If a 0.20 kg apple fell 7.0 m
  before hitting Newton, what was its change in PE
  during the fall?
• A 40.0 kg child is in a swing that is attached to
  ropes 2.00 m long. Find the gravitational PE
  associated with the child relative to the childs
  lowest position under the following conditions
• a. When the ropes are horizontal
• b. When the ropes make a 30.0 degree angle
  with the vertical
• c. At the bottom of the circular arc

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Potential Energy

• What is the potential energy given to a 100 kg
  boulder that is lifted 2 m if it is
• Lifted straight up
• Slid up a ramp that is 4 m long
• Walked up the stairs
• 4. The staples inside a stapler are kept in place
  by a spring with a relaxed length of 0.115 m. If
  the spring constant is 51.0 N/m, how much elastic
  PE is stored in the spring when the length is
  0.150 m?

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Kinetic Energy

• Kinetic Energy the energy of motion
• Depends on speed and mass
• KE ½ mv2
• If the velocity is doubled, the kinetic energy is
  quadrupled
• Kinetic Energy of a moving body is equal to its
  the work required to bring it to that speed from
  rest, or the work that object can do while
  brought to rest
• Fd ½ mv2
• using this theoryan object moving twice as
  fastwill take four times the work to bring it to
  a stop
• a car going 60 m/s will skid four times as far as
  a car going 30 m/s when its brakes are locked

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Kinetic Energy

• Determine the kinetic energy of a 1000.-kg roller
  coaster car that is moving with a speed of 20.0
  m/s.
• 2. A greyhound at a race track can run with a
  kinetic energy of 2560 J. What is the speed of
  the 20.0 kg greyhound?

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Work Energy Theorem

• Work changes kinetic energyif no change in
  energy occurs, then no work is done
• Work ?E
• 1. A student wearing frictionless in-line skates
  on a horizontal surface is pushed by a friend
  with a constant force of 45 N. How far must the
  student be pushed , starting from rest, so that
  her final KE is 353 J?

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Conservation of Energy

• When energy changes from one form to another, it
  always transforms without net loss or gain.
• Law of Conservation of Energy
• Energy cannot be created or destroyed.
• It can be transformed form one form into another,
  but the total amount of energy never changes

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Conservation of Energy

• In an isolated system where there are no
  mechanical energy losses due to friction
• ?KE ?PE
• All the kinetic and potential energy before an
  interaction equals all the kinetic and potential
  energy after the interaction
• KEo PEo KEf PEf

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Conservation of Energy

• Conservation of energy on a roller coaster ride
  means that the total amount of mechanical energy
  is the same at every location along the track.
• The amount of kinetic energy and the amount of
  potential energy is constantly changing yet the
  sum of the kinetic and potential energies is
  everywhere the same.
• This is illustrated below - the total mechanical
  energy of the roller coaster car is 40 000 Joules.

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Conservation of Energy

• In a wild shot, Bo flings a pool ball of mass m
  off a 0.68 m high pool table, and the ball hits
  the floor with a speed of 6.0 m/s. How fast was
  the ball moving when it left the table?
• A pendulum bob is released from some initial
  height such that the speed of the bob at the
  bottom of the swing is 1.9 m/s. What is the
  initial height of the bob?

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Machines

• Machine a device that helps do work by changing
  the magnitude or direction of the applied force
• Simple Machines
• Lever
• Pulley
• Incline
• Wheel and Axles/Gear
• Screw
• Wedge

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Levers

• Three ways to set up a lever
• fulcrum between the force and the load
• playground seesaw
• directions of input and output are opposite (push
  downlift up)
• http//www.enchantedlearning.com/lgifs/Lever1.gif
• load is between the fulcrum and the input
• wheelbarrow
• forces are on the same side of the fulcrum (push
  uplift up)
• http//www.enchantedlearning.com/lgifs/Lever2.gif
• fulcrum is at one end load is at the other
  input force is applied between them
• your bicep muscles are connected to the bones in
  your forearm in this way
• Fishing rod
• http//www.enchantedlearning.com/lgifs/Lever3.gif

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Levers

• The closer a load is to the fulcrum, the less
  effort is needed.
• The less effort means more distance to move the
  effort.
• Fd Fd
• Work is the amount of force times the distance
  (how far down you had to push).

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Pulleys

• A pulley is a kind of lever
• A single pulley simply reverses the direction of
  a force. When two or more pulleys are connected
  together, they permit a heavy load to be lifted
  with less force. The trade-off is that the end of
  the rope must move a greater distance than the
  load
• http//library.thinkquest.org/J002079F/images/sing
  le_pulley.gif

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Pulleys

• A single pulley works like a type 1 lever
• The lever distances are the radius of the pulley
  therefore the input distance equals the output
  distancethe mechanical advantage equals 1
• A single pulley can also work like a type 2 lever
• The fulcrum is at the end of the lever therefore
  the level distance is the diameter of the pulley
  and the mechanical advantage is 2to lift the
  mass up 1 meter the girl must pull the rope up 2
  m.
• Only supporting ½ of the weight of the load

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Pulleys
Mechanical Advantage of a pulley system (if the
pulleys are equal in size) is equal to the number
of strands of rope supporting the system This
pulley system has 2 ropes that are lifting the
weight of the loadtherefore the amount of work
required to lift the load is equal to ½ of the
loads weight.
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Inclined Plane

• The inclined plane is a plane surface set at an
  angle, other than a right angle, against a
  horizontal surface. The inclined plane permits
  one to overcome a large resistance by applying a
  relatively small force through a longer distance
  than the load is to be raised.

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Efficiency

• In an ideal situation, where frictional forces
  are negligible, work input equals work output
• The Actual Mechanical Advantage (AMA) of a
  machine is the ratio of the magnitude of the
  force out (resistance) to the magnitude of the
  force in (effort)
• The Ideal (Theoretical) Mechanical Advantage
  (IMA) is based only on the geometry of the system
  and does not take frictional effects into account
• The IMA is the ratio of the distance in (effort
  distance) to the distance out (resistance
  distance)
• AMA output force input force
• IMA input distance output distance

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Efficiency

• No machine is perfect, so you will always get out
  less work than you put in.
• Efficiency is the ratio of the work output to the
  work input.
• Efficiency work output work input
• Efficiency AMA IMA
• Efficiency has no units and is usually
  represented as a percent.

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Efficiency

• A crate of bananas weighing 3000. N is shipped
  from South America to New York, where it is
  unloaded by a dock worker who lifts the crate by
  pulling with a force of 200. N on the rope of a
  pulley system. What is the actual mechanical
  advantage of the pulley system?
• Two clowns, of mass 50.0 kg and 70.0 kg
  respectively, are in a circus act performing a
  stunt with a trampoline and seesaw. The smaller
  clown stands on the lower end of the seesaw
  (which is 0.80 m away from the fulcrum) while the
  larger clown jumps from the trampoline onto the
  raised side of the seesaw (2.40 m away from the
  fulcrum), propelling his friend into the air.
• a. What is the ideal mechanical advantage of
  the seesaw?
• b. If the larger clown exerts a force of 850. N
  on the seesaw as he jumps, how much force is
  exerted on the smaller clown? (assume the lever
  is 100 efficient)

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Efficiency

• Jack and Jill went up the hill to fetch a pail of
  water. At the well, Jill used a force of 20.0 N
  to turn a crank handle of radius 0.400 m that
  rotated an axle of radius 0.100 m, so that she
  could raise a 60.0 N bucket of water.
• a. What is the ideal mechanical advantage of
  the wheel?
• b. What is the actual mechanical advantage of
  the wheel?
• c. What is the efficiency of the wheel?

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Efficiency

• Clyde, the stubborn 3500 N mule, refuses to walk
  into the barn, so Farmer MacDonald must drag him
  up a 5.0 m ramp to his stall, which stands 0.50 m
  above ground level.
• a. What is the ideal mechanical advantage of
  the ramp?
• b. If Farmer MacDonald needs to exert 450 N
  force on the mule to drag him up the ramp with a
  constant speed, what is the actual mechanical
  advantage of the ramp?
• c. What is the efficiency of the ramp?

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Energy for Life

• Every living cell is like a machine
• Need energy supply