WORK AND ENERGY

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WORK AND ENERGY

• Another Way to Look at Motion

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• The most important concept in science!

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Whats so Great About Energy?

• Its a scalar forget those vector headaches
• Its useful in all of physics and in other
  sciences
• Its conserved, meaning the total amount of it
  doesnt change

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What is energy?

• Difficult to define precisely.
• Exists in many different forms

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Work

• The product of the magnitude of displacement
  times the component of force parallel to
  displacement
• W Fd

F
d
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Work(more precisely)

• The product of the magnitude of displacement
  times the component of force parallel to
  displacement
• W Fpd cos q

F
q
d
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Units of Work and Energy

• SI unit newton-meter joule
• 1 J 1 n m
• Obsolete units you might run across
• In cgs system unit is erg dyne-cm
• In British system ft-lb
• 1 J 107 ergs 0.7376 ft-lb

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Who Does More Work?

• A weightlifter holding up 200Kg
• (Force, no displacement)

• A baby lifting a feather
• (Small force, some displacement)

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Who Does More Work?

• A weightlifter holding up 200Kg
• (Force, no displacement)
• No Work!

• A baby lifting a feather
• (Small force, some displacement)
• Some work

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Work or no work?
Lifting force is up, but displacement is
horizontal therefore
No work is done on refrigerator
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Work or No Work
A mass circles at constant speed, held by a string
Force is along string, toward center
Therefore, no work is done
Force is perpendicular to motion
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Calculate the work

• 20 Kg crate is pulled 50m horizontally by a 100N
  force
• W Fd 100N x 50m 5000Joules

FN
F 100N
mg
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Work to Climb a Mountain
Work force x distance

• How much work is
• required for a 70 Kg
• person to climb
• 1000 m up a peak?

Hint use F mg
Only up component of displacement contributes
Answer 6.86 x 105 J
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Work Done By Sun on Earth

• How much is there?

FG
v
NONE!
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ENERGY

• The ability to do work (an imperfect definition)
• Many types exist mechanical (potential,
  kinetic), heat, light, electrical, magnetic,
  nuclear
• They can change from one to another
• The sum of all of them (total energy)is conserved

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Energy Conversion Example

• What form of energy comes into the projector?
• What forms are produced?

Answer electrical
Answer light, heat, sound, kinetic, magnetic
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Common Forms of Energy
Mechanical

• Kinetic energy of motion
• Potential energy of position

A pendulum converts energy back and forth from
potential to kinetic.
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Law of Conservation of Energy

• In any process total energy is neither decreased
  nor increased
• It can change from one form to another
• It can be transferred from one body to another,
  but
• IT CAN NOT BE CREATED NOR DESTROYED

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Kinetic Energy

• Energy of Motion
• Translational and rotational
• TRANSLATIONAL KE ½ m v2

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Derivation of ½ mv2

• Consider a mass accelerated uniformly from rest
  to velocity v
• Work done W F x d
• F ma
• W mad
• v2 v02 2ad
• W m d (v2 v02)/2d ½ mv2
• (v0 0)

a (v2 v02)/2d
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Derivation of ½ mv2

• Consider a mass accelerated uniformly from rest
  to velocity v
• Work done W F x d
• F ma
• W mad
• v2 v02 2ad
• W m d (v2 v02)/2d ½ mv2
• (v0 0)

a (v2 v02)/2d
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Examples

• Find the kinetic energy of a 70 kg person walking
  at 1.0 m/s.
• KE 1/2mv2 35kg x (1m/s)2 35J
• Find the kinetic energy of a 0.01 kg bullet
  traveling at 1000 m/s.
• KE 1/2mv2 0.5 x 0.01 x (1000m/s)2
• KE 5000J

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Why is it so dangerous to get shot?

• Bullet deposits lots of energy in small area
• What about momentum (mv)?
• Find momentum of man
• 70 kg m/s
• Find momentum of bullet
• 10 kg m/s

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Why is a comet or asteroid crash on Earth so
dangerous?

• Find the kinetic energy of a 1014 Kg asteroid
  whose speed is 50 km/sec.
• KE ½ mv2 0.5 x 1014 x (5 x 104 m/s)2
• 12.5 x 1022 J 1.25 x 1023 J

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Work-Energy Principle

• The net work done on an object equals the change
  in its kinetic energy
• Wnet DKE
• Work that increases KE is positive
• Work that decreases KE is negative

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How Much Work?

• Is needed to give a car of mass 1000kg a speed of
  10 m/s?
• W Kinetic Energy gained
• W ½ mv2
• W 0.5 x 1000kg x (10m/s)2
• W 50,000 J 5 x 104 J

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Force Required

• What average force is needed to do this if the
  distance is 100m?
• W F x D
• F W/D KE/D 50,000 / 100 500N

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How Much Work

• is required to accelerate a 1000Kg car from 30 to
  40 m/s?
• Use W 1/2mv22 - 1/2mv12

• Answer 3.5 x 105 joules

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Gravitational Potential Energy

• An object held high has the potential to do work
• PEgrav mgy
• Reference level of zero PE is arbitrary

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How Much PE?

• How much PE does a 100kg crate get when raised
  100m?
• PE mgh use g 10 N/kg
• PE 100kg x 10N/kg x 100m
• PE 100,000 J
• PE 1.0 x 105 J

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Roller Coaster

• What speed will a frictionless roller coaster
  have at the bottom of a 40m high hill assuming
  zero speed at the top of the hill?
• PE lost KE gained
• mgh ½ mv2
• 2gh v2
• v (2gh)1/2
• v (2 x 10 x 40)1/2 (800)1/2

Answer v 28 m/s
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Law of Conservation of Energy

• In any process total energy is neither decreased
  nor increased
• It can change from one form to another
• It can be transferred from one body to another,
  but
• IT CAN NOT BE CREATED NOR DESTROYED

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Conservation of Mechanical Energy

• In absence of friction or other non-conservative
  forces
• KE PE constant

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Conservative Force

• Work done does not depend on path taken
• Potential energy can be defined
• Example lifting an object against gravity

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Non Conservative or Dissipative Force

• Work done depends on path
• No potential energy function can be defined
• Example pushing an object against friction
• W Fd mFNd mmgd

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Power

• The rate that work is done
• P work/time Fd/time Fv
• Unit joules/sec watt
• 746 watts 1 horsepower

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Power

• The rate that work is done
• P work/time Fd/time Fv
• Unit joules/sec watt
• 746 watts 1 horsepower

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Simple Machines

• Machines that make work easier by increasing
  force or increasing distance

All simple machines trade force for distance
they cant increase both
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Examples of Simple Machines

• Lever
• Inclined Plane
• Screw
• Gear
• Wheel and Axle
• Pulley

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Lever

• See saw
• Pry bar
• Screw driver used to pry
• Fork, pencil
• Paint brush
• Which of these increase force?

Courtesy www.lkwdpl.org/schools/elempath/
simplemachines
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Inclined Plane

• Ramp
• Knife
• Road up hill
• Screwdriver pushed in

Courtesy www.disabled.driverinfo.btinternet.co.uk/
acctocar.html
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Screw

• Inclined plane wrapped around a cylinder

Q Is a screwdriver an example of a screw?
Courtesy www.uen.org/.../ view_activity.cgi?activi
ty_id6528
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Gear

• Wheel with teeth that mesh
• Changes speeds
• Increases or decreases force
• Used in auto and marine transmissions

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Wheel and Axle

• A lever wrapped in a circle
• Axle is normally fixed to wheel

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Pulley

• Axle turns freely
• Types
• Single fixed
• Single moveable
• One fixed one moveable
• Block and tackle

Courtesy www.conductortrain.com/.../apprentice/
skills/doc9.shtml
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Work In Work Out

• In absence of friction the work you put into a
  simple machine equals the work that comes out
• Fin Din Fout Dout
• Fout/ Fin Din/ Dout
• Illustrates the trade-off between force and
  distance
• You cant get something for nothing without
  violating conservation of energy

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Mechanical Advantage

• Fout/ Fin is called mechanical advantage,
  actual mechanical advantage(AMA) to be exact.
• Din/ Dout is called ideal mechanical advantage
  (IMA)
• In a real machine AMA is always less than IMA
  because of friction

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Small and Large Mechanical Advantage

• Machines that increase force greatly are said to
  have large mechanical advantage
• Example pry bar
• Machines that increase distance and decrease
  force have mechanical advantage less than one
• Example paint brush

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Efficiency

• AMA e x IMA
• e is called efficiency
• All machines have an efficiency less than one so
  as not to violate?

Energy Conservation!
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Lever Example

• A certain lever lifts a weight of 20N with an
  effort force of only 5N. Assuming ideal
  efficiency, over what distance will the effort
  force act to lift the weight by 0.1 meter?

Answer 0.4m
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Pulley Example

• A pulley system has an ideal mechanical advantage
  of 2.
• (a) What effort force will be required to lift
  500N?
• (b) if the efficiency is only 80, would more
  force be required or less?

250 N
more
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Review

• Why cant a simple machine have an efficiency
  greater than 1 (100) ?

It would violate the law of conservation of
energy.
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Compound Machines

• Many real machines are combinations of simple
  machines