Work, Power

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Work, Power Energy

• Basic Terminology and Concepts

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Review

• Newtons Laws
• Used to analyze motion of an object
• Net force on a mass ? acceleration
• Acceleration ? change in velocity over time
• Used to predict final state of an object's motion

What are other ways to look at motion?
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Motion Based on Work and Energy

• Objective
• Understand and calculate the effect of work on
  the energy of an object (or system of objects)
• Predict the resulting velocity and/or height of
  the object from energy information

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Basic Terminology

• Work
• Total mechanical energy
• Potential energy
• Kinetic energy
• Power

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Work

• A force acting upon an object to cause a
  displacement
• For a WORK to be done
• 1. Displacement MUST happen
• 2. Force MUST cause the displacement
• 3. Force and displacement must be parallel

What are some examples of work?
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Examples

• a horse pulling a plow through the fields
• a father pushing a grocery cart down the aisle of
  a grocery store
• a freshman lifting a backpack full of books
• (would a junior do work like this?)
• a weightlifter lifting a barbell above her head
• a shot-putter launching the shot, etc.
• climbing a flight of stairs

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Work
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Work or NOT?

• A teacher applies a force to a wall and becomes
  exhausted.
• A book falls off a table and free falls to the
  ground.
• A rocket accelerates through space.

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Answers

• No. The wall is not displaced.
• Yes! The is a downward force (gravity) which acts
  on the book to displace it.
• Yes. The expelled gas is the force which
  accelerates the rocket through space.

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What about this one? Be careful!

• A waiter carries a tray full of meals above his
  head by one arm across the room.
• Consider the following
• In which direction is the force exerted on the
  tray?
• Which direction does the tray move?
• Are those directions parallel?

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Answer We need to be specific because there are
two forces.

• The normal force is exerted vertically on the
  tray.
• The tray moves horizontally.
• Since those are not in the same direction, there
  is no work done on the tray by the normal force.
• There is a horizontal frictional force in the
  same direction as the horizontal displacement.
• Therefore, friction does work on the tray!

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A Force Does NO WORK When It Is Perpendicular to
the Displacement
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Force at an Angle

• The tension in the chain pulls upward and
  rightward.
• Fido moves rightward.
• Only the horizontal part (component) of the
  tension does work on Fido.
• The ANGLE determines the component of the force
  which actually causes a displacement.
• We wont do this mathematically.

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Which angle is used?

• The angle between the force vector and the
  displacement vector.
• NOT the angle of ascent in this case
• Direction of pull
• Displacement direction

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Describing Work Mathematically

• Work Force x Displacment W Fd

• Force and displacement are rightward. ? WORK IS
  DONE!!!
• Force left, displacement right. ? NEGATIVE WORK
  IS DONE!!!
• Force up, displacement left. ? NO WORK!!!

When angle 0 or 180, WORK IS DONE!
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Perpendicular force

• REMEMBER!
• A vertical force CANNOT cause horizontal
  displacement!

When angle 90, NO WORK IS DONE!!!
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Work and Gravity

• Work Force displacement
• When something freefalls, the force it exerts is
  mg (mass acceleration due to gravity). g
  -9.8 m/s2.
• Displacement of object is height (h).
• Work mgh

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Units of Work (and Energy)

• The joule (J)
• 1 joule 1 newtonmeter
• 1 J 1 Nm

Each set of units is equivalent to a force unit
times a displacement unit.
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Summary

• Work is a force acting upon an object to cause a
  displacement.
• Three quantities must be known in order to
  calculate the amount of work.
• Force
• Displacement
• Angle between the force and the displacement.
• If angle is 90, NO WORK IS DONE!!!

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Power

• When you exert a force over a distance, that is
  called work.
• But work takes time!
• Does the amount of work change if you do it over
  an hour vs. in 5 minutes?

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Power Calculation

• Power is the rate at which work is done
• Power Work / time
• P W / t

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Units of Power

• Units of Power Units of Work / Units of Time
• joules / second
• 1 joule / second 1 watt
• Units of Power watts (W)
• Joules/sec Watts!

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Machines

• Machines change the magnitude and/or direction of
  forces.
• multiplying the force
• can also multiply the distance
• NOTHING WORKS FOR FREE!!!
• Work is CONSERVED
• work input work output
• (Fd)input (Fd)output
• So if we cant get any free work out of the deal,
  why bother?

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Machines

• Machines can make work easier
• Less input force more input distance
• More output force less output distance
• Examples using a jack to lift a car
• Machines can increase speed
• More input force less input distance
• Less output force more output distance
• Examples bicycle gears

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Mechanical Advantage

• Mechanical Advantage how much a machine
  multiplies force or distance

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Mechanical Advantage

• Calculate the mechanical advantage of a ramp that
  is 5.0 m long and 1.5 m high.
• Given
• input distance 5.0 m
• output distance 1.5 m
• Unknown mechanical advantage

• Equation
• Plug Chug

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Simple Machines
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Work and Energy

• What is the relationship?

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Objectives

• Explain the relationship between energy and work
• Define potential energy and kinetic energy
• Calculate kinetic energy and gravitational
  potential energy
• Distinguish between mechanical and non-mechanical
  energy
• Identify non-mechanical forms of energy

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What is Energy?

• Energy the ability to do work
• Units joules, J (same as work)
• Why?
• Definition of work
• Transfer or transformation of energy
• Transfer is often from one system to another
• It takes ENERGY to do WORK!!!

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Work Energy Example

• Rubber band or slingshot or bow
• You stretch the rubber band.
• Energy is transferred from you to the band.
• Do you do work on the rubber band?
• You release the rubber band.
• Energy is transferred from the rubber band to the
  projectile.
• Amount of energy transferred is measured by
  work done on the projectile.
• Transfer of Energy (bow arrow)
• Work on bow ? Energy in bow ? Work on arrow

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Potential Energy

• How does the rubber band get energy?
• Where is the energy in the stretched rubber band?
• Where is the energy upon release?

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Potential Energy

• Def stored energy energy of position
• Results from the relative position of objects in
  the system.
• rubber band distance between the two ends
• Stored energy occurs if something is stretched or
  compressed (elastic)
• clock spring
• bungee cord

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Gravitational Potential Energy

• Gravitational potential energy
• PE that an object has by virtue of its HEIGHT
  above the ground
• GPE mass x freefall acceleration x height
• GPE mgh (Fd)
• mg weight of the object in Newtons (F)
• h distance above ground (d)
• GPE stored Work done to lift object

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GPE Example - Solved

• A 65 kg rock climber ascends a cliff. What is
  the climbers gravitational potential energy at a
  point 35 m above the base of the cliff?
• Given
• m 65 kg
• h 35 m
• Unknown GPE ? J

• Equation
• PE mgh
• Plug Chug
• PE (65 kg)(9.8 m/s2)(35 m)
• Answer
• GPE 22000 J

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GPE Example - Unsolved

• What is the gravitational potential energy of a
  2.5 kg monkey hanging from a branch 7 m above the
  jungle floor?
• Given
• m 2.5 kg
• h 7 m
• Unknown GPE ? J

• Equation
• GPE mgh
• Plug Chug
• GPE (2.5 kg)(9.8 m/s2)(7m)
• Answer
• GPE 171.5 J

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Kinetic Energy

• Def the energy of a moving object due to its
  motion
• Moving objects will exert a force upon impact
  (collision) with another object.
• KE ½ (mass) (velocity)2
• KE ½ (mv2)

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The Impact of Velocity

• Which variable has a greater impact on kinetic
  energy mass or velocity?
• Velocity! Its SQUARED!
• Velocity as a factor
• Something as small as an apple
• At a speed of 2 m/s 0.2 J
• At a speed of 8 m/s 3.2 J(4 x velocity 16x
  energy)

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KE Example - Solved

• What is the kinetic energy of a 44 kg cheetah
  running at 31 m/s?
• Given
• m 44 kg
• v 31 m/s
• Unknown
• KE ? J

• Equation
• KE ½ mv2
• Plug Chug
• KE ½ (44 kg)(31 m/s)2
• Answer
• KE 21000 J

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KE Example - Unsolved

• What is the kinetic energy of a 900 kg car moving
  at 25 km/h (7 m/s)?
• Given
• m 900 kg
• v 7 m/s
• Unknown KE ? J

• Equation
• KE ½ mv2
• Plug Chug
• KE ½ (900 kg)(7 m/s)2
• Answer
• KE 22050 J

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Conservation of Energy

• Objectives
• Identify and describe transformations of energy
• Explain the law of conservation of energy
• Where does energy go when it disappears?
• Analyze the efficiency of machines

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Other Forms of Energy

• Mechanical Energy the total energy associated
  with motion
• Total Mechanical Energy Potential Energy
  Kinetic Energy
• Examples roller coasters, waterfalls

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Other Forms of Energy

• Heat Energy average kinetic energy of atoms
  molecules
• The faster they move, the hotter they get!
• Ex. Boiling water

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Other Forms of Energy

• Chemical Energy potential energy stored in
  atomic bonds
• When the bonds are broken, energy is released
• Ex. Combustion (burning), digestion, exercise

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Other Forms of Energy

• Electromagnetic Energy kinetic energy of moving
  charges
• Energy is used to power electrical appliances.
• Ex. Electric motors, light, x-rays, radio waves,
  lightning

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Other Forms of Energy

• Nuclear Energy potential energy in the nucleus
  of an atom
• Stored by forces holding subatomic particles
  together
• Ex. Nuclear fusion (sun), Nuclear fission
  (reactors, bombs)

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Conservation of Energy

• The Law of Conservation of Energy
• Energy cannot be created nor destroyed, but can
  be converted from one form to another or
  transferred from one object to another
• Total Energy of a SYSTEM must be CONSTANT!

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Conservation of Energy

• Total Mechanical Energy Kinetic Potential
• TME KE PE
• TME must stay the same!
• If a system loses KE, it must be converted to PE
• In reality some is converted to heat
• We will USUALLY consider frictionless systems ?
  only PE KE

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Energy Conversions in aRoller Coaster

• Energy changes form many times.
• Energy from the initial conveyor
• Work stored Grav. Potential Energy
• Some PE is converted to KE as it goes down
• Some KE is converted to PE as it goes up
• Where does the coaster have max. PE?
• Where does the coaster have min. PE?
• Where does the coaster have max. KE?
• Where does the coaster have min. KE?
• Where could energy be lost?
• Friction, vibrations, air resistance

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Conservation of EnergyExample Problem

• You have a mass of 20 kg and are sitting on your
  sled at the top of a 40 m high frictionless hill.
  What is your velocity at the bottom of the hill?
• Given
• m 20 kg
• hi 40 m
• vi 0 m/s
• Unknown
• vf ?

• Equations
• TMEi TMEf
• PEi KEi PEf KEf
• PE mgh
• KE ½ mv2

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Efficiency

• Does work input always equal energy output?
• NO! Energy may be lost to friction.
• No machine is perfect!
• Efficiency a quantity, usually expressed as a
  percentage, that measures the ratio of useful
  work output to work inputefficiency useful
  work output / work input

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Efficiency

• A sailor uses a rope and an old squeaky pulley to
  raise a sail that weighs 140 N. He finds that he
  must do 180 J of work on the rope in order to
  raise the sail by 1 m (doing 140 J of work on the
  sail). What is the efficiency of the pulley?
• Given
• Work input 180 J
• Useful work output 140 J
• Unknown
• Efficiency ?

• Equation
• Efficiency useful work output / work input
• Plug Chug
• Efficiency 140 J / 180 J 0.78
• Efficiency 0.78 x 100 78
• Answer
• Efficiency 78