Work_ Energy and Power

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					Work, Power & Energy

  Basic Terminology and Concepts

    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

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

    Objective:
      Understand and calculate the effect of work
       on the energy of an object (or system of
      Predict the resulting velocity and/or height
       of the object from energy information
Basic Terminology

    Work
    Total mechanical energy
    Potential energy
    Kinetic energy
    Power

    A force acting upon an object to cause a

        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?

   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
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

    A rocket accelerates through space.

    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.
What about this one? Be careful!

    A waiter carries a tray full of meals
     above his head by one arm across the

    Consider the following:
      In which direction is the force exerted on the
      Which direction does the tray move?
      Are those directions parallel?
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!
A Force Does NO WORK When It Is
Perpendicular to the Displacement
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
                 We won’t do this
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
Describing Work Mathematically
    Work = Force x Displacment   W = F*d

    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!
Perpendicular force

        A vertical force
         CANNOT cause

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

    Work = Force * displacement

    When something freefalls, the force it
     exerts is m*g (mass * acceleration due to
     gravity). g = -9.8 m/s2.

    Displacement of object is height (h).
        Work = m*g*h
Units of Work (and Energy)

    The joule (J)
        1 joule = 1 newton*meter

        1 J = 1 N*m

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

    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!!!

  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?
Power Calculation

    Power is the rate at which work is done

            Power = Work / time
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!
    Machines change the magnitude and/or
     direction of forces.
        “multiplying the force”
        can also multiply the distance
        Work is CONSERVED
             work input = work output
             (F*d)input = (F*d)output
    So if we can’t get any free work out of the
     deal, why bother?

    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
Mechanical Advantage

    Mechanical Advantage: how much a
     machine multiplies force or distance

                      output force input distance
         mech. adv.              
                      input force output distance
Mechanical Advantage
    Calculate the                        Equation:
     mechanical advantage                                   input distance
     of a ramp that is 5.0 m                 mech. adv. 
                                                            output distance
     long and 1.5 m high.
        Given:                           Plug & Chug:
             input distance = 5.0 m
             output distance = 1.5
                                           mech.adv.         3.3
                                                       1.5 m
        Unknown: mechanical
Simple Machines
 Simple Machine   How Does It   Examples
  Wheel & Axle
 Inclined Plane
Work and Energy

  What is the relationship?
    Explain the relationship between energy and work
    Define potential energy and kinetic energy
    Calculate kinetic energy and gravitational potential
    Distinguish between mechanical and non-
     mechanical energy
    Identify non-mechanical forms of energy
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!!!
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
             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
Potential Energy

    How does the rubber band get

    Where is the energy in the stretched
     rubber band?

    Where is the energy upon release?
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
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
GPE Example - Solved
  A 65 kg rock climber       Equation:
   ascends a cliff. What is     PE = mgh
   the climber’s
   gravitational potential    Plug & Chug:
   energy at a point 35 m
                              PE = (65 kg)(9.8 m/s2)(35 m)
   above the base of the
                              GPE = 22000 J
     m = 65 kg
     h = 35 m
 Unknown: GPE = ? J
GPE Example - Unsolved
    What is the gravitational   Equation:
     potential energy of a 2.5     GPE = mgh
     kg monkey hanging from
     a branch 7 m above the
     jungle floor?               Plug & Chug:
                                 GPE = (2.5 kg)(9.8 m/s2)(7m)
   m = 2.5 kg
                                 GPE = 171.5 J
 Unknown: GPE = ? J
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)
The Impact of Velocity

    Which variable has a greater impact
     on kinetic energy: mass or velocity?
        Velocity! It’s 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)
KE Example - Solved

  What is the kinetic      Equation:
   energy of a 44 kg            KE = ½ mv2
   cheetah running at
   31 m/s?                  Plug & Chug:
 Given:                  KE = ½ (44 kg)(31 m/s)2
   m = 44 kg
   v = 31 m/s            Answer:
                         KE = 21000 J
   KE = ? J
KE Example - Unsolved

  What is the kinetic      Equation:
   energy of a 900 kg           KE = ½ mv2
   car moving at 25
   km/h (7 m/s)?            Plug & Chug:
  Given:                KE = ½ (900 kg)(7 m/s)2
        m = 900 kg
                            Answer:
        v = 7 m/s
                                KE = 22050 J
    Unknown: KE = ? J
Conservation of Energy

    Objectives
      Identify and describe transformations of
      Explain the law of conservation of
      Where does energy go when it
      Analyze the efficiency of machines
Other Forms of Energy

    Mechanical Energy – the total energy
     associated with motion
      Total Mechanical Energy = Potential Energy
       + Kinetic Energy
      Examples: roller coasters, waterfalls
Other Forms of Energy

    Heat Energy – average kinetic energy of
     atoms & molecules
      The faster they move, the hotter they get!
      Ex. Boiling water
Other Forms of Energy

    Chemical Energy – potential energy
     stored in atomic bonds
      When the bonds are broken, energy is
      Ex. Combustion (burning), digestion,
Other Forms of Energy

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

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

    Total Energy of a SYSTEM must be
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
  In reality… some is converted to heat
  We will USUALLY consider frictionless
   systems  only PE & KE
Energy Conversions in a
Roller 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
Conservation of Energy:
Example Problem
  You have a mass of 20          Equations:
   kg and are sitting on             TMEi = TMEf
   your sled at the top of a
                                     PEi + KEi = PEf + KEf
   40 m high frictionless
   hill. What is your
   velocity at the bottom of          PE = mgh
   the hill?                          KE = ½ mv2
  Given:
     m = 20 kg
     hi = 40 m
     vi = 0 m/s
  Unknown:
     vf = ?

    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 input

     efficiency = useful work output / work input
    A sailor uses a rope and an         Equation:
     old squeaky pulley to raise a    Efficiency = useful work output /
     sail that weighs 140 N. He           work input
     finds that he must do 180 J of
     work on the rope in order to        Plug & Chug:
     raise the sail by 1 m (doing
     140 J of work on the sail).
     What is the efficiency of the    Efficiency = 140 J / 180 J = 0.78
    Given:                           Efficiency = 0.78 x 100% = 78%
        Work input = 180 J
        Useful work output = 140
                                         Answer:
         J                                  Efficiency = 78%

    Unknown:
        Efficiency = ? %