Work_ Power_Efficiency_ Energy

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					Work, Power,Efficiency,

       MHR Chapters 6, 7
Specific Curriculum Outcomes
    analyse quantitatively the relationships among force, distance, and work (325-9)
   analyse quantitatively the relationships among work, time, and power (325-10)
   design and carry out an experiment to determine the efficiency of various machines (212-3,213-2,213-3,214-7)

   Transformation, Total Energy, and Conservation
   analyse quantitatively the relationships among mass, speed, and thermal energy, using the law of conservation of
    energy (326-1 )
   describe quantitatively mechanical energy as the sum of kinetic and potential energies (326-5)
   o compare empirical and theoretical values of total energy and account for discrepancies (214- 7)
   o analyse quantitatively problems related to kinematics and dynamics using the mechanical energy concept (326-6)
   o analyse common energy transformation situations using the closed system work-energy theorem (326- 7)
   o analyse and describe examples where technological solutions were developed based on scientific understanding ( 116-4)
   o determine the percentage efficiency of energy transformation (326-8)
   o design an experiment, select and use appropriate tools, carry out procedures, compile and organize data, and interpret
    patterns in the data to answer a question posed regarding the conservation of energy (212-3, 212-8, 213-2, 214-3, 214-11,
   o distinguish between problems that can be solved by the application of physics-related technologies and those that cannot
   o determine which laws of conservation, momentum, and energy are best used to analyse and solve particular real-life problems
    in elastic and inelastic interactions (326-4)


   Technological Implications
    analyse and describe examples where energy- and momentum-related technologies were developed and improved over time
    (115-5, 116-4)
   describe and evaluate the design of technological solutions and the way they function using principles of energy and momentum
   explain the importance of using appropriate language and conventions when describing events related to momentum and energy
Key terms
   Work
   Energy
   Power
   Efficiency
   Conservation of energy
   Kinetic energy
   Gravitational Potential Energy
   Elastic Potential Energy
   Total Mechanical Energy
   Energy-related concepts are essential in
   Some different forms of energy are:
   Kinetic, Gravitational Potential, Elastic
    Potential, Chemical Potential, Thermal,
    Nuclear, Biochemical, Electrical etc
   Every living and dynamic process in nature
    involves conversion of energy from one form
    to another e.g. photosynthesis, combusting
    gasoline and other fossil fuels, using
   In Science 10 you learned about the energy
    of the Sun driving weather patterns on the
    Earth and providing energy input for
Work and Energy Defined
   Work is one way to transfer energy between
    different objects e.g. a rope is used to pull a
    crate, a baseball is thrown by a pitcher.
   In Physics, work is done when a force acts on
    an object as the object moves from one place
    to another. The meaning differs from the
    everyday use of the word.
   Work can be positive or negative. Positive
    work results in an increase in kinetic energy.
   W=F·d·cosθ or W=Fdcosθ
   In words, work is defined as the dot product
    of force and displacement. This is the first
    time you are multiplying vectors in this class.
    The dot product is one way to multipy two
    vectors. The product, however, is not a
    vector; it is a scalar. The direction of the
    work will always be in the direction of the
    displacement so it will not change.
Work and Energy
   If work is the product of force and
    displacement,the units for work are Newtons
   1 N·m Ξ 1 Joule (Ξ means defined as)
   If you examine the formula W=Fdcosθ Fcosθ
    is also the x component of the force, so if the
    displacement is along the x, then work can
    also be found by multiplying the x-component
    of the force and the displacement
Work and Energy

   Energy is defined as the ability to do work so
    the units for energy are also Joules and
    energy is also a scalar.
   Kinetic energy is defined as the energy of
    motion whereas gravitational potential energy
    is defined as the stored energy an object has
    because work was done on the object against
    the gravitational field.
   Ek = ½ mv2 where Ek is kinetic energy
    (aka KE) in Joules, m = mass in kg and
    v = velocity in m/s

   Ep = mgh where Ep is gravitational
    potential energy (aka GPE) , m = mass
    in kg, and h is height (or vertical
    displacement) in m
Stored energy in a Spring
   If you have every stretched a spring or rubber band
    and released it, you would have observed that the
    work you did in stretching the spring or rubber band
    is stored in the spring/band and can be released.
    Another example of this is the spring above a garage
    door. When these doors are installed, some of the
    strings are “torqued” so that they hold about 200-300
    pounds of force. It is this stored energy that
    essentially lifts the garage door. The drive
    mechanism does provide some of the lift.
Stored energy in a Spring
   The work done in stretching or
    compressing a spring is stored in the
    spring as elastic potential energy.
   Ee = ½ kx2 where Ee is elastic potential
    energy in Joules, k is the spring or force
    constant in N/m and x is the amount of
    stretch or compression in m
   Power is defined as the time rate of
    doing work or the time rate of energy
    transfer. The unit of power is the Watt.
    A 13 W compact fluorescent bulb
    changes 13 joules of electrical energy
    into mainly light and some heat every
   1 Watt Ξ 1 Joule/s 1 W Ξ 1 J/s
Work Kinetic Energy Theorem
   Experimental evidence and everyday
    experience suggests that when the
    work done on an object increases its
    motion, then the kinetic energy of the
    object increases. This is known as the
    Work-Kinetic Energy Theorem.
   W = ΔEk = Ek final – Ek initial
Example 1
   Sebastien does work on a curling 3.0 kg
    curling stone by exerting a force of 35
    N over a displacement of 2.0 m.
   A) How much work is done on the
   B) Assuming the stone started from rest
    and neglecting friction, what was the
    final velocity of the stone upon release?
Solution to Example 1
   W = Fdcosθ = (35 N)(2.0 m) cos 0°
   W = 70. J
   W = Ek final – Ek initial
   70. J = ½ mv2 = ½ (3.0 kg) v2

   v = √(70. J/1.5 kg) = 2.16 m/s
   v = 2.2 m/s (in the direction of motion)
Work and Gravitational
Potential Energy
   Gravitational potential energy is measured in relation
    to a reference (or zero) level. A convenient choice of
    reference level is the surface of the Earth. If work is
    done in lifting a book from a desk to a book shelf,
    then there is an increase in gravitational potential
    energy of the book at the book shelf level relative to
    the desk as work has been done against the
    gravitational field. We say that the work done
    becomes “stored” gravitational potential energy.
    Symbolically this is

   W = ∆Eg = Eg final – Eg initial
Work and Gravitational PE
   W = Eg final – Eg initial
   W = mg∆h
   Example 2: A grade 11 physics student
    of mass 50.0 kg walks up the stairs at
    CHS and undergoes a change in vertical
    displacement of 10.0 m. How much
    work was done by the student?
Solution to Example 2
   W = mg∆h
   W = (50.0 kg)(9.81 m/s²)(10.0 m)
   W = 4905 J → 4.90 x 10³ J (3 sig figs)
   Note that this is also 4.90 kJ
Work Energy Theorem
   If doing work on an object increases
    different forms of energy such as
    kinetic and gravitational potential, then
    we can generalize the work kinetic
    energy theorem to the following:

   W = ∆E
Example 3
   Jess pushes her 10. kg trunk up a 2.0 m high
    ramp starting from rest. At the top of the
    ramp, the trunk is moving at 3.0 m/s.
    Neglecting friction, how much work was done
    on the trunk?
   W = ∆E = ∆Ek + ∆Eg
   W = (½mvf2 - ½mvi²) + (mg∆h)
   W = (45 J – 0 J) + (196.2 J) =241.2 J
   W = 240 J (2 sig fig)