# Work_ Power_Efficiency_ Energy

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```					Work, Power,Efficiency,
Energy

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,
326-4)
   o distinguish between problems that can be solved by the application of physics-related technologies and those that cannot
(118-8)
   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
(116-6)
   explain the importance of using appropriate language and conventions when describing events related to momentum and energy
(114-9)
Key terms
   Work
   Energy
   Power
   Efficiency
   Conservation of energy
   Kinetic energy
   Gravitational Potential Energy
   Elastic Potential Energy
   Total Mechanical Energy
Introduction
   Energy-related concepts are essential in
science.
   Some different forms of energy are:
   Kinetic, Gravitational Potential, Elastic
Potential, Chemical Potential, Thermal,
Nuclear, Biochemical, Electrical etc
Introduction
   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
electricity.
   In Science 10 you learned about the energy
of the Sun driving weather patterns on the
Earth and providing energy input for
ecosystems.
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.
Formulas
   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
·metres
   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.
Energy
   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
   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
second.
   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.
Symbolically:
   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
stone?
   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)

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