Work, Power,Efficiency, Energy

1
Work, Power,Efficiency, Energy

• MHR Chapters 6, 7

2
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)

3
Key terms

• Work
• Energy
• Power
• Efficiency
• Conservation of energy
• Kinetic energy
• Gravitational Potential Energy
• Elastic Potential Energy
• Total Mechanical Energy

4
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

5
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.

6
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.

7
Formulas

• WFdcos? or WFdcos?
• 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.

8
Work and Energy

• If work is the product of force and
  displacement,the units for work are Newtons
  metres
• 1 Nm ? 1 Joule (? means defined as)
• If you examine the formula WFdcos? Fcos? 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

9
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.

10
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

11
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.

12
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

13
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 ? 1 Joule/s 1 W ? 1 J/s

14
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 ?Ek Ek final Ek initial

15
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?

16
Solution to Example 1

• W Fdcos? (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 v(70. J/1.5 kg) 2.16 m/s
• v 2.2 m/s (in the direction of motion)

17
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

18
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?

19
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

20
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

21
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)