1. UNIT B: ENERGY FLOW IN TECHNOLOGICAL SYSTEMS
Chapter 1: Motion, Work, and Energy

2. B1.1 Motion Uniform Motion
Motion is the change in position of an object over time.
Speed is the rate of motion of an object.
Uniform motion describes an object moving at a constant speed in a straight line.
Uniform motion is almost impossible to maintain, so the term average speed is usually used.

3. Use the following equation to determine the average speed of an object:

4. Practice Problem 1
A huge ocean wave, or tsunami, travels a distance of 4.0 x 106 m in 3.6 x 104 s. Calculate the average speed of the tsunami.
Practice Problem 2
A Concorde airplane could fly at an average speed of 694 m/s. Calculate how long it would have taken the Concorde to fly around the world (4.00 x 104 km).
Practice Problem 3
An electric train is travelling at an average speed of 694 m/s for 4 .0 s. Calculate the distance travelled by the train.

5. Distance-Time Graphs – Uniform Motion
The line of best fit of a distance-time graph showing uniform motion is a straight line.

6. The slope of any line is equal to the change in vertical direction divided by the change in horizontal direction.
The slope of a distance-time graph is equal to the average speed of the object.
Use the following formula to calculate the slope of a graph:

7. Practice Problem 4
Use the following table of data to plot a distance-time graph. Calculate the slope of the graph and state what the slope represents.
Time
Distance
0.0 s
0.0 m
1.0 s
12.0 m
2.0 s
24.0 m
3.0 s
36.0 m
4.0 s
48.0 m
5.0 s
60.0 m

9. Speed-Time Graphs – Uniform Motion
A speed-time graph showing uniform motion will have a straight, horizontal line of best fit.
Total distance traveled is equal to the area under the line.

10. Practice Problem 5
Use the following data to construct a speed-time graph. Calculate the area under the line.
Time (s)
Speed (m/s)
0.0
5.00
2.0
4.0
6.0
8.0
10.0

12. B1.2 Velocity

13. Distance and Displacement
Distance refers to how far an object travels, regardless of direction.
Distance is a scalar quantity – e.g. Δd = 8 m.

15. How to Identify Vector Directions
When working with vector quantities, assign each direction as either positive or negative.
[Up] and [right] are positive; [down] and [left] are negative.
[N] and [E] are positive; [S] and [W] are negative.
Practice Problem 6
A ball rolls 10.0 m [S], hits a wall, and rolls back a distance of 15.0 m [N]. Determine the distance travelled by the ball. Determine the displacement of the ball.

16. Velocity
Velocity is the rate at which an object changes its position.
Velocity is a vector quantity; speed is a scalar quantity.
Use the following equation to calculate average velocity:

17. Practice Problem 7
A car passes a 50 km [N] marker on a highway at time 0. The car passes a 150 km [N] marker at time 30 minutes. What is the average velocity of the car in km/h?
Practice Problem 8
A cyclist is travelling at 9.1 m/s [E] from school to home. It takes him 16 minutes to get home. What is the displacement from the cyclist’s school to home?

18. Using Graphs to Analyze Average Velocity
The slope of a position-time graph represents the average velocity.
A straight line of best fit indicates that the motion is uniform.

19. A velocity-time graph can also be used to analyze motion.
A velocity-time graph showing uniform motion will have a straight, horizontal line of best fit.
The area under the line of a velocity-time graph is equal to the total displacement of the object.

20. Position of Object (m) [E]
Practice Problem 9
Use the following table of data to draw a position-time graph. Calculate the slope of the graph and state what the slope represents.
Time (s)
Position of Object (m) [E]
0.0
2.0
49.8
4.0
100.0
6.0
150.1
8.0
199.9
10.0
250.2

22. Velocity of Object (m/s) [E]
Practice Problem 10
Use the following table of data to draw a velocity-time graph. Calculate the area under the line and state what this value represents.
Time (s)
Velocity of Object (m/s) [E]
0.0
7.0
2.0
4.0
6.0
8.0
10.0

24. B1.3 Acceleration Types of Acceleration
Acceleration (non-uniform motion) is the change in velocity in a given time interval – can be positive or negative.
Acceleration is a vector quantity so both magnitude and direction must be given, unless otherwise indicated by the question. If no direction is provided, assume the direction is positive.

25. Positive Acceleration

26. Negative Acceleration

27. Using Formulas to Analyze Accelerated Motion
Use the following formula to calculate acceleration:

28. Practice Problem 11
A racing car accelerates from rest to a speed of 200 km/h (55.6 m/s) [E] in 6.00 s. What is the acceleration of the car?
Practice Problem 12
An object starts from rest and accelerates at 1.30 m/s2 [N] for 6.00 s. What is the final velocity of the object?
Practice Problem 13
A car driver applies the brakes and slows down from m/s [E] to 5.00 m/s [E] in 4.00 s. Determine the car’s acceleration.

29. Position-Time Graphs – Non-Uniform Motion
The slope of a position-time graph showing positive acceleration will be a curve with an increasing slope.

30. The slope of a position-time graph showing negative acceleration will be a curve with decreasing slope.

31. Practice Problem 14
Use the following data to construct a position-time graph of an object travelling with accelerated motion. Use the graph to describe the motion between t = 0.0 s and t = 3.0 s; t = 3.0 s and t = 6.0 s; t = 6.0 s and t = 8.0 s.
Time (s)
Position (m) [E]
0.0
1.0
10.0
2.0
40.0
3.0
90.0
4.0
140.0
5.0
190.0
6.0
240.0
7.0
270.0
8.0
290.0

33. Velocity-Time Graphs – Non-Uniform Motion
The slope of a velocity-time graph showing positive acceleration will be increasing.

34. The slope of a velocity-time graph showing negative acceleration will be decreasing.
The slope of a velocity-time graph is equal to the object’s acceleration.
The area under the line is equal to the total displacement.

35. Practice Problem 15
Use the following data to construct a velocity-time graph of an object travelling with accelerated motion. Use the graph to describe the motion between t = 0.0 s and t = 3.0 s; t = 3.0 s and t = 6.0 s; t = 6.0 s and t = 8.0 s.
Time (s)
Position (m) [E]
0.0
1.0
2.0
4.0
3.0
6.0
5.0
7.0
8.0

37. B1.4 Work and Energy
Force
A force (measured in Newtons or kg∙m/s2) is a push or a pull.
Force is a vector quantity.
Inertia refers to the tendency of an object at rest to stay at rest and an object in motion to stay in motion, unless acted on by a force.

38. An object at rest will only move when an unbalanced force is applied to it through a distance – that is the force acting in one direction is greater than the force acting in the opposite direction.

39. Force is calculated using the following formula:
Note that 1 N = 1 kg•m/s2

40. Practice Problem 16
Calculate the force required to lift a 10 kg chair off of the ground. The acceleration due to gravity is 9.81 m/s2.
Practice Problem 17
Calculate the force of gravity acting on a 55 kg person. The acceleration due to gravity is 9.81 m/s2.

41. Work
Whenever a force moves an object through a distance that is in the direction of the force, then work is done on the object.
If the object does not move, then there is NO work being done.

42. Use the following formula to calculate work done on an object:

43. The Joule can be derived from fundamental units.
Force = mass (kg) x acceleration (m/s2) = kg∙m/s2 = N
Work = force (N) x distance (m) = N∙m = kg∙m2/s2 = J
Practice Problem 18
Calculate the work required to lift a 400 N box 1.2 m off the ground.
Practice Problem 19
A large crane did 2.2 x 104 J of work in lifting a demolition ball a vertical distance of 9.5 m. Calculate the average force exerted by the chain of the crane on the demolition ball.

44. The area under the line of a force-distance graph represents the amount of work done.
Practice Problem 18
Calculate the amount of work done from the following graph.

45. Practice Problem 19
Calculate the amount of work done from the following graph.

46. The Relationship between Work and Energy
Energy is defined as the ability to do work, therefore W = ΔE, or work is equal to the change in energy.
When work is done an object gains energy.
In the absence of any outside forces, such as friction, the total work input is equal to the total work output/energy output.

47. Practice Problem 20
A weightlifter does 4.80 x 103 J of work lifting a barbell. How much energy is gained by the barbell?
Practice Problem 21
A student picks up a 3 kg textbook off of the floor and places it on a shelf 1.3 m above the ground. Recall that acceleration due to gravity is 9.81 m/s2. Calculate the amount of energy gained by the book.

48. UNIT B: ENERGY FLOW IN TECHNOLOGICAL SYSTEMS
Chapter 2: Energy in Mechanical Systems

49. B2.1 Forms of Energy Chemical Energy
Chemical energy is the potential energy stored in the chemical bonds of compounds (e.g. food, ATP, and fossil fuels).

50. Electrical Energy and Magnetism
Electrical energy is the work done by moving charges.
Moving charges produce magnetic fields.
Metals in which electrons can move freely are magnetic.
Electromagnet: electric current moving through a wire produces a magnetic field.
Moving a magnet through a coil of wire causes an electric current to move through the wire.

51. Nuclear and Solar Energy
Nuclear energy is the potential energy stored in the nucleus of an atom.
When the nucleus of the atom is split (nuclear fission) or when the nuclei of two atoms combine (nuclear fusion), this energy is released.
Solar energy results from a hydrogen-hydrogen nuclear fusion reaction with the release of radiant energy.

52. Motion and Energy
Kinetic energy is the energy an object has due to its motion.
Gravitational potential energy is the energy an object has due to its position relative to the Earth’s surface.
Mechanical energy is the sum of an object’s kinetic energy and gravitational potential energy.

53. Heat and Energy
The amount of thermal energy in a substance is determined by the average kinetic energy of the individual atoms.
Atoms move or vibrate more quickly in hot substances than in cold substances.
Heat refers to the transfer of thermal energy from one object to another.
Thermodynamics is the study of the interrelationships of heat, work, and energy.

54. Joule’s Experiments
The figure below illustrates Joule’s experiment that supports a connection between potential energy, kinetic energy, and heat.
As the masses fall, their gravitational potential energy is converted to the kinetic energy of the paddles.
The kinetic energy of the paddles is transformed into the thermal energy of the water.

55. Joule performed another experiment in which a falling block hits a stationary block.
The kinetic energy of the falling block is transformed into the thermal energy of the stationary block.

56. B2.2 Potential Energy Elastic Potential Energy
Elastic potential energy is the energy stored in an object that is stretched or compressed and will return to its original form if released.
For example, a person applies a force to push a diving board down giving the diving board elastic potential energy. The elastic potential energy is then converted into the kinetic energy of the diver.

57. Chemical Potential Energy
Energy stored in the bonds of chemical compounds.
Any substance that can be used to do work through a chemical reaction has chemical potential energy.

58. Gravitational Potential Energy
Potential energy is stored energy; the potential to do work.
When an object is lifted above the Earth’s surface a force is being applied to overcome the force of gravity.
The energy stored in an object at any position above the Earth is called gravitational potential energy.

61. The equation that determines the weight/force of gravity of an object from its mass is:
𝑾 =𝒎 𝒈
Weight (N) = mass (kg) x acceleration due gravity (m/s2)
𝑭𝑮 =𝒎 𝒈
Force of gravity(N) = mass (kg) x acceleration due gravity (m/s2)

62. Practice Problem 1
Calculate the weight of a person on Earth with a mass of 64 kg.
Practice Problem 2
Calculate the mass of an object that weighs 1209 N on the surface of the moon (g = m/s2).

63. Use the following formulas to calculate gravitational potential energy:
Ep (J) = mass (kg) x acceleration due to gravity (m/s2) x height (m)
Note: use the scalar value of acceleration due to gravity for all calculations involving gravitational potential energy – 9.81 m/s2.
Ep = W= Fd= mgh

64. Practice Problem 3
A child with a mass of 25.0 kg is at the top of a slide in an amusement park. If the vertical height of the slide is m, calculate the gravitational potential energy of the child relative to the ground.
Practice Problem 4
An 800 g bird has 47.0 J of gravitational potential energy when it is perched high up in a tree. Calculate the bird’s vertical height from the ground.

65. Practice Problem 5
A hanging sign is 3.00 m above the ground and has 1.47 x 103 J of gravitational potential energy. Calculate the mass of the sign.
Practice Problem 6
A 55.0-kg diver standing on a diving platform has a gravitational potential energy of 5.40 x 103 J. What is the vertical height of the diving platform?

66. B2.3 Kinetic Energy Ek = ½ mv2 Kinetic Energy and Motion
Kinetic energy is the energy associated with the motion of an object.
Use the following formula to calculate the kinetic energy of an object:
Kinetic Energy (J)= ½ (mass of the object in kg) x (speed in m/s2)
Ek = ½ mv2

67. Work done by a person to move an object is equal to the kinetic energy gained by the object.
A snowball with a mass and a speed will have a certain amount of kinetic energy.
Another snowball with twice the mass and the same speed should have twice the kinetic energy.
A third snowball with the same mass but twice the speed will have four times as much kinetic energy.

68. Practice Problem 7
Use the formula for kinetic energy to show how the Joule is derived from fundamental units.
Practice Problem 8
A 3.00 kg ball is pushed horizontally at a speed of m/s. Calculate the kinetic energy of the ball at the moment it starts to move.

69. Practice Problem 9
The kinetic energy of an object moving at a speed of m/s was determined to be J. What is the mass of the object?
Practice Problem 10
Calculate the kinetic energy of an electron with a mass of x kg moving at a uniform speed of 2.00 x 105 m/s.
Practice Problem 11
What is the speed of an 800 kg automobile if it has a kinetic energy of 9.00 x 104 J?

70. B2.4 Mechanical Energy Mechanical Energy
Mechanical energy is defined as the energy due to the motion and position of an object.
Since an object can have both kinetic and potential energy at the same time, mechanical energy can be calculated using the following formula:
Em= Ep + Ek

71. Practice Problem 12
A seagull flying horizontally at 8.00 m/s carries a clam with a mass of 300 g in its beak. Calculate the total mechanical energy of the clam when the seagull is 30.0 m above the ground.
Practice Problem 13
A 55.0 kg high-jump athlete leaps into the air in an attempt to clear the bar. At the top of the leap, the athlete has a total mechanical energy of 3.00 x 103 J and is moving at m/s. Calculate the gravitational potential energy of the athlete.

72. Practice Problem 14
A construction worker drops a 2.00 kg hammer from a roof. When the hammer is 50.0 m above the ground, it has a total mechanical energy of 1.88 x 103 J. Calculate the kinetic energy of the hammer.

73. potential energy kinetic energy
Law of Conservation of Energy
The law of conservation of energy states that the total amount of energy in a system remains constant – it can only be transformed from one from to another.
Thus, in the absence of outside forces, kinetic energy may be converted to potential energy and vice-versa without loss, so the total amount of mechanical energy remains constant.
potential energy kinetic energy
Ep Ek

76. Practice Problem 15
A 10.0 kg water balloon is dropped from a height of 12.0 m. Calculate the speed of the balloon just before it hits the ground.
Practice Problem 16
A 30.0 kg child on a trampoline jumps vertically into the air at an initial speed of 1.60 m/s. Calculate how high the child will rise.
Practice Problem 17
A 20.0 g dart is fired from a dart gun with a speed of m/s. The total mechanical energy of the dart is J. Calculate the gravitational potential energy of the dart.

77. B2.5 Energy Conversions Evidence of Energy Conversions
Motion – kinetic energy
Change in position – gravitational potential energy
Change in shape – elastic potential energy
Change in temperature – thermal energy

78. Energy Conversions in Natural Systems
Photosynthesis converts light energy, carbon dioxide, and water into chemical energy in the form of glucose.
In cellular respiration, chemical energy in the form of glucose is converted into chemical energy in ATP (and heat) and eventually into the energy needed for life processes.

79. Fossil fuels are formed from dead organisms compressed over time
Fossil fuels are formed from dead organisms compressed over time. Combustion reactions convert chemical energy in fossil fuels into thermal energy.

80. Energy Conversions in Technological Systems
Hydroelectric dams convert the potential energy of water stored behind the dam into electrical energy:
Gravitational potential energy → Kinetic energy of water → kinetic energy of turbine blades → kinetic energy of coil of wire within magnetic field → electrical energy

81. A coal-burning power station (thermal power station) converts the chemical energy of fossil fuels into electrical energy:
Chemical potential energy → thermal energy of water → kinetic energy of steam → kinetic energy of turbine blades → kinetic energy of coil of wire within magnetic field → electrical energy

82. Solar cells convert solar energy directly into electricity.

83. In hydrogen fuel cells, hydrogen reacts with oxygen to form water and release energy.

84. Nuclear Energy Conversions
Nuclear power can be used to generate electricity in thermal power stations.
In the CANDU (CANadian Deuterium Uranium) reactor, uranium undergoes nuclear fission, releasing nuclear energy as radiation.
Darlington, ON Nuclear Plant

85. Nuclear potential energy → thermal energy of water → kinetic energy of steam → kinetic energy of turbine blades → kinetic energy of coil of wire within magnetic field → electrical energy

86. UNIT B: ENERGY FLOW IN TECHNOLOGICAL SYSTEMS
Chapter 3: Principles of Thermodynamics

87. B3.1 Laws of Thermodynamics
Systems
A system is a set of interconnected parts; everything else is considered the environment.
The study of the interrelationships between heat, work, and energy in a system is called thermodynamics.
The study of thermodynamics began out of efforts to produce heat engines.

88. An open system is one that exchanges both matter and energy with its surroundings (e.g. a tree).
A closed system is one that cannot exchange matter but can exchange energy with its surroundings (e.g. the Earth).
An isolated system is one that cannot exchange matter or energy with the environment (e.g. the Universe).

89. The First Law of Thermodynamics
The first law of thermodynamics states that energy cannot be created or destroyed. It can only be transformed from one form to another, and the total amount of energy never changes.
In other words, the amount of energy put into a system must equal the amount of mechanical energy output plus heat lost by the system.

90. The Second Law of Thermodynamics
The second law of thermodynamics states that thermal energy always flows naturally from a hot object to a cold object.

91. Video – Early Theories of Heat Video – Steam Engine History
B3.2 Development of Engine Technology – Read p in textbook
Video – Early Theories of Heat
Video – Steam Engine History

92. B3.3 Useful Energy and Efficiency
The purpose of a machine is to convert the initial energy input to the type of desired energy output.
Energy input refers to the initial energy source.
Useful energy output refers to the energy that was converted to perform the useful work output.
All energy output that is not being used to do useful work is considered waste energy (e.g. energy lost due to friction).

93. Consider the input energy, useful output energy, and waste energy in the following situations:
Light bulb
Truck
Human body

94. Efficiency
Efficiency is a measurement of how effectively a machine converts energy input into useful energy output. It is calculated using the following formula:
𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦= 𝑢𝑠𝑒𝑓𝑢𝑙 𝑤𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 𝑡𝑜𝑡𝑎𝑙 𝑤𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡
Percent efficiency is calculated using the following formula:
𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦= 𝑢𝑠𝑒𝑓𝑢𝑙 𝑤𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 𝑡𝑜𝑡𝑎𝑙 𝑤𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡 x100 %

95. Practice Problem 1
A crane lifts a load of construction materials from the ground to the second floor of a building. The crane does x 104 J of work input while doing 8.00 x 103 J of useful work output. What is the percent efficiency of the crane?
Practice Problem 2
An internal combustion engine with an efficiency of 15.0% is used to do 3.20 x 104 J of useful work. Calculate the mechanical energy input that had to be supplied by the combustion of fuel in the engine.

96. Practice Problem 3
The percent efficiency of a machine is 35.0%. What is the input energy required if a 2.00 x 103 kg object is to be lifted m?
Practice Problem 4
A person exerts 150 J of energy lifting a 10.0 kg box onto a shelf that is 1.4 m above the ground. Calculate the efficiency of this energy transformation.

97. B3.4 Energy Applications Energy Supply – Solar Energy Sources
Solar radiation is the radiant energy emitted from the fusion reactions within the Sun.
Wind energy is the result of convection currents to due the unequal heating and cooling of the Earth. Wind energy can be used to move turbines (indirect solar energy).

98. Water energy results when surface water is heated by the Sun, which drives the hydrological cycle. Falling water can be used to move a turbine (indirect solar energy).
Biomass is any form of organic matter that can be combusted to release chemical potential energy (indirect solar energy).
Fossil fuels are formed from dead plants and animals and can be combusted to release energy (indirect solar energy).

99. Energy Supply – Non-Solar Energy Sources
Nuclear energy is obtained from the conversion of mass to energy in either a fission or fusion reaction.
Geothermal energy is thermal energy from the core of the Earth. It is only useful as a source of energy in active geological regions (i.e. hot springs and volcanoes).

100. Tidal energy involves the movement of ocean water caused by the gravitational pull of the moon. In areas where the difference between high tide and low tide is significant, the water can be used to produce electricity.

101. Renewable and Non-Renewable Energy Sources
Renewable energy sources are continually and infinitely available (solar, wind, water, geothermal, tidal, and biomass).
Non-renewable energy sources are limited and irreplaceable (nuclear and fossil fuels).

102. Energy Demand
There are several factors that have caused increased demand for energy:
The amount of energy used per person has increased exponentially.
World population is growing exponentially.
Many societies now use non-renewable energy sources rather than renewable sources as the primary source of energy.

104. The Effects of Energy Use
The extraction and combustion of fossil fuels negatively affects ecosystems in many ways:
Ecosystem disruptions
Oil spills
Release of greenhouse gases
Release of chemicals that contribute to acid rain
Wabamun, AB

105. Energy Consumption and Conservation
As energy use continues to rise, eventually fossil fuels will be depleted.
Alternative energy sources must be developed, however this is expensive and difficult to incorporate.
Until feasible alternative energy sources are developed, conservation and improved efficiency is key.

106. Cogeneration is the process of using waste energy from one process to power a second process (e.g. the steam from a thermal power station could be used to heat a building before returning to the combustion chamber to be reheated).

107. Sustainable Development
Sustainable development is economic development that meets the needs of current generations without compromising the needs of future generations.