PHYSICS 20
Unit 3: Circular Motion, Work, and Energy
Unit C: Circular Motion, Work and Energy
Themes: Energy and Equilibrium
Overview:
In this unit, students extend their study of kinematics and dynamics to uniform circular motion and to mechanical energy, work and powerThis unit builds on:
- Grade 8 Science, Unit D: Mechanical Systems
- Grade 9 Science, Unit E: Space Exploration
- Science 10, Unit B: Energy Flow in Technological Systems
- Physics 20, Unit A: Kinematics and Unit B: Dynamics
Unit C will require approximately 30% of the time allotted for Physics 20.
Focusing Questions:
- What conditions are necessary to maintain circular motion?
- How does an understanding of conservation laws contribute to an understanding of the universe?
- How can mechanical energy be transferred and transformed?
General Outcomes:
There are two major outcomes in this unit.Students will:
C1. explain circular motion,using Newton’s laws of motion
C2. explain that work is a transfer of energy and that conservation of energy in an isolated system is a fundamental physical concept
Key Concepts:
The following concepts are developed in this unit and may also be addressed in other units or in other courses. The intended level and scope of treatment is defined by the outcomes.Key Concepts:- uniform circular motion
- planetary and satellite motion
- Kepler’s laws
- mechanical energy
- conservation of mechanical energy
- work-energy theorem
- isolated systems
- power
General Outcome 2
C2. Students will explain that work is a transfer of energy and that conservation of energy in an isolated system is a fundamental physical concept.Specific Outcomes for Knowledge
Students will:
20–C2.1k define mechanical energy as the sum of kinetic and potential energy 6.3
20–C2.2k determine, quantitatively, the relationships among the kinetic, gravitational potential and total mechanical energies of a mass at any point between maximum potential energy and maximum kinetic energy 6.1, 6.2
20–C2.3k analyze, quantitatively, kinematics and dynamics problems that relate to the conservation of mechanical energy in an isolated system 6.3
20–C2.4k recall work as a measure of the mechanical energy transferred and power as the rate of doing work 6.4
20–C2.5k describe power qualitatively and quantitatively 6.4
20–C2.6k describe, qualitatively, the change in mechanical energy in a system that is not isolated. 6.3
20–C2.2k determine, quantitatively, the relationships among the kinetic, gravitational potential and total mechanical energies of a mass at any point between maximum potential energy and maximum kinetic energy 6.1, 6.2
20–C2.3k analyze, quantitatively, kinematics and dynamics problems that relate to the conservation of mechanical energy in an isolated system 6.3
20–C2.4k recall work as a measure of the mechanical energy transferred and power as the rate of doing work 6.4
20–C2.5k describe power qualitatively and quantitatively 6.4
20–C2.6k describe, qualitatively, the change in mechanical energy in a system that is not isolated. 6.3
Specific Outcomes for Science, Technology and Society (STS) (Nature of Science Emphasis)
Students will:
20–C2.1sts explain that concepts, models and theories are often used in interpreting and explaining observations and in predicting future observations
• estimate the energy released during a meteoritic impact with Earth’s surface
• analyze the gravitational collapse of a star
• examine how a planet can provide a gravity assist to a space probe
• analyze the transformation of kinetic and potential energy of an orbiting object at perihelion and aphelion
20–C2.2sts explain that the products of technology are devices, systems and processes that meet given needs; however, these products cannot solve all problems
• evaluate the design and efficiency of energy transfer devices in terms of the relationships among mechanical energy, work and power
• analyze the use of irrigation systems and water wheels used by different cultures, such as the Incas
20–C2.3sts evaluate whether Canadian society supports scientific research and technological development to facilitate a sustainable society, economy and environment
• investigate and report on a technology developed to improve the efficiency of energy transfer as a means of reconciling the energy needs of society with its responsibility to protect the environment and to use energy judiciously.
• estimate the energy released during a meteoritic impact with Earth’s surface
• analyze the gravitational collapse of a star
• examine how a planet can provide a gravity assist to a space probe
• analyze the transformation of kinetic and potential energy of an orbiting object at perihelion and aphelion
20–C2.2sts explain that the products of technology are devices, systems and processes that meet given needs; however, these products cannot solve all problems
• evaluate the design and efficiency of energy transfer devices in terms of the relationships among mechanical energy, work and power
• analyze the use of irrigation systems and water wheels used by different cultures, such as the Incas
20–C2.3sts evaluate whether Canadian society supports scientific research and technological development to facilitate a sustainable society, economy and environment
• investigate and report on a technology developed to improve the efficiency of energy transfer as a means of reconciling the energy needs of society with its responsibility to protect the environment and to use energy judiciously.
Specific Outcomes for Skills (Nature of Science Emphasis)
Students will:
20–C2.1s formulate questions about observed relationships and plan investigations of questions, ideas, problems and issues
• design an experiment to demonstrate the conservation of energy;
e.g., Is energy conserved in a collision? (IP–NS1, IP–NS2).
• design an experiment to demonstrate the conservation of energy;
e.g., Is energy conserved in a collision? (IP–NS1, IP–NS2).
Performing and Recording
Students will:
20–C2.2s conduct investigations into relationships among observable variables and use a broad range of tools and techniques to gather and record data and information
• perform an experiment to demonstrate the law of conservation of energy (PR–NS3)
• research the development of the law of conservation of energy, using library and Internet sources (PR–NS1) [ICT C1–4.1].
• perform an experiment to demonstrate the law of conservation of energy (PR–NS3)
• research the development of the law of conservation of energy, using library and Internet sources (PR–NS1) [ICT C1–4.1].
Analyzing and Interpreting
Students will:
20–C2.3s analyze data and apply mathematical and conceptual models to develop and assess possible solutions
• use free-body diagrams to organize and communicate solutions to work-energy theorem problems (AI–NS1)
• solve, quantitatively, kinematics and dynamics problems, using the work-energy theorem (AI–NS3) [ICT C6–4.1]
• analyze data to determine effective energy conservation strategies;
e.g., analyze whetherlowering the speed limit or modifying the internal combustion engine saves more energy in vehicles (AI–ST2, AI–SEC3) [ICT C7–4.2].
• use free-body diagrams to organize and communicate solutions to work-energy theorem problems (AI–NS1)
• solve, quantitatively, kinematics and dynamics problems, using the work-energy theorem (AI–NS3) [ICT C6–4.1]
• analyze data to determine effective energy conservation strategies;
e.g., analyze whetherlowering the speed limit or modifying the internal combustion engine saves more energy in vehicles (AI–ST2, AI–SEC3) [ICT C7–4.2].
Communication and Teamwork
Students will:
20–C2.4s work collaboratively in addressing problems and apply the skills and conventions of science in communicating information and ideas and in assessing results
• use integrated software effectively and efficiently to reproduce work that incorporates data, graphics and text (CT–NS2) [ICT P4–4.3].
• use integrated software effectively and efficiently to reproduce work that incorporates data, graphics and text (CT–NS2) [ICT P4–4.3].
Note: Some of the outcomes are supported by examples. The examples are written in italics and do not form part of the required program but are provided as an illustration of how the outcomes might be developed.
Links to Mathematics
The following mathematics outcomes are related to the content of Unit C but are not considered prerequisites.Concept Mathematics Course, Strand and Specific Outcome
Data Collection and Analysis
Grade 9 Mathematics,Statistics and Probability (Data Analysis),Specific Outcome 3 Measurement and Unit Conversions
Mathematics 10C, Measurement, Specific Outcomes 1 and 2;
Mathematics 10-3, Measurement, Specific Outcome 1;
Mathematics 20-3, Algebra, Specific Outcome 3
Trigonometry
Mathematics 10C, Measurement, Specific Outcome 4;
Mathematics 10-3, Geometry, Specific Outcomes 2 and 4
Rate and Proportions
Mathematics 20-2, Measurement, Specific Outcome 1
Graph Analysis
Mathematics10C, Relations and Functions,Specific Outcomes 1, 4 and 7;
Mathematics 20-3, Statistics,Specific Outcome1
Solving Equations
Grade 9 Mathematics, Number, Specific Outcome 6;
Mathematics 20-1, Algebra and Number, Specific Outcome 6;
Mathematics 30-2, Relations and Functions, Specific Outcome 3
Scale Diagrams
Mathematics 20-2, Measurement,Specific Outcome 2;
Mathematics 20-3, Geometry, Specific Outcome 2
Slope
Mathematics10C, Relations and Functions,Specific Outcome 3 and 5;
Mathematics 20-3, Algebra, Specific Outcome 2
Powers
Mathematics10C, Algebra and Number, Specific Outcome 3
Note: The use of systems of equations, the quadratic formula and trigonometric ratios for angles greater than 90º is not required in this unit
.
Unit Themes and Emphases
- Energy, Equilibrium and Systems
- Nature of Science
- Scientific Inquiry
Focusing Questions
- What is necessary to maintain circular motion?
- How does an understanding of conservation laws contribute to an understanding of the Universe?
- How can mechanical energy by transferred and transformed?
Chapter 6. In An Isolated System, Energy Is Transferred From One Object To Another Whenever Work Is Done
Key Concepts
- Work, mechanical energy, and power
- The Work-energy theorem
- Isolated and non-isolated systems.
- The law of conservation of energy
Learning Outcomes
- Use the law of conservation of energy to explain the behaviors of objects within isolated systems.
- Describe the energy transformations in isolated and non-isolated systems using the work-energy theorem
- Calculate power output.
STS
- Explain that models and theories are used to interpret and explain observations.
- Explain that technology cannot solve all problems
- Express opinions on the support found in Canadian society for science and technology measures that work toward a sustainable society.
.
6.1 Work and Energy
Work is the transfer of energy that occurs when a force acts over a displacement. It is a scalar quantity measured in joules.F - force, N
d - displacement, m
Potential energy is the energy a body has because of its position or configuration. It is a scalar quantity measured in Joules.
Kinetic energy is the energy a body has because of its motion. It is a scalar quantity measured in Joules.
Energy - the ability to do work
Work – a measure of the energy transferred when a force acts over a given displacement. It is calculated as the product of the magnitude of applied force and the displacement of the object in the direction of that force
Gravitational potential energy – the energy of an object due to its position above the surface of Earth
m - mass, kg
g - acceleration due to gravity = 9.81 m/s2
h - height, m
Reference point – an arbitrarily chosen point from which distances are measured
Elastic potential energy – the energy resulting from an object being altered from its standard shape, without permanent deformation
k - spring constant, N/m
x - stretch or compression
Es = | kx2 |
2 |
k - spring constant, N/m
x - stretch or compression, m
Kinetic energy – the energy due to the motion of an object
Ek = | mv2 |
2 |
m - mass, kg
v - velocity, m/s
.
6.2 Mechanical Energy
Work done by a net force causes a change in kinetic energy.The work-energy theorem states that the work done on a system is equal to the sum of the changes in the potential and kinetic energies.
Mechanical energy is the sum of the potential and kinetic energies.
Mechanics – the study of kinematics, statics, and dynamics
Mechanical energy – the sum of potential and kinetic energies
Work-energy theorem - the product of the force and distance
.
6.3 Mechanical Energy In Isolated and Non-isolated Systems
The law of conservation of energy states that in an isolated system, the mechanical energy is constant.A simple pendulum is a good approximation of an isolated system in which energy is conserved.
A conservative force does not affect the mechanical energy of a system.
In non-isolated systems, the mechanical energy may change due to the action of non-conservative forces.
Isolated system – a group of objects assumed to be isolated from all other objects in the universe
Non-isolated system – a system in which there is an energy exchange with the surroundings
Conservation of energy - the total amount of energy in a conservative system (No outside forces) stays the same.
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6.4 Work and Power
Power is defied as the rate of ding work. Power is calculated by find the ratio of the work done to the time required to do the work. It is measured in Watts.Power may be calculated by taking the product of the force doing the work and the average speed.
Power – the rate of doing work
P = | W |
t |
W - work or energy, J
t - time, s
Efficiency – ratio of the energy output to the energy input of any system
% efficiency = | input energy | × 100% |
output energy |
input energy - the energy put into the energy conversion, J
output energy - the energy removed from the energy conversion, J