PHYSICS 20
Unit 3: Circular Motion, Work, and Energy
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?
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 1
C1. Students will explain circular motion, using Newton’s laws of motion.Specific Outcomes for Knowledge
Students will:
20–C1.1k describe uniform circular motion as a special case of two-dimensional motion 5.1
20–C1.2k explain, qualitatively and quantitatively, that the acceleration in uniform circular motion is directed toward the centre of a circle 5.1
20–C1.3k explain, quantitatively, the relationships among speed, frequency, period and radius for circular motion 5.2
20–C1.4k explain, qualitatively, uniform circular motion in terms of Newton’s laws of motion 5.2
20–C1.5k explain, quantitatively, planetary and natural and artificial satellite motion, using circular motion to approximate elliptical orbits 5.3
20–C1.6k predict the mass of a celestial body from the orbital data of a satellite in uniform circular motion around the celestial body 5.3
20–C1.7k explain, qualitatively, how Kepler’s laws were used in the development of Newton’s law of universal gravitation. 5.3
20–C1.2k explain, qualitatively and quantitatively, that the acceleration in uniform circular motion is directed toward the centre of a circle 5.1
20–C1.3k explain, quantitatively, the relationships among speed, frequency, period and radius for circular motion 5.2
20–C1.4k explain, qualitatively, uniform circular motion in terms of Newton’s laws of motion 5.2
20–C1.5k explain, quantitatively, planetary and natural and artificial satellite motion, using circular motion to approximate elliptical orbits 5.3
20–C1.6k predict the mass of a celestial body from the orbital data of a satellite in uniform circular motion around the celestial body 5.3
20–C1.7k explain, qualitatively, how Kepler’s laws were used in the development of Newton’s law of universal gravitation. 5.3
Specific Outcomes for Science, Technology and Society (STS) (Nature of Science Emphasis)
Students will:
20–C1.1sts explain that the process of scientific investigation includes analyzing the evidence and providing explanations based upon scientific theories and concepts
• examine the role of orbital perturbations in the discovery of outer planets
• examine the evidence for extra-solar planets
20–C1.2sts explain how science and technology are developed to meet societal needs and expand human capability
• explain the functions, applications and societal impacts of geosynchronous satellites
20–C1.3sts explain that the goal of technology is to provide solutions to practical problems
• analyze the principles and applications of circular motion in daily situations
– explain the use of a centrifuge in industry or research
– explain the motion of a car moving with constant speed through a curve
– explain the motion of carnival or playground rides moving in a horizontal plane and/or a vertical plane
– explain the operation of a potter’s wheel.
• examine the role of orbital perturbations in the discovery of outer planets
• examine the evidence for extra-solar planets
20–C1.2sts explain how science and technology are developed to meet societal needs and expand human capability
• explain the functions, applications and societal impacts of geosynchronous satellites
20–C1.3sts explain that the goal of technology is to provide solutions to practical problems
• analyze the principles and applications of circular motion in daily situations
– explain the use of a centrifuge in industry or research
– explain the motion of a car moving with constant speed through a curve
– explain the motion of carnival or playground rides moving in a horizontal plane and/or a vertical plane
– explain the operation of a potter’s wheel.
Specific Outcomes for Skills (Nature of Science Emphasis)
Students will:Initiating and Planning
Students will:
20–C1.1s formulate questions about observed relationships and plan investigations of questions, ideas, problems and issues
• design an experiment to investigate the relationships among orbital speed, orbital radius, acceleration and force in uniform circular motion(IP–NS2) Vc lab, Fc lab
• explore design characteristics of structures that facilitate circular motion;
e.g., How is banking used on a racetrack to make high-speed turns safer? ??????
• design an experiment to investigate the relationships among orbital speed, orbital radius, acceleration and force in uniform circular motion(IP–NS2) Vc lab, Fc lab
• explore design characteristics of structures that facilitate circular motion;
e.g., How is banking used on a racetrack to make high-speed turns safer? ??????
Performing and Recording
Students will:
20–C1.2s 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 investigate the relationships among net force acting on an object in uniform circular motion and the object’s frequency, mass, speed and path radius (PR–NS3)
• perform an experiment to investigate the relationships among net force acting on an object in uniform circular motion and the object’s frequency, mass, speed and path radius (PR–NS3)
Analyzing and Interpreting
Students will:
20–C1.3s analyze data and apply mathematical and conceptual models to develop and assess possible solutions
• organize and interpret experimental data, using prepared graphs or charts (AI–NS1)[ICTC7–4.2]
• construct graphs to show relationships among frequency, mass, speed and path radius
• summarize an analysis of the relationships among frequency, mass, speed and path radius (AI–NS6)
• solve, quantitatively, circular motion problems in both horizontal and vertical planes, using algebraic and/or graphical vector analysis (AI–NS3) [ICT C6–4.1]
• organize and interpret experimental data, using prepared graphs or charts (AI–NS1)[ICTC7–4.2]
• construct graphs to show relationships among frequency, mass, speed and path radius
• summarize an analysis of the relationships among frequency, mass, speed and path radius (AI–NS6)
• solve, quantitatively, circular motion problems in both horizontal and vertical planes, using algebraic and/or graphical vector analysis (AI–NS3) [ICT C6–4.1]
Communication and Teamwork
Students will:
20–C1.4s work collaboratively in a ddressing problems and apply the skills and conventions of science in communicating information and ideas and in assessing results
• select and use appropriate numeric, symbolic, graphical or linguistic modes of representation to communicate findings and conclusions (CT–NS2).
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 • select and use appropriate numeric, symbolic, graphical or linguistic modes of representation to communicate findings and conclusions (CT–NS2).
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
Chapter 5: Newton’s Laws Can Explain Circular Motion
Key Concepts
- Uniform circular motion
- Planetary and satellite motion
- Kepler’s Laws
Knowledge
- Describe uniform circular motion as a special case of two-dimensional motion
- Explain centripetal acceleration and force
- Explain, quantitatively, the relationships among speed, frequency, period, and radius for circular motion
- Explain, qualitatively, uniform circular motion using Newton’s laws of motion.
- Explain, quantitatively, the motion of orbiting bodies by using circular motion to approximate elliptical orbits.
- Predict the mass of a celestial body from orbital data
- Explain, qualitatively, how Kepler’s laws were used to develop Newton’s universal law of gravitation.
STS
- Explain the process of scientific inquiry
- Illustrate how science and technology are developed to meet society’s needs and expand human capabilities.
- Analyze circular motion in daily situations.
5.1 Defining Circular Motion
The velocity of an object moving with circular motion is tangent to the circle and 90o to the radial line.| |vc| = | 2πr |
→
|
| T |
r - radius, m
T - period, time for one orbit, s
Centripetal acceleration and centripetal force are both directed toward the centre of the circle.
| |ac| = | v2 |
→
|
| r |
v - velocity centripetal, m/s
r - radius, m
| |ac| = | 4 π2 r |
→
|
| T2 |
r - radius, m
T - period, s
Axle – shaft on which a wheel rotates
Axis of rotation – imaginary line that passes through the centre of rotation perpendicular to the circular motion
Uniform circular motion – motion in a circular path at a constant speed
Centripetal acceleration – acceleration acting toward the centre of a circle
Centripetal force – force acting toward the centre of a circle causing an object to move in a circular path
ANIMATION OF CENTRIPETAL ACCELERATION
ANIMATION OF CENTRIPETAL FORCE
| |Fc| = | mv2 |
→
|
| r |
m - mass, kg
v - velocity, m/s
r - radius, m
| |Fc| = | 4 π2mr |
→
|
| T2 |
m - mass, kg
r - radius, m
T - period, s
5.2 Circular Motion and Newton’s Laws
The velocity of circular motion can be determined by dividing the circumference by the period.The centripetal acceleration of an object is determined by the velocity squared divided by the radius.
Newton’s second law states and can be applied to centripetal acceleration. A car making a turn experiences a centripetal acceleration and force that is created by the force of friction between the tires and the road.
The minimum speed necessary to move an object through a vertical loop equates centripetal force with gravitational force. Centripetal force can be equated to the gravitational force for planetary objects.
Centripetal acceleration and force can be determined using period and frequency instead of speed.
Cycle – one complete back-and-forth motion or oscillation
Revolution – one complete cycle for an object moving in a circular path
Period – the time required for an object to make one complete oscillation (cycle)
Frequency – the number of cycles per second measured in hertz (Hz)
RPM – revolutions per minute
5.3 Satellites and Celestial Bodies in Circular Motion
Kepler formulated three laws that explained the motion of planets in the solar system.- All planets in the solar system have elliptical orbits with the Sun at one focus
- A line drawn from the Sun to a planet sweeps out equal areas in equal times.
- The ratio of a planet’s orbital period squared to its orbital radius cubed is a constant. All the objects orbiting the same focus (e.g. planets, the sun) have the same constant.
KEPLER's 1ST LAW ANIMATION
KEPLER'S 2nd LAW ANIMATION
Newton recognized the reason that Kepler’s laws were correct: for Earth-Moon system. He also found a way to determine the mass of an object from the period of a celestial body orbiting it.
The discovery of Uranus and Pluto occurred because of the apparent disturbances in the orbit of the planets. Extrasolar planets have been discovered by examine perturbations in stars’ movements.
Humans have placed a variety of artificial satellites into orbit to meet society’s needs.
Kepler’s laws -
| Ta2 | = | Tb2 |
| ra3 | rb3 |
ra - radius of planet a's orbit
Tb - planet b's period of orbit
rb - radius of planet b's orbit
Any units are legitimate but both times need to use the same units, and the radii need to use the same units.
Ellipse
Eccentricity
Orbital period
Orbital radius
Satellite
Artificial satellite
Orbital perturbation – irregularity or disturbance in the predicted orbit of a planet
Extra solar planet
Program of Studies
Alberta Physics 20
Program of Studies
Alberta Physics 20
Program of Studies
Contact me:
BCHS Barrhead AB
Steven Montgomery
steven.montgomery@pembinahills.caBCHS Barrhead AB
Textbook
Physics 20 & 20 Textbook (2009)
Physics 20 & 20 Textbook (2009)