PHYSICS 20
Unit 2: Dynamics
Unit B: Dynamics
Themes: Change and Systems
Overview:
In this unit, students investigate causes of change in the position and velocity of objects and systems in a study of dynamics and gravitation. The concept of fields is introduced in the explanation of gravitational effects.This unit builds on:
- • Grade 7 Science, Unit D: Structures and Forces
- • Grade 8 Science, Unit D: Mechanical Systems
- • Science 10, Unit B: Energy Flow in Technological Systems
- • Physics 20, Unit A: Kinematics
Unit B will require approximately 25% of the time allotted for Physics 20.
Focusing Questions:
- How does the understanding of forces help humans improve or change their environment?
- How do the principles of dynamics influence the development of new mechanical technologies?
- What role do gravitational effects play in the universe?
General Outcomes:
There are two major outcomes in this unit. Students will:- B1. explain the effects of balanced and unbalanced forces on velocity
- B2. explain that gravitational effects extend throughout the universe.
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.
- Newton’s laws of motion
- inertia
- vector addition
- static and kinetic friction
- gravitational force
- Newton’s law of universal gravitation
- gravitational field
General Outcome: B2 Students will explain that gravitational effects extend throughout the universe.
Specific Outcomes for Knowledge
Students will:
20–B2.1k identify the gravitational force as one of the fundamental forces in nature
20–B2.2k describe, qualitatively and quantitatively, Newton’s law of universal gravitation
20–B2.3k explain, qualitatively, the principles pertinent to the Cavendish experiment used to determine the universal gravitational constant, G
20–B2.4k define the term “field” as a concept that replaces “action at a distance” and apply the concept to describe gravitational effects
20–B2.5k relate, qualitatively and quantitatively, using Newton’s law of universal gravitation, the gravitational constant to the local value of the acceleration due to gravity
20–B2.6k predict, quantitatively, differences in the weight of objects on different planets.
20–B2.2k describe, qualitatively and quantitatively, Newton’s law of universal gravitation
20–B2.3k explain, qualitatively, the principles pertinent to the Cavendish experiment used to determine the universal gravitational constant, G
20–B2.4k define the term “field” as a concept that replaces “action at a distance” and apply the concept to describe gravitational effects
20–B2.5k relate, qualitatively and quantitatively, using Newton’s law of universal gravitation, the gravitational constant to the local value of the acceleration due to gravity
20–B2.6k predict, quantitatively, differences in the weight of objects on different planets.
Specific Outcomes for Science, Technology and Society (STS) (Nature of Science Emphasis)
Students will:
20–B2.1sts explain that concepts, models and theories are often used in interpreting and explaining observations and in predicting future observations (NS6a)
• compare apparent weightlessness and zero net gravity
• investigate the existence and shape of globular star clusters
• explain tidal forces on Earth
• describe the forces required to accelerate the Mars rover on Earth and on Mars
• explore the evolution of theories of gravity, using different worldviews.
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.
• compare apparent weightlessness and zero net gravity
• investigate the existence and shape of globular star clusters
• explain tidal forces on Earth
• describe the forces required to accelerate the Mars rover on Earth and on Mars
• explore the evolution of theories of gravity, using different worldviews.
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.
Specific Outcomes for Skills (Nature of Science Emphasis)
Initiating and PlanningStudents will:
20–B2.1s formulate questions about observed relationships and plan investigations of questions, ideas, problems and issues
• identify, define and delimit questions to investigate;
e.g., What is the relationship between the local value of the acceleration due to gravity and the gravitational field strength? (IP–NS1).
Performing and Recording • identify, define and delimit questions to investigate;
e.g., What is the relationship between the local value of the acceleration due to gravity and the gravitational field strength? (IP–NS1).
Students will:
20–B2.2s conduct investigations into relationships among observable variables and use a broad range of tools and techniques to gather and record data and information
• determine, empirically, the local value of the acceleration due to gravity (PR–NS2)
• explore the relationship between the local value of the acceleration due to gravity and the gravitational field strength (PR–NS1) [ICT C7–4.2].
Analyzing and Interpreting • determine, empirically, the local value of the acceleration due to gravity (PR–NS2)
• explore the relationship between the local value of the acceleration due to gravity and the gravitational field strength (PR–NS1) [ICT C7–4.2].
Students will:
20–B2.3s analyze data and apply mathematical and conceptual models to develop and assess possible solutions
• list the limitations of mass-weight determinations at different points on Earth’s surface (AI–NS4)
• treat acceleration due to gravity as uniform near Earth’s surface (AI–NS3).
Communication and Teamwork • list the limitations of mass-weight determinations at different points on Earth’s surface (AI–NS4)
• treat acceleration due to gravity as uniform near Earth’s surface (AI–NS3).
Students will:
20–B2.4s work collaboratively in addressing 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.
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 topics are related to the content of Unit B 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 ConversionsMathematics 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 Outcome 1 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 Outcomes 3 and 5;
Mathematics 20-3, Algebra, Specific Outcome 2
Area Calculations
Mathematics 10-3, Measurement, Specific Outcome 4
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.
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Unit Themes and Emphasis
- Change and systems
- Social and environmental contexts
- Problem-solving skills
Focusing Questions:
- How does an understanding of forces help humans interact with their environment?
- How do the principles of dynamics affect mechanical and other systems?
- What role does gravity play in the universe?
Chapter 4: Gravity Extends Throughout The Universe
Key Concepts
- Gravitational force
- Newton’s law of universal gravitation
- Gravitation field
Knowledge
- Identify gravity as a fundamental force in nature
- Describe Newton’s law of universal gravitation
- Explain the Cavendish experiment
- Define and apply the concept of a gravitational field
- Compare gravitational field strength and acceleration due to gravity
- Predict the weight of objects on different planets
STS
- Explain that concepts, models, and theories help interpret observations and make predictions.
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4.1 Gravitational Forces due to Earth
Gravitational force is a fundamental force.The 4 fundamental forces are natural and cannot be affected by humans.
Gravity, electromagnetic, strong nuclear and weak nuclear.
Gravitational force – attractive force between any two objects due to their mass
Action-at-a-distance force – force that acts even if the objects involved are not touching
Field – three-dimensional region of influence
Gravitational field – region of influence surrounding any object that has mass
Earth’s gravity field goes towards the centre of the earth.
In a large scale it is spherical.
In a small scale the lines are parallel and point down.
Galileo studied gravity by dropping objects from the top of the leaning tower of Pisa.
He discovered mass did not affect the time it took two same sized and shaped objects to fall.
Newton was lying on his back when an apple fell and landed on his stomach. He started to think about gravity and how it affects objects.
Used as evidence of the Copernican model of the solar system.
Einstein said that gravity is bending of space-time
This is often shown as the bending of space-time diagrams.
Imagine the spheres are planets orbiting the Sun.
Light has no mass so it is not directly affected by gravity.
Light always travels in a straight line through space, but if space is bent by gravity, light moves in a curve because space is curved, not because gravity affects light.
Gravitational lensing
Warp drive
Wormhole
Gravitational field strength is the ratio of gravitational force to mass at a specific location.
The units of gravitational field strength are:
Weight – gravitational force exerted on an object by a celestial body
True Weight:
Ex. What is the weight of Mr. Montgomery who has a mass of 87 kg?
Review Questions
What is a force field?What is weight?
What are the units for the gravitational field?
What does the force of gravity pull on?
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4.2 Newton’s Law of Universal Gravitation
Newton’s law of universal gravitation states that the gravitational force of attraction between any two masses is directly proportional to the product of the masses and inversely proportional to the square of the separation distance between the centres of both masses.Newton studied gravity and determined that gravity was affected by the mass of the two objects and the distance between them. However he never developed an experiment to find the values.
Torsion balance – device used to measure very small forces
Cavendish’s experiment
Henry Cavendish used a torsion balance to determine how the force of gravity is affected by the distance between two objects and the mass of the objects.
Graph the following
Newton’s law of gravitation:
Fg = | Gm1m2 |
r2 |
G - gravitational constant of the universe, 6.67×10-11 Nm2/kg2
m1 - mass of first object, kg
m2 - mass of second object, kg
r - radius of orbit, distance between objects, m
Ex. What is the gravitational force between the sun 1.98×1031 kg and the earth 5.98×1024 kg when the two are 1.49×1011m apart?
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4.3 Relating Gravitational Field Strength to Gravitational Force
Newton’s law of gravitation can be used to determine the magnitude of gravitational field strength anywhere in the universe.The magnitude of gravitational field strength at a location is numerically equal to the magnitude of gravitational acceleration.
g = | Gm |
r2 |
G - gravitational constant of the universe, 6.67×10-11 Nm2/kg2
m - mass of planetoid, kg
r - radius of planetoid, m
Ex. What is the acceleration due to gravity at the surface of the Earth? Calculate it from Earth’s mass and radius.
The value of g at Earth’s surface depends on latitude, altitude, the composition of Earth’s crust, and Earth’s rotation about its axis.
Free fall is the condition where the only force acting on an object is the gravitational force. True weightlessness is the condition in which for an object and on the object.
The true weight of an object is equal to the gravitational force acting on the mass, and depends on location.
Apparent weight is the negative of the normal force acting on an object.
Gravitational field strength:
Apparent weight: