How do changes in position, velocity, and acceleration allow us to predict the paths of moving objects and systems?
How do the principles of kinematics influence the development of new mechanical technologies?
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
This unit prepares students for further study, in subsequent units and physics courses, of Newton’s laws, periodic motion and particles in electric and magnetic fields.
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: B1. explain the effects of balanced and unbalanced forces on velocity.
Specific Outcomes for Knowledge
Students will:
20–B1.1k explain that a nonzero net force causes a change in velocity
20–B1.2k apply Newton’s first law of motion to explain, qualitatively, an object’s state of rest or uniform motion
20–B1.3k apply Newton’s second law of motion to explain, qualitatively, the relationships among net force, mass and acceleration
20–B1.4k apply Newton’s third law of motion to explain, qualitatively, the interaction between two objects, recognizing that the two forces, equal in magnitude and opposite in direction, do not act on the same object
20–B1.5k explain, qualitatively and quantitatively, static and kinetic forces of friction acting on an object
20–B1.6k calculate the resultant force, or its constituents, acting on an object by adding vector components graphically and algebraically
20–B1.7k apply Newton’s laws of motion to solve, algebraically, linear motion problems in horizontal, vertical and inclined planes near the surface of Earth, ignoring air resistance.
Specific Outcomes for Science, Technology and Society (STS) (Social and Environmental Contexts Emphasis)
Students will:
20–B1.1sts explain that the goal of technology is to provide solutions to practical problems, that technological development includes testing and evaluating designs and prototypes on the basis of established criteria, and that the products of technology cannot solve all problems (ST1, ST5d, ST6) [ICT F2–4.4] • assess the design and use of injury-prevention devices in cars and sports in terms of Newton’s laws of motion • explain how buffalo jumps represented a technological solution to food supply problems and describe the advantages and limitations of such a technique
20–B1.2sts explain that science and technology are developed to meet societal needs and that society provides direction for scientific and technological development (SEC1, SEC4) [ICT F2–4.8]
• discuss the use of seat belts in school buses
20–B1.3sts explain that scientific knowledge and theories develop through hypotheses, the collection of evidence, investigation and the ability to provide explanations (NS2) • analyze the trajectory of lunar dust particles as illustrated in a video.
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 (Science and Technology Emphasis)
Initiating and Planning
Students will:
20–B1.1s formulate questions about observed relationships and plan investigations of questions, ideas, problems and issues • identify questions to investigate arising from practical problems; e.g., What are the relationships among acceleration, mass and force acting on a moving object? (IP–ST1).
Performing and Recording
Students will:
20–B1.2s conduct investigations into relationships among observable variables and use a broad range of tools and techniques to gather and record data and information
• conduct experiments to determine relationships among force, mass and acceleration, using available technologies; e.g., using interval timers or motion sensors to gather data (PR–ST3) [ICT C6–4.4] • research the use of kinematics and dynamics principles in everyday life; e.g., research traffic accident investigation methods, using the Internet and/or interviews (PR–ST1).
Analyzing and Interpreting
Students will:
20–B1.3s analyze data and apply mathematical and conceptual models to develop and assess possible solutions • analyze a graph of empirical data to infer the mathematical relationships among force, mass and acceleration (AI–NS6) [ICT C6–4.1] • use free-body diagrams to describe the forces acting on an object (AI–NS1).
Communication and Teamwork
Students will:
20–B1.4s 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–ST2).
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.
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.
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.
GRAVITY VECTOR FIELDS ANIMATION
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?
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
Fg - force of gravity, N
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?
Fg =
Gm1m2
r2
Fg =
6.67×10-11Nm2/kg2 × 1.98×1031 kg × 5.98×1024 kg
(1.49×1011 m)2
Fg =
3.557293275×1023 N
Fg =
3.56×1023 N [attractive]
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 - acceleration due to gravity, m/s2 [down]
G - gravitational constant of the universe, 6.67×10-11 Nm2/kg2
m - mass of planetoid, kg
r - radius of planetoid, m
ACCEL AS A FUNCTION OF DISTANCE ANIMATION
Ex. What is the acceleration due to gravity at the surface of the Earth? Calculate it from Earth’s mass and radius.
g =
Gm
r2
g =
Gm
r2
g =
6.67×10-11Nm2/kg2 × 5.98×1024 kg
(6.37×106 m)2
g =
9.81 m/s2 [down]
The value of g at Earth’s surface depends on latitude, altitude which affect the radius at that point and the composition of Earth’s crust which affects the density and mass of Earth under that point, and Earth’s rotation about its axis which introduces circular motion forces.
Free fall is the condition where the only force acting on an object is the gravitational force. True weightlessness is the condition in which Fg→= 0 N for an 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.
