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SPH4U Grade 12 University Physics: Dynamics Unit – 20/ 90 classesThe expectations in bold are considered the most important. This is because they encompass much of the knowledge desired from the course (please see Section One: Desired Results/Goals) and are fundamental to pursuing university physics. Being able to use vector quantities is important in math courses such as Calculus and Linear Algebra. Overall ExpectationsB1. analyse technological devices that apply the principles of the dynamics of motion, and assess thetechnologies’ social and environmental impact;B2. investigate, in qualitative and quantitative terms, forces involved in uniform circular motion andmotion in a plane, and solve related problems;B3. demonstrate an understanding of the forces involved in uniform circular motion and motion in a plane.Specific ExpectationsB1.1 analyse a technological device that applies the principles of linear or circular motionB1.2 assess the impact on society and the environment of technological devices that use linear or circular motionB2.1 use appropriate terminology related to dynamics, including, but not limited to: inertial and non-inertial frames of reference, components, centripetal, period, frequency, static friction, and kinetic frictionB2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methodsB2.3 analyse, in qualitative and quantitative terms, the relationships between the force of gravity, normal force, applied force, force offriction, coefficient of static friction, and coefficient of kinetic friction, and solve related two-dimensional problems using free-body diagrams, vector components, and algebraic equationsB2.4 predict, in qualitative and quantitative terms, the forces acting on systems of objectsB2.5 analyse, in qualitative and quantitative terms, the relationships between the motion of a system and the forces involvedB2.6 analyse, in qualitative and quantitative terms, the forces acting on and the acceleration experienced by an object in uniform circular motion in horizontal and vertical planes, and use free-body diagrams and algebraic equations to solve related problemsB2.7 conduct inquiries into the uniform circular motion of an objectB3.1 distinguish between reference systems (inertial and non-inertial) with respect to the real and apparent forces acting within such systemsB3.2 explain the advantages and disadvantages of static and kinetic friction in situations involving various planesB3.3 explain the derivation of equations for uniform circular motion that involve the variables frequency, period, radius speed, and massScientific and Career Exploration ExpectationsA1.5 conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and dataA1.6 compile accurate data from laboratory and other sources, and organize and record the data, using appropriate formats, including tables, flow charts, graphs, and/or diagramsA1.12 use appropriate numeric (e.g., SI and imperial units), symbolic, and graphic modes of representationA1.13 express the results of any calculations involving data accurately and precisely, to the appropriate number of decimal places or significant figuresStage One: Desired Results/Goals KinematicsMotion can be represented using velocity-time, acceleration-time, and displacement-time graphsOne-dimensional motion can also be represented with equations, derived from velocity-time graphsFive key equations can be used to solve uniformly accelerating problems; the acceleration of gravity is considered uniform at 9.8 m/s2 when you are relatively close to the surfaceDisplacement vectors can be used to describe displacement in two dimensions and total displacement can be found by adding the horizontal and vertical components of vectors using trigonometry Velocity in two dimensions is described as the change in total displacement over timeVelocity vectors can be subtracted, after being broken into components, using the vector property vf – vi = vf + (-vi ) to find the change in velocity and acceleration in 2-D can be represented as the change in velocity over change in timeProjectile motion has the following properties: horizontal motion is constant, horizontal component of acceleration is zero, vertical acceleration is constant because of gravity, horizontal and vertical components are independent but share the same timeProjectile motion can be analyzed using horizontal and vertical components, trigonometry, and kinematic equationsA frame of reference is a coordinate system to which motion is described and relative velocity is the velocity of an object relative to a certain frame of referenceDynamicsFree body diagrams show all the forces acting on an object at one timeThe net force on an object is the sum of all forces acting on the object and it 2-D it is easier to add forces when they are in their horizontal and vertical componentsNewton’s First Law of Motion is that if the external net force on an object is zero, the object will remain at rest or contune moving at constant velocityNewton’s Second Law of Motion is that if the net force is not zero, the object will accelerate in the direction of the net force, Fnet = maNewton’s Third Law of Motion is that for every action force there exists and equal and opposite reactionWeight is the gravitational force exerted by Earth on an object; mass is different from weightObjects in equilibrium have a net force of zero so both the x and y components of force are zeroIf an object is not in equilibrium, it is accelerating (Newton’s 2nd Law)Kinetic and static friction opposes motionThe coefficient of friction is the ratio of kinetic friction to the normal force while the coefficient of static friction is the ratio of the maximum force of static friction to the normal force ( so that no relative motion occurs)Uniform Circular MotionAn inertial frame of reference is one that moves at a constant or zero velocity; the law of inertia holdsA fictitious force is an apparent but non-existent force used to explain objects motion within accelerating ( non-inertial) frames of referenceApparent weight is the magnitude of normal force in a non-inertial frame of reference ( example, standing on a scale in an elevator going down will be less than mg)Centripetal acceleration is the instantaneous acceleration that is directed toward the center of a circular path (objects moving in a circular pathFrequency is the number of rotations of an object per unit of time or the inverse of the periodThere are three equation to determine centripetal acceleration a = v2/r , a = 4π2r/T2 , a = 4 π2rf2Newton’s Second Law and the equation for centripetal acceleration can be combined into the equation F = mv2/rA centrifuge is a rapidly rotating device used to separate substances and simulate the effects of gravityCentrifugal force is a fictitious force in a rotating, non-inertial frame of referenceLearning SkillsSkillEvidence for TeacherWork IndependentlyPerformance on tests and how time is spent working in classTeamworkLabs and collaborative group problemsOrganizationHow lab reports and notes are organizedClean and set-up labs and data collection gathered and organized appropriatelyInitiativeCompletion of homework, submitting assignments on timeStage Two: Assessment EvidenceDynamics Problems (of learning) Vector ActivityUniform Acceleration Lab Nerf Gun LabRoad Rage InvestigationKinematics TestDynamics TestAssessment Evidence Rationale: The dynamics problems students will complete following the Full Solution Template helps students develop their ability to problem solve. The focus is to show them how to think and approach problems by providing them with steps they need to follow. This is an example of “of learning”; students ability to answer the question will be marked out of 3 ( 0 – no work shown, 1- some attempt made, 2-several minor errors, 3-perfect or near perfect solution) to quickly provide them with feedback on how they are doing. This portion is more about coaching the students rather than testing them. The vector activity was a way to engage kinesthetic learners and to have students get practice with adding vectors. This is a skills needed for many of the problems they will be encountering so getting additional practice in a fun way is useful. The uniform acceleration lab is a simple lab used to make sure students have a good understanding of motion and uniform acceleration. It is also a lab they will be completing early on to see what their lab write up skills are like. It will be marked for learning but as they complete more labs throughout the semester, a low lab mark may be dropped if they improve. The Nerf Gun lab is an interesting example of projectile motion. Students will again have practice thinking critically about sources of error and problem solving as thy complete calculations. The road rage investigation comes at the end of the unit as a way for students to explore some applications of kinematics. This problem uses all of the problem solving skills they have been developing. It is a summative assessment piece. The two tests are used because the unit is long. They make sure that the students’ skills are being tested individually and are used as summative assessment. Stage Three: Daily Lesson PlanningStandards Connection: What will students learn and do?Instructional Plan: What activities will engage students and contribute to their learning?Ongoing Assessment: How will you assess student learning on an ongoing basis?Standard: IndicatorLesson Objective(s)Instructional StrategiesStudent ActivitiesAssessment Type0 KINEMATICSStudents will learn about uniform motionPrior Knowledge: Students will be shown four images of a ramp with a ball on it where the ball is pushed up the ramp (one with the ball at the base of the ramp, the other halfway up the ramp, another with a ball at the top of the ramp and a fourth where the ball is coming back down the ramp halfway. They will be asked where the acceleration was the greatest. Gravity is uniform acceleration when relatively close to the Earth’s surface (9.8m /s2). A feather and ball are shown to have the same acceleration when falling in the Earth’s largest vacuum as seen hereStudents will complete a simple lab on uniform acceleration, with a cart rolling down a ramp. The instructions can be found here. Materials: : Ball, books to stack, 1 m track (with a groove for the ball), stopwatch, protractor, notebook, computer with ExcelThe modified version can be found below as it includes graphing in Excel and discussion questions. Lab report (assessment for learning)1B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methodsStudents will be able to understand multiple representations of motion on a graph and will practice describing motion using graphsThis simulation shows how to obtain graphs from motion: Motion Using GraphsExamples of how to obtain v-t and a-t graphs from d-t graphs will be shown in class as well as how to convert from v-t to d-tThis activity compares position, velocity and acceleration graphs; students will complete part 1 & 2 of the activity with the focus on motion graphs will complete practice questions converting between graph typesAs learning: observation of student work 2B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methodsStudents will be able to derive the five key equations used to solve uniformly accelerating problems from motion graphs Computer simulationEquation DerivationSample problemsStudents will complete part 2 of the moving man simulation from the resource provided from the website that focuses on uniform acceleration if they did not complete it the day beforeThey will complete selected practice problemsAs learning: observation of student work 3B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methodsA1.6 A1.12 A1.13Students will be able to analyze displacement vectors in 2-D by using trigonometryBrief lesson on how to add vectors using components or cosine and sine lawStudent ActivityActivity: walk to the school library using vectors and find your total displacement (assuming we can walk through walls!) using meter sticks and protractors.Show all of you calculations, organized in a logical order, and state your final displacement. For learning: marking of vector activity, looking at vector addition and calculations4B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methodsStudents will be able to solve 2-D velocity and acceleration problems using the adding/subtracting of vectors and uniform acceleration equationsA couple of sample problems will be completed in class.Students will then have time to finish two problems on their own, following the format sheet given. Give a collectable problem on the answering a physics question sheet modified from Meyer CreationsOf learning, mark sheet out of 3 ( 0 – no work shown, 1- some attempt made, 2-several minor errors, 3-perfect or near perfect solution) 5, 6, 7B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methodsA1.6 A1.12 A1.13Students will be able to solve problems involving projectile motion when projectile is launched horizontally and non-horizontallyProjectile motion simulation found here involving a cannonVector analysis shown here for a non-horizontally launched projectile found hereActivity on Page 50 Students will complete projectile motion problems.Students will spend one lesson completing the Nerf Gun Projectile Motion Lab to find the muzzle speed of the gun using projectile motion analysis. This lab will not have a formal write up required. Materials: Nerf gun, stopwatch, meter stick,Optional: iPad with Vernier Video Physics app students can record the motion using the video recording and it tracks motionLab Calculations and conclusions (and optional video) 8B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector components, and algebraic methodsStudents will be able to solve problems using the notion of relative velocity Relative motion example demo with a water balloon being dropped out of a car motion practice questionsSample Problems; use a draw, analyze sheetHomework: Create a list of the key topics we have learnt and write down any questions you have about them for the review tomorrow Of learning ( Collection of Problem Sheet)9 ReviewPractice problems and review concepts using student-generated questions and textbook reviewStudents will ask questions about types of questions or concepts they were confused by Observation of student work and answers10Kinematics Test3 problems, obtained from Meyers, C. Sample Test QuestionsTests problem solving ability; has students use the same format as homework questionsSummative testDYNAMICS11B2.1, B2.4 predict, in qualitative and quantitative terms, the forces acting on systems of objectsStudents will be able to explain phenomena using Newton’s LawsUse a short investigation using masses and pulleys to introduce Newton’s laws (Bruni, D. et al, 2012, pg. 61)The investigation on Page 61 of the Nelson Physics TextbookObservation of investigation 12, 13 B2.3, B2.4, B2.5Apply newton’s laws to problemsActivity: Weight changing in an elevatorHave student volunteers weight themselves in class then check their weight in an elevatorCan also show a Wolfram Alpha simulationExplore why you weigh less when moving down; have students use the POE modelElevator POE ActivityTextbook problems completed using Homework TemplateObservation as learningAssessment of learning as they complete the problems assigned14B2.3, B2.1, B3.2Students will be able to understand the effects of friction, both static and kineticHook: Have students rub their hands together, ask them to explain what is happeningShow friction at a molecular level using ActivityPractice problems done in stationsObservation as and of learning15B2.6, B2.7, B3.1, B3.3Uniform circular motionLesson note content and simulation found hereDiscussion and simulationExit Ticket with small UCM problem on itObservation and Exit Ticket14 B2.6, B2.7, B3.1Centripetal accelerationDemo: Swing a Bucket of Water Materials: water, rope/string &tray with water, bucketAddress the misconception of “centripetal force”; it is fictitious Teach how to derive the 3 centripetal acceleration equationsStudent Activity: Predict Observe Explain the demoSample questions done in groups on whiteboardsObservation of group work 15 B1.1, B1.2B2.6Rotating Frames of ReferenceStudents will read the case study on centrifuges and the Coriolis effect, and artificial gravity (Page 125 – 127 and 128-129 of the textbook; see References)After the activity we will consolidate with a short note and problem. Students will read the pages, making notes on definitions, key concepts and questions they have. They will then be moved to groups of three where they will answer each other’s questions and after explain one of the topics to the other group members in a round robin. Materials: textbook, sticky notes(to put questions on textbook), lined paperObservation as learning through round robin16B2.2, B2.6A1.6 A1.12 A1.13Culminating Crime TaskStudents will be given class time to complete a crime scene activityStudents will complete the Road Rage activity in pairs; playing the role of Forensic Physicist to help determine how a car accident occurred. A student handout is provided. Hints can be given as needed. They will be assessed on their individual write up. Students write a report, summarizing their mathematical process, sources of error, and recommendations to police. 17ReviewPractice problems and review concepts using student-generated questions and textbook reviewStudents will ask questions about types of questions or concepts they were confused by Observation of student work and answers18Dynamics Unit TestConceptual questions adapted from here Summative TestDay 0 Lab 1: Acceleration Lab Modified from : To study the motion of a body moving along an inclined plane.MATERIALS: Ball, books to stack, 1 m track (with a groove for the ball), stopwatch, protractor, notebook, computer with Excel PROCEDURE:Stack some books and set one side of the molding on the books to create a ramp.Use the protractor to measure the angle between the ramp and the floor. Adjust the stack of books until you can get the ramp as close to 30° as possible. Record the final angle in your notebook.Use the ruler or meter stick to mark 10 cm intervals along the ramp, starting at the floor and going upward.Set the golf ball at a measured distance along the ramp. Time how long it takes for the golf ball to hit the floor after your let the ball go. Record both the distance you let the ball go and the time it takes for the ball to travel the length of the ramp.Repeat step for at different lengths along the ramp.Graph your results. Put time on the x-axis, and distance traveled on the y-axis. Do you notice any patterns?Calculate the velocity at each interval and plot that on another graph with time on the x-axis. Use Excel to determine the slope of the graph v-t graph. Calculate the acceleration for the points you tested using the equation??a = 2d / t2Repeat the experiment with 2 different ramp angles.DISCUSSION QUESTIONS: What do you understand by uniformly accelerated motion? How might you change the experiment to reduce sources of error?For each graph, describe any patterns you notice. .What did you notice when you repeated the experiment with different angles? What must have caused the golf ball to increase in speed?Is it possible for the ball to have a zero acceleration? Explain. Use what you have learnt to describe concerns associated with driving downhill. Lab Marking Scheme and Checklist: Title: 1 markObjective: 1 markMaterials: 1 markProcedure: 1 markD-T Graph: - proper title: 1 mark-labelled axes: 1 mark- accurate data: 1 mark-description of purpose: 1 markV-T graph:- proper title: 1 mark-labelled axes: 1 mark- accurate data: 1 mark-slope calculation: 1 mark-description of purpose: 1 markResults: 10 marks -spelling and grammar-data organized in labelled tables-correct units-sample calculations shown-results are presented in a logical order; conclusions are not drawn in this portionDiscussion: 14 marks- all discussion questions are answered- results are referenced appropriately in answersConclusion: 5 marks- was the purpose of the lab achieved? What did you learn?Day 3 Vector Activity Vector Activity ( K/U /10)Using a meter stick and a protractor to measure your pathway to the _____________________. You will add your vectors (and assume there are not any walls!) to find your total displacement. Show your drawings and recordings. Please show all of your calculations.Drawing and Recordings /5 (neatness, significant figures, completeness) Calculations /5 Day 4 General Problem Solving Sheet Homework SheetProblem: A: Pictorial Representation B: Physics RepresentationC: Word Representation: Describe what happens in words without numbers. Write down any assumptions.D: Mathematical Representation: Describe the steps you use. Use correct units and significant figures. Day 10 KINEMATICS TEST Total: /30Please answer the following questions to the best of your ability on the lined paper provided. Provide a Pictorial Representation, Physics Representation (include vectors and measurements), and Mathematical Representation (solving through explained steps and correct units/significant figures) for full marks.1. (10 marks) A stuntman stands on top of a highway overpass which is 6.70 m above the road surface. A truckdrives along the highway and underneath the overpass maintaining a steady speed of 120 km/h. A switch on the roadsurface is triggered when the truck runs over it. The switch turns on a light and shows the stuntman when to step offthe overpass and land safely on top of the truck. The truck roof is 2.35 m above the road surface. How far from theoverpass should the switch be positioned?2. (10 marks) In a thrilling scene, Mr. Bond is supposed to run off the edge of a balcony. He will pass right through a lowerwindow in a building across from the balcony. The bottom of the target window is located 5.7 m below Mr. Bond’sstarting point and 4.7 m across from the balcony. The window is 2.3 m high. From your careful training sessions withthe actor, you know he can reliably run horizontally off the balcony at 4.5 m/s. His safety is your responsibility. Willhe make it through the window?3. (10 marks) In a dramatic scene from the latest James Bond movie, Mr. Bond is driving his fancy high-tech car along ahighway at 253 km/h. He sees a giant boulder at the top of a cliff which the bad guy releases. The boulder dropsvertically from rest towards the highway below. Bond does the smart thing and hits the gas as soon as the boulderstarts to move, hoping to pass underneath the boulder before it lands. You are the stunt coordinator for this scene. Theboulder starts 67.5 m above the highway. The car accelerates at 1.31 m/s2 and begins accelerating 260.0 m awayfrom the landing site. Will the stuntman in the car survive?Marking Scheme for Each Question: 2 – Communication: correct significant figures and units5 – Thinking and Inquiry: ability to identify information needed and asked for, use physics concepts to solve3 – Knowledge and Understanding: correct formulas/ process usedDay 11 InvestigationDay 16 Forensics Physics Report Student Handout: Report Checklist: K/U: /5 C: /5 T: /15 A: /5 Total: /30Please type your report. The results page may be completed by hand neatly. Length Requirements:Cover Page: 1 pageIntroduction: ? - 1 pageResults: 1 -3 pages including the diagramConclusion: ? - 1 pageCorrect spelling, grammar, formal voice, organized report (C- 4 marks) Cover Page; addressed to the correct parties (C - 1 mark) Introduction: a brief summary of what you were investigating; reliable information given (K/U - 5 marks)Results: Organized calculations you completed; including a labelled physics diagram (T/I – 15 marks)Correct units, each step is explained, correct significant figuresConclusion: Discuss what the calculations mean. Cleary identify which scenario your evidence supports (A -5 marks) Day 17 DYNAMICS TEST Total: /30Please answer the following questions to the best of your ability on the lined paper provided. Provide a Pictorial Representation, Physics Representation (include forces on free body diagrams), and Mathematical Representation (solving through explained steps and correct units/significant figures) for full marks.1. You and your friends are eager to earn another bonus mark for your physics class. You decide to try out some physicsby taking a bathroom scale onto a stand-up rollercoaster (the riders are always in a standing position). Before the ridestarts, you stand on the scale and note that it reads 65 kg. The ride starts and at the top of the first loop you are upside-downand your scale reads 77 kg. You estimate that the loop has a radius of 15 m. How fast were you going at the topof the loop? (10 marks)2. You are the chief engineer designing a new luge track for the Sochi winter Olympics in 2014. You are designing astraight run down an incline. The luge sled will enter this section with a speed of 84.6 km/h and must not exceed 143km/h by the end of it after travelling a distance of 312 m. Determine the maximum angle of the incline. You mayassume the track is frictionless. (10 marks)3. You are driving home from the cottage and pulling a trailer behind your car. There is a steep hill with a 12o inclinethat you must drive up. You read the instructions for the trailer hitch which keeps the trailer attached to your car. Thehitch can withstand a maximum force of 4.3 x 103 N. The car has a mass of 1.1 x 103kg. The trailer has a total mass (including the stuff inside) of 2.7 x 102 kg. There is rolling friction between the trailer and road with μr = 0.15 (treatthis just like kinetic friction). You start from the bottom of the hill at rest (a stop sign). What is the top speed youcould achieve after driving 45.0 m up the hill? (10 marks)Marking Scheme for Each Question: 2 – Communication: correct significant figures and units5 – Thinking and Inquiry: ability to identify information needed and asked for, use physics concepts to solve3 – Knowledge and Understanding: correct formulas/ process usedThe following are resources that were referred to in the Daily Plan; they are organized by each day for ease of use.ReferencesCourse Textbook (Used Throughout): Brunl, D. et al. (2012). Physics 12: University Preparation. Toronto, Ontario: Nelson Education Ltd. DayCitationDescription0Bjornsson, E. (2015) Acceleration on an Inclined Plane. Retrieved 01/03/15 from Education Inc. (2004). 1.2 Analyzing Motion Using Graphs. Retrieved 08/02/15 from of Colorado. (2015). Phet Interactive Simulations: The Moving Man. Retrieved 08/02/15 from for motion graphsStudent activity: simulation with handout234Meyer. (2015). Grade 12 Physics Student Workbook. Page 22. Retrieved 01/03/15 from Solution Format Sheet5,6,7 University of Colorado. (2015). Phet Interactive Simulations: Projectile Motion. Retrieved 02/03/15 from Physics Classroom. (2015). Non-Horizontally Launched Projectiles. Retrieved 02/03/15 from . (2010). Unit 1-Vector Kinematics: Nerf Gun Projectile Lab. Retrieved 27/02/15 from gun Lab8UCAELI. (2012). Relative Motion Demonstration. Retrieved 02/03/15 from , C. (n.d) Sample Questions from Recent Tests. Retrieved 02/03/15 from questions1112,13Wolfram Demonstration Project. (2015). Weight of a Person Riding in an Elevator. Retrieved 24/02/15 from of Colorado. (2015). Friction. Retrieved 24/02/15 from Physics Classroom. (2015). Uniform Circular Motion. Retrieved 02/03/15 from Physics. (2014). Forensics: Road Rage. Retrieved 27/02/15 from , C.(n.d). Sample Questions from Recent Tests. Retrieved 02/03/15 from questions ................
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