AMME2500 Engineering Dynamics:Assignment 3 (10%)General Information:• This assignment is due Saturday 5th June 11:59pm• Late assignments will be deducted 5% (5 marks out of a possible 100) foreach day late, starting from midnight on the day after the assignment isdue and including weekends. Assignments that are 10 days late or morewill receive zero marks.• Any special consideration requires you to go through the SpecialConsideration process via Sydney Student.• Any incidence of academic dishonesty or plagiarism will result in theissue being followed up with the Academic Honesty Coordinator and thenonto the University Registrar, and will result in zero marks for thisassessment, and may result in automatic failure of this unit of study. Formore information on academic honesty, see:https://sydney.edu.au/students/academic-dishonesty-andplagiarism.html• This assignment should take the average student 8 hours to complete.Assignment Objectives:• In this assignment, you will study the dynamic behaviour of a system ofyour choice. You will use the theoretical principles and analysistechniques developed in the course so far to develop and solve theequations of motion from an example of your selected system.• The assignment will test your ability to perform research into yoursystem, draw relationships between dynamics theory and real systems,make approximations, and to make realistic predictions about the motionof the system.Assignment Instructions:• Choose one of the systems suggested at the end of the assignment.• Choose at least one of the following theoretical concepts in dynamics todescribe your system/problem and its dynamic behaviors:o Work and Energy of particles or rigid bodieso Linear and/or angular momentum of particles or rigid bodieso Kinematics and/or kinetics of particles, rigid bodies or machines• You will perform research into the dynamics of your chosen system anduse the chosen theoretical concepts in dynamics to describe the approachto predicting the motion of the system.• You will develop a specific example of your system (with realisticnumbers derived from research) and use principles in dynamics to deriveequations of motion for your example. You will solve the equations ofmotion using analytical and/or numerical methods and present anddiscuss your results/predictions in relation to the expected systembehaviors uncovered through your own research.• You will write a report in which you discuss the dynamics of the chosensystem and present your example, results and discussion. Your reportmust use the following structure:o Introduction (approx. one page):Describe the system under considerationDescribe in your own words your chosen concepts indynamics used to describe the dynamic behaviors of yoursystem in general terms, and describe how these conceptscan be used to examine your chosen system.o System/Problem Example (approx. two pages):Provide an example of your system, and use this example todevelop/solve equations of motion for the systemconsidered.Your example should include realistic measurements forthe physical structure, mass, inertia, force/torque, velocity,acceleration etc. that are sourced from your research orappropriately reasoned.Draw free body diagrams of your system, detailing andrationalizing any approximations you have made, thenapply theoretical principles to develop equations of motion.o Results and Discussion (approx. two pages)Solve your equations of motion using analytical and/ornumerical methods and present results illustrating thebehavior of your systemDiscuss the system motion/behavior using your results andrelate this to the expected system behavior from yourresearch.o ReferencesProvide citations for all researched information, figures etc.o Appendix: MATLAB/Octave codeIf you use MATLAB/Octave code in this assignment, pleaseprovide it in an appendixo The main body of the report (includes the Introduction, Example,Results and Discussion) has a strict page limit of no more than fivepages. Your references and appendix are not included in the pagelimit.Submission Instructions:• You should submit a single report file (pdf or word doc format) accordingto the report format outlined above. The main body of the report shouldbe no more than five pages; the references and optional MATLAB codeappendix are not part of the five-page limit. The report should have yourname and SID clearly written at the top. You will submit this report usingTurnitin on the course’s Canvas site by Saturday 5th June 11:59pm.Assessment Criteria:• Report and Written communication (30%)o Has the problem/system been clearly described and presented?o Have the chosen theoretical concepts in dynamics been properlyexplained?o Has research on the system considered been performed andappropriate reference to external sources made (e.g. textbooks,websites, journal/conference articles etc.)? •Application of dynamics principles to your chosen problem/system(40%) o Has an appropriate theoretical model for the behavior of thesystem under consideration been developed? Have appropriateapproximations been made?o Have schematics of the system and freebody diagrams beendeveloped and clearly presented?o Are the equations/theory correctly applied to develop equations ofmotion for the system, or to evaluate specific motion cases?• Depth, detail and creativity (30%)o Has the system been considered in an appropriate level of detail?o Have numerical modeling techniques/simulation or other physicalexperiments been recorded to validate the proposed motion of thesystem detailed in the example and results?Other Important Points:• When presenting calculations and results:o Show only your relevant calculations and working, clearlyillustrated diagrams with relevant variables indicated and workingunits (use SI units unless otherwise specified)o You may submit working using either (a) typed mathematicalsymbols (LaTeX/Microsoft equations etc.) and computer-drawndiagrams or (b) handwritten working and diagrams that will bescanned or photographed for electronic submission.o Ensure scanned/photographed working is legible. If the tutorcannot read your work, you will receive zero marks for thatsection of the report.o Graphs and plots must be clearly titled, with correct use of axislabels and legends, units must be specified• Any sections of written text in the report must be in a machine-readableformat (i.e. no scanned hand written text in your report, must by typed)• When presenting MATLAB code in your appendix, comment your codethoroughly and perform important steps in the calculations on separatelines of codeSuggested SystemsSystem A: Roller Coaster Vertical Loop During a roller coaster ride, a verticalloop is a section of the track in whichthe car undergoes a complete 360oturn for which passengers are upsidedown at the top of the loop. Questionsto consider: • How are these systemsdesigned from the perspectiveof safety and fun forpassengers?• How is the track shaped andhow is the speed of the carcontrolled?• What are theaccelerations/force vectorsexperienced by passengersalong the track?System B: Dynamics of a Medieval Catapult A catapult is a ballistic deviceused to launch a projectile overlarge distances without the aid ofexplosives. Examples include theTrebuchet shown here, but youcan choose to analyse differentdesigns. Questions to consider:• Mechanically speaking,how were catapultsdesigned to transfer forcesand mechanical energy toa projectile?• How were the speed andangle for which theprojectile was launchedcontrolled and determinedbased on a desired target? System C: Collision Ball Sports: Billiards or Ten Pin Bowling Billiards (or Snooker, Pool) and TenPin Bowling are two sports thatinvolve predicting the behaviours ofrigid bodies undergoing collisions.Questions to consider:• In billiards, how is a cue-ballstruck in order to direct acoloured ball into a pocket?What role does the frictionbetween the balls and tableplay?• In ten pin bowling, how doesthe ball achieve the requiredspeed and angle to knock downas many of the pins as possible?How do the pins and ballinteract during a strike? System D: Kinematics and Forces in a Reciprocating Engine In a reciprocating engine, forcesinduced by pressure on a piston headare used to drive the rotational motionof a crank shaft. Questions to consider:• In a reciprocating engineconsisting of a piston,connecting rod and crankshaft,what is the relationshipbetween the angular and linearaccelerations and velocities?• How do these vary over theengine rotation angle, and howdo the size/length of thesecomponents effect theacceleration of the piston?• What implication does this havetowards vibration? System E: Rocket Launch into Earth Orbit A rocket that launches a spacecraftfrom the ground into an orbit aroundthe Earth provides enough velocity tothe spacecraft to achieve a steadyorbit under the influence of gravity.Questions to consider:• What are the forces that acton a rocket during a launch?• How big must a rocket be andhow much propellant must itburn to achieve a typical lowearth orbit of 400km abovethe surface of the Earth?• Why do rockets use multiple“stages”?
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