STELLENBOSCH UNIVERSITY FACULTY OF ENGINEERING STUDY GUIDE 1. MODULE DATA 2008 MODULE CODE MODULE US CREDITS 20753 APPLIED MATHEMATICS B154 15 (Dynamics) YEAR 1 LECTURING LOAD HOME DEPARTMENT PER WEEK : SEMESTER 1 Applied Mathematics 4, 0p, 2t, 0s LECTURERS OFFICE NUMBER(S) TELEPHONE NO(S) P.H. Crous A415 808-4227 K. Hunter A312 808-4218 M. Cloete A504 808-4212 CLASSIFICA- Mathematics Basic Engineering Design & Computing Complemen- TION OF Science Science Synthesis & IT tary Studies KNOWLEDGE AREAS 20% 50% 30% 0% 0% 0% PREREQUISITE PREREQUISITE PASS PREREQUISITE (P40) CO-REQUISITE MODULES (P50) None Engineering Maths 115, None Applied Mathematics B124 ASSESSMENT METHOD CLASS MARK FINAL MARK DETAILS CALCULATION FORMULA Exam See Yearbook Parts 1 Sept test: 70% P = 0.4K + 0.6E and 11 for Tutorial tests: 30% regulations 2. SPECIFIC OUTCOMES AND ASSESSMENT CRITERIA CAPABILITIES (These are the objectives of the module) A student who completes this model will be able to: Define the basic principles of kinematics and particle dynamics Build mathematical models i.e. translate problems in words to symbols, equations and drawings. Analyse mechanical systems by applying Newton's Second Law, the Principle of Work and Energy, Energy conservation, Conservation of Momentum and the Impulse-Momentum Principle. Solve problems with simple harmonic motion. FOR PERFORMANCES ASSESSMENT CRITERIA RANGE STATEMENTS (This is the type of question a student can (The examiners will give credit if the student (These statements describe the nature and expect in the exams and tests. More than successfully performs the following tasks) complexity of the required performance) one of these performances can be expected in a single exam or test question). Define basic concepts, ex. Give a clear explanation of the Be confident with the defi- Statics, dynamics, force, required concept. nitions of a variety of basic displacement, etc. principles in dynamics. A particle moves along a Differentiate and integrate the Have knowledge of straight line according to a given equation using the initial differentiation and given equation v = f(t). Find conditions. Calculate the integration. the position, velocity, dis- required quantities. tance travelled, acceleration and average velocity after a given number of seconds. The v-t graph of a particle Find the equations of the Have knowledge of moving between two points velocity over different time differentiation and is given. Find the s-t and a-t intervals. Differentiate and integration and the drawing graphs for the same time integrate the velocities to find of the applicable graphs. interval. the equations of the required graphs. Draw neat graphs with all the necessary intercepts. A particle is moving along a Find the time for the particle to Have knowledge of circular path at an accele- travel the required distance. differentiation and integra- ration a(t). Find the magni- Calculate the normal and tion and the relationship tude of the acceleration at a tangential components of the between velocity, given point on the path. acceleration at the given point. acceleration and position. The position of a particle is Differentiate the given equations Have knowledge of given by the relationship r = correctly and substitute in the differentiation and the usage f1(t) and =f2(t). Find the appropriate velocity and of velocity and acceleration velocity and acceleration of acceleration equations. equations in polar the particle after a few coordinates. seconds. FOR PERFORMANCES ASSESSMENT CRITERIA RANGE STATEMENTS Apply Newton's 2nd Law to Isolate different sections of the Be able to identify the different systems eg. given system, write down all the different forces and their projectile motion, circular necessary equations in two accelerations. Knowledge of motion, inclined planes, mutually perpendicular integration, differentiation pulley systems, springs, etc. directions and solve. and application of Newton II. Apply the Principle of Work Find all the forces which do Have knowledge of positive and Energy to the above work. Determine the work done and negative work. systems . by each force and apply the Have knowledge of the principle of work and energy. application of the work- energy principle. Apply the Impulse- Find the impulse of the relevant Be confident with the Momentum Principle to forces and their change in impulse-momentum above systems. momentum. principle and its application. Apply the principle of Identify conservative forces and Be confident with the conservation of energy to apply the principle. concepts of conservative conservative systems. systems. 3. CONTENTS OF THE MODULE AND SCHEDULE REFERENCE : J.L. Meriam & L.G. Kraige, Engineering Mechanics DYNAMICS, 5'th ed. SI, John Wiley, 2002. WEEK Reference SUBJECT 1. 2.1-2.2 Kinematics: relationships between velocity, position and acceleration. Graphical representation of velocity, acceleration, etc. 2. 2.3-2.4 Curvilinear motion; Projectile motion. 3. 2.5-2.6 Normal and tangential components; Polar coordinates 4. 2.6-2.7 Polar coordinates; Cylindrical coordinates; Dependent motions. 5. 2.8-2.9 Relative motion, dependent motion (ex. pulleys)) 6. 3.1-3.4 Kinetics of particles: Newton's laws; Equations of motion. TEST WEEK VACATION 7. 3.1-3.5 Normal and tangential components; Polar coordinates. 8. 3.6 Work done by a force; Work Energy Principle. 9. 3.7 Power; Conservative forces; Potential Energy; Conservation of Energy. 10. 3.8-3.9; 8.1-8.2 Impulse and Momentum; Simple Harmonic Motion 11. 3.10; 4.1-4.2 Angular impuls and angular momentum; Kinetics op systems 12. 4.3-4.5 Kinetics of systems 4. TESTS AND EXAMS (a) There will be a short test at the end of each tutorial. This test will cover the work done during the preceding week and the tutorial. (b) The semester test takes place during the test week at the end of the third term (7th week). This test is compulsory. (c) There is one optional test (valskermtest) during the 4th term. This test is especially for those students who at that stage do not have an average mark of 40% for admission to the exam. The average of the optional test and the testweek test will be used in calculating the classmark. (d) All tests will contribute towards the classmark. (e) The examination will consist of a 3 hour paper which will cover all the work done in the course. (f) Non-programmable calculators – as prescribed for the first semester – may be used in tests and examinations. (g) Tests and examinations will be of the closed book format. 5. TUTORIALS (a) Every week students will receive a set of problems during the tutorial. These problems are based on the work done in the class during the preceding week. (b) Students will get approximately 2 hours to work on these problems. The lecturer and 2 student assistants will be present to answer questions. (c) At the end of the tutorial a short test on a similar problem will be given. (d) The solution of the tutorial test and most of the tutorial problems will be handed out at the end of the tutorial. (e) Attendance at all tutorials is compulsory –also for students repeating the subject. Leave of absence will only be granted on the presentation of a medical certificate or written permission from the Registrar. (f) The textbook, class notes and a pocket calculator should always be brougt to the tutorial. 6. GENERAL STUDY HINTS (a) Do regular revision of the work done during the lectures. Homework problems will be given on a regular basis. Although these problems are not examined, it is in the students interest to do and understand these problems. If you do not understand the work, do not hesistate to contact your lecturer. (b) Do not fall behind. Each week the work builds on that of the previous week. PEOPLE REPEATING THE COURSE Students repeating the subject and who have timetable clashes, should contact their lecturer. All students repeating the subject are compelled to write the weekly tutorialtest. PREREQUISITES The following two prerequisites (PP 40 ) are applicable: Engineering Mathematics 115 and Applied Mathematics B124.