STELLENBOSCH UNIVERSITY FACULTY OF ENGINEERING STUDY GUIDE 1. MODULE DATA 2005 MODULE CODE MODULE 20753 YEAR APPLIED MATHEMATICS B154 (Dynamics) 1 SEMESTER US CREDITS 1 LECTURING LOAD PER WEEK : 16 HOME DEPARTMENT Applied Mathematics 4, 0p, 2t, 0s LECTURERS OFFICE NUMBER(S) P.H. Crous G.J.F.Smit K. Hunter W.Grundlingh A415 A411 A312 A314 Basic Science Mathematics PREREQUISITE MODULES PREREQUISITE PASS PREREQUISITE (P40) (P50) None Engineering Maths 115, Applied Mathematics B124 ASSESSMENT DETAILS METHOD CLASS MARK CALCULATION Sept test: 70% Tutorial tests: 30% 20% Exam 50% Engineering Science 808-4227 808-4219 808-4218 808-4220 CLASSIFICATION OF KNOWLEDGE AREAS See Yearbook Parts 1 and 11 for regulations TELEPHONE NO(S) 30% Design & Synthesis 0% Computing & IT Complementary Studies 0% 0% CO-REQUISITE None FINAL MARK FORMULA P = 0.4K+0.6E 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. FOR PERFORMANCES ASSESSMENT CRITERIA RANGE STATEMENTS (This is the type of question a student can expect in the exams and tests. More than one of these performances can be expected in a single exam or test question). (The examiners will give credit if the student successfully performs the following tasks) (These statements describe the nature and complexity of the required performance) Define basic concepts, ex. Statics, dynamics, force, displacement, etc. Give a clear explanation of the required concept. Be confident with the definitions of a variety of basic principles in dynamics. A particle moves along a straight line according to a given equation v = f(t). Find the position, velocity, distance travelled, acceleration and average velocity after a given number of seconds. Differentiate and integrate the given equation using the initial conditions. Calculate the required quantities. Have knowledge of differentiation and integration. The v-t graph of a particle moving between two points is given. Find the s-t and a-t graphs for the same time interval. Find the equations of the velocity over different time intervals. Differentiate and integrate the velocities to find the equations of the required graphs. Draw neat graphs with all the necessary intercepts. Have knowledge of differentiation and integration and the drawing of the applicable graphs. A particle is moving along a circular path at an acceleration a(t). Find the magnitude of the acceleration at a given point on the path. Find the time for the particle to travel the required distance. Calculate the normal and tangential components of the acceleration at the given point. Have knowledge of differentiation and integration and the relationship between velocity, acceleration and position. The position of a particle is given by the relationship r = f1(t) and =f2(t). Find the velocity and acceleration of the particle after a few seconds. Differentiate the given equations correctly and substitute in the appropriate velocity and acceleration equations. Have knowledge of differentiation and the usage of velocity and acceleration equations in polar coordinates. FOR PERFORMANCES ASSESSMENT CRITERIA RANGE STATEMENTS Apply Newton's 2nd Law to different systems eg. projectile motion, circular motion, inclined planes, pulley systems, springs, etc. Isolate different sections of the given system, write down all the necessary equations in two mutually perpendicular directions and solve. Be able to identify the different forces and their accelerations. Knowledge of integration, differentiation and application of Newton II. Apply the Principle of Work Find all the forces which do and Energy to the above work. Determine the work done systems . by each force and apply the principle of work and energy. Have knowledge of positive and negative work. Have knowledge of the application of the workenergy principle. Apply the ImpulseMomentum Principle to above systems. Find the impulse of the relevant forces and their change in momentum. Be confident with the impulse-momentum principle and its application. Apply the principle of conservation of energy to conservative systems. Identify conservative forces and apply the principle. Be confident with the concepts of conservative 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 1. Reference 2.1-2.2 SUBJECT Kinematics: relationships between velocity, position and acceleration. Grpahical 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 Equations of motion; Normal and tangential components. 8. 3.5 Normal and tangential components, Polar coordinates. 9. 3.6 Work done by a force; Work Energy Principle. 10. 3.7 Power; Conservative forces; Potential Energy; Conservation of Energy. 11. 3.8-3.9 12. 3.10 Angular Momentum. 13. 4.1- Kinetics of systems of particles. Impulse and Momentum. 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.