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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 (P40)       CO-REQUISITE
MODULES                (P50) 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