STELLENBOSCH UNIVERSITY
FACULTY OF ENGINEERING
STUDY GUIDE
1. MODULE DATA 2006
MODULE CODE
MODULE
20753
YEAR
APPLIED MATHEMATICS B154
(Dynamics)
1
SEMESTER
US CREDITS
LECTURING LOAD
PER WEEK :
1
15
HOME DEPARTMENT
Applied Mathematics
4, 0p, 2t, 0s
LECTURERS
OFFICE NUMBER(S)
P.H. Crous
G.J.F.Smit
K. Hunter
A415
A411
A312
Basic
Science
Mathematics
PREREQUISITE
MODULES
PREREQUISITE PASS
PREREQUISITE (P40)
(P50) 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
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.
 Solve problems with simple harmonic motion.
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. 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
11.
3.9; 8.1-8.2
12.
8.2
Impulse and Momentum.
Impulse and Momentum; Simple Harmonic Motion
Simple Harmonic Motion
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.