PC-FT-APPM121.1-1
Resources/Hulpmiddels:
Requirements for this paper/Benodighede vir hierdie vraestel:
Answer Scripts/
Antwoordskrifte:
Attendance Slips (Fill-in Paper)/
Presensiestrokies (Invulvraestel):
Scrap Paper/
Rofwerkpapier
Multi-choice cards (A5)/
Multikeusekaarte (A5)
X
Multi-choice cards (A4)/
Multikeusekaarte (A4)
Graph Paper/
GrafiekPapier
Calculators/
Sakrekenaars
Laptop (Power not provided)/
Skootrekenaar (Krag word nie voorsien nie)
X
Type of Assessment/
Tipe Assessering:
Exam Opportunity:1
Duration/
Tydsduur:
2 Hrs 00 Min
Paper Number/
Vraestel Nommer:
1
Maximum Marks/
Maksimum Punte:
100
Module Code/
Modulekode:
APPM121
Module Description/
Module Beskrywing:
STATICS AND MATHEMATICAL MODELLING
Examiner(s)/
Eksaminator(e):
Dr Sonica Froneman-PC;Dr MD
Temkan-PC;
Date/
Datum:
2019/10/31
Time/
Tyd:
14:00
Qualification/
Kwalifikasie:
BIng
Internal/Interne
Moderator(s):
External Moderator(s)/
Eksterne Moderator(s):
Prof Japie Spoelstra-PC;
Submission of answer scripts/Inhandiging van antwoordskrifte: ORDINARY
Vraag 1
Question 1
Bepaal grafies watter van die volgende twee eweredighede die beste pas by die gegewe stel data.
Determine graphically which of the following proportionalities is the best fit to the given set of data.
(a)
y ∝ x2
OF/OR
y
x
4
1
11
2
(b)
y ∝ x3
56
5
80 107
6
7
(10)
175
9
215
10
Vraag 2
Question 2
Ons stel belang in die grootte van ’n krater gevorm
deur ’n ontploffing. Bepaal ’n verwantskap tussen
die radius van die krater, r, die digtheid van die
grond, ρ, gravitasieversnelling, g, en die energie
van die plofstof, E.
We are interested in the size of a crater formed
in an explosion. Determine a relationship for the
radius of the crater, r, in terms of the density of
the soil, ρ, acceleration due to gravity, g, and the
energy of the explosive, E.
(10)
Vraag 3
Question 3
Los die volgende differensiaalvergelyking met die
gegewe aanvangsvoorwaarde op. Jy kan die antwoord in implisiete vorm los.
Solve the following differential equation together
with the boundary condition. You may leave the
answer in implicit form.
y ′ + x(y 2 + y) = 0,
y(2) = 1
(10)
Vraag 4
Question 4
Die 60 kg skyf in die skets rus op ’n ruwe hellende
vlak. Bepaal die krag P wat nodig is vir ewewig.
The 60 kg disc in the figure rests on a rough inclined plane. Determine the force P that is needed
for equilibrium.
(10)
Fig: Vraag/Question 4
Fig: Vraag/Question 5
APPM 121 Paper No. 1/Vraestel Nr. 1 — Exam 1st Opp/Eksamen 1ste Gel — Full-time/Voltyds
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Vraag 5
Question 5
Die massas en lengtes van die twee homogene balke
wat die struktuur vorm, word getoon in die skets.
Bepaal die pen-reaksies by A, B en C.
The masses and lengths of the two homogeneous
beams that make up the structure are shown in
the figure. Determine the magnitude of the pin
reactions at A, B and C.
(20)
Vraag 6
Question 6
’n 120 N gewig is vas aan die kabel wat om die 50 N
homogene drom gedraai is. Die staaf wat aan die
drom vas is word gedra deur ’n druklaer by A en
’n gly-laer by B. Die drom word in ewewig gehou
deur die vertikale krag P wat op die handvatsel
van die katrol werk. Bepaal P en die reaksiekragte
by A en B. Verwaarloos die gewigte van die staaf
en handvatsel.
A 120 N weight is attached to the cable that
is wrapped around the 50 N homogeneous drum.
The shaft attached to the drum is supported by a
thrust bearing at A and a slider bearing at B. The
drum is kept in equilibrium by the vertical force
P acting on the handle of the crank. Determine P
and the reactions at A and B. Neglect the weights
of the crank and the shaft.
(20)
Fig: Vraag/Question 7
.
Fig: Vraag/Question 6
Vraag 7
Question 7
Die silinder en die blok is verbind met ’n horisontale kabel. Bepaal die grootste koppel C wat op
die silinder uitgeoefen kan word sonder om die
ewewig van die stelsel te versteur. Neem aan beide
liggame is homogeen.
The cylinder and the block are connected by a horizontal cord. Determine the largest couple C that
can be applied to the cylinder without disturbing
the equilibrium of the system. Assume that both
bodies are homogeneous.
(20)
Totaal/Total 100
APPM 121 Paper No. 1/Vraestel Nr. 1 — Exam 1st Opp/Eksamen 1ste Gel — Full-time/Voltyds
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