APPLIED MATHEMATICS
B124 STATICS
Lecture 1
� 𝑭𝑭 = 𝟎𝟎
Course Information
• Lecturer: Dr. Prince Nchupang (pnchupang@sun.ac.za, Room 3013 Decanting building)
• Convenor: Dr. Andie de Villiers (andiedevilliers@sun.ac.za)
• Textbook: R.C. Hibbeler, Engineering Mechanics STATICS, 15th Edition in SI Units
2023
• STEMLearn
• AMB124@SUN.ac.za
• Calculators: Non-programmable
Applied Mathematics | Toegepaste Wiskunde| Ezisentyenzisiweyo Izibalo
Course Information
• Lectures: Monday, Tuesday, Thursday, Friday
• Tutorial sessions: Wednesday - 14:00 - 16:00
• Facilitated Group Learning Sessions: Tuesdays: 17:00- 19:00 (venue TBA)
• Calculation of final mark (check module framework)
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
Lectures and Tutorials
Monday
08:10-09:00
Tuesday
Wednesday
Lecture
Lecture
10:10-11:00
11:10-12:00
12:10-13:00
Consultation
Consultation
13:10-14:00
14:10-15:00
Tutorial
15:10-16:00
Tutorial (test)
Applied Mathematics | Toegepaste Wiskunde| Ezisentyenzisiweyo Izibalo
Friday
Lecture
Lecture
09:10-10:00
Thursday
Mechanics
Statics
(B124)
Rigid-bodies
Mechanics
Fluids
Dynamics
(B154)
Deformable
bodies
• Statics is the study of bodies that are at rest or move with constant velocity
Chapter one
Learning outcome
• Understand the basic quantities and idealization of mechanics.
• To state Newton’s Laws of Motion and Gravitation.
• To apply International System (SI) of Units correctly.
• Understand the standard procedures for performing numerical calculations.
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
Fundamental Concepts
Basic quantities: length, time, mass, and force
International System of Units
Quantity Length
Mass
Force
SI units
meter
kilogram
Newton* (N)
m
kg
*Derived unit
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
kg ⋅ m
s2
Newton’s Laws of Motion
Force is a push or pull of one body on another.
1st law
𝐅𝐅 = 𝟎𝟎 ⇒ 𝐚𝐚 = 𝟎𝟎
2nd law
𝐅𝐅 = 𝐦𝐦𝐦𝐦
3rd law
Newton’s Law of Gravitational Attraction
Force is a push or pull of one body on another.
Gravitational law: 𝐅𝐅 = 𝐺𝐺
𝑊𝑊 = 𝑚𝑚𝑚𝑚
𝑚𝑚1 𝑚𝑚2
𝑟𝑟 2
where
𝑔𝑔 = 𝐺𝐺𝑚𝑚2 /𝑟𝑟 2 , 𝑚𝑚 = 𝑚𝑚1
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
Fundamental Concepts
Idealizations (assumptions)
• Particle – has mass but size is negligible
• Rigid body – doesn’t deform (combination of particles)
• Concentrated force – represent the effect of loading
which is assumed to act at a point on a body
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
Fundamental Concepts
Prefixes of units
Exponential form
1 000 000 000
109
1 000 000
106
1 000
103
(1/1 000) of 0.001
10-3
(1/1 000 000) of 0.000 001
10-6
(1/1 000 000 000) of 0.000 000 001 10-9
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
Prefix
giga
mega
kilo
milli
mikro
nano
SI symbol
G
M
k
m
μ
n
Fundamental Concepts
Prefixes of units
Rules for units
Example
Products of units are notated with ⋅
m⋅s vs ms
Don’t add the prefix in the denominator (except kg)
kN/m
NOT N/mm
Mm/kg NOT m/mg
The exponential power refers to the unit and the prefix
Write numbers in terms of their base units and express
calculated result with a single prefix
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
𝜇𝜇N2 =(𝜇𝜇N)2 = 𝜇𝜇N ⋅ 𝜇𝜇N
(50 kN)(60 nm) = [50(103) N][60(10-9) m]
= 3000 (10-6) N⋅m=3(10-3) N⋅m
= 3 mN⋅m
Fundamental Concepts
Numerical Calculations
•
1
Dimensional homogeneity e.g. 𝑠𝑠 = 𝑣𝑣𝑣𝑣 + 𝑎𝑎𝑡𝑡 2
2
• Significant figures:
• Five significant figures: 23400 = 23.400(103 )
• Three significant figures: 23400 = 23.4(103 )
• Leading zeros are not significant for less than 1: 0.00823 = 8.23(10−3 )
• Rounding off numbers (use the memory of your calculator)
• Only the final answer should be rounded off
Applied Mathematics | Toegepaste Wiskunde | Ezisentyenzisiweyo Izibalo
Fundamental Concepts
Class exercise (2 minutes)
• Round off to three significant numbers
• 3.4655
• 76.334
• 0.0035476
• 56700
Fundamental Concepts
Evaluate each and express with SI-units and an appropriate prefix:
(a) (50 mN)(6 GN)
(b) (400 mm)(0.6 MN)2
(c) 45 MN3/900Gg
Useful tools (High school revision)
Right-angle triangle
Opposite
𝐎𝐎pposite
sin 𝜃𝜃 =
𝐇𝐇ypotenuse
Adjacent
SOH-CAH-TOA
𝜃𝜃
𝐀𝐀djacent
cos 𝜃𝜃 =
𝐇𝐇ypotenuse
𝐎𝐎pposite
tan 𝜃𝜃 =
𝐀𝐀djacent
Useful tools (revision)
SOH-CAH-TOA
𝑦𝑦
𝑦𝑦
𝜃𝜃
𝑐𝑐
𝑎𝑎
𝑏𝑏
𝑎𝑎
cos 𝜃𝜃 =
𝑐𝑐
𝑏𝑏
sin 𝜃𝜃 =
𝑐𝑐
𝑏𝑏
tan 𝜃𝜃 =
𝑎𝑎
𝑥𝑥
𝑝𝑝
𝜃𝜃
𝑞𝑞
𝑟𝑟
𝑝𝑝
cos 𝜃𝜃 =
𝑟𝑟
𝑞𝑞
sin 𝜃𝜃 =
𝑟𝑟
𝑝𝑝
tan 𝜃𝜃 =
𝑞𝑞
𝑥𝑥
Useful tools
Cosine law:
𝐶𝐶 =
𝐴𝐴2 + 𝐵𝐵2 − 2𝐴𝐴𝐴𝐴 cos 𝑐𝑐
Sine law:
𝐴𝐴
𝐵𝐵
𝐶𝐶
=
=
sin 𝑎𝑎 sin 𝑏𝑏 sin 𝑐𝑐
• Angles on a straight line add up to 180°
• Angles in a triangle add up to 180°
• Vertically opposite angles are equal