MA3002 Solid Mechanics and Vibration, Part 1: Solid Mechanics
Solution to Tutorial 6
(Fracture mechanics of ductile materials)
Q6.1 A sheet of aluminium alloy of length L = 300 mm, width W = 100 mm and thickness
B = 10 mm has a central through-thickness c
MA3002 Solid Mechanics and Vibration, Part 1: Solid Mechanics
Solution to Tutorial 7
(Fatigue)
Q7.1 A shaft of circular cross-section is subjected to a steady bending moment of 1500 Nm
and simultaneously to an alternating bending moment of 1000 Nm in the
2015 PH1012 Tut 5: More about Forces, Impulse and Momentum
1. [A J86/II/8] When a body moves through a fluid, a retarding force due to turbulence may
be experienced. In the case of a sphere of radius moving with speed through a stationary
fluid of density
2015 PH1012 Tut 3: Newtons Laws 1 and 2D Kinematics
Part 1
1. [G4.24] The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. What
maximum upward acceleration can it give the elevator without breaking?
2. [G4.36] A train locomotive is
2015 PH1012 Tut 1: Basics / Thermal Physics / Archimedes Principle
1. Giancoli P13.7 How The Earth is not a uniform sphere, but has regions of varying density. Consider a
simple model of the Earth divided into three regionsinner core, outer core, and mant
2015 PH1012 Tut 2: Thermal Physics / 1D Kinematics
Part 1
1. Giancoli P17.9 Super Invar, an alloy of iron and nickel, is a strong material with a very low
coefficient of thermal expansion (0.20 106 /C). A 1.6-m-long tabletop made of this alloy is
used for
2015S1 PH1012: Physics A
Propulsion
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Week 5 & 6
"Heavier than air flying machines are impossible."
Lord William Thomson Kelvin (1824-1907)
"I think ther
2015S1 PH1012: Physics A
Vectors and 2D Kinematics
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Week 3
Giancoli Chap 3.1 3.9
"The secret of success is to know something nobody else knows."
- Arist
2015S1 PH1012: Physics A
More about forces
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Week 4
Giancoli Chap 5.1, 5.6, 14.1
"Sometimes it is not enough that we do our best; we must do what is requ
2015 PH1012 Tut 4: Motion and Dynamics in 2D
Part 1
1. [G3.61] A child, who is 45 m from the bank of a river, is being carried helplessly downstream by the
rivers swift current of 1.0 m/s. As the child passes a lifeguard on the rivers bank, the lifeguard
PH1012 Tut 6: Propulsion, Equilibrium, Work Done and Energy
1. [A level, J96] (a) A toy rocket consists of a plastic bottle which is partially filled with water. The
space above the water contains compressed air, as shown below. At one instant during the
MH1810 Math 1 Part 1 Algebra
Tang Wee Kee
Nanyang Technological University
(Nanyang Technological University)
Complex Numbers
1 / 66
Imaginary number
Does the quadratic equation x 2 + 1 = 0 have a real root? That is, are
there real numbers x at which x 2
MH1810 Math 1 Part 3 Dierentiation
Tang Wee Kee
Nanyang Technological University
(Nanyang Technological University)
Dierentiation Rules
1 / 29
Dierentiability and Continuity
Theorem
If a function f is dierentiable at x = c then f is continuous at x = c.
P
MH1810 Math 1 Part 3 Dierentiation
Tang Wee Kee
Nanyang Technological University
(Nanyang Technological University)
Derivatives
1 / 35
Tangent
Consider a curve and a xed point P on a curve. What is a tangent to a
curve at a point?
(Nanyang Technological U
MH1810 Math 1 Part 1 Algebra
Tang Wee Kee
Nanyang Technological University
(Nanyang Technological University)
Complex Numbers
1 / 27
Intuitive Idea of a Limit
Example (Intuitive Idea)
Let f (x ) = x 2 . What happens to f (x ) for values of x near 2?
(a) U
Nanyang Technological University
SPMS/Division of Mathematical Sciences
2015/16 Semester 1
MH1810 Mathematics I
Tutorial 2
Reading: Lecture slides on Vectors & ThomasCalculus: Chapter 12 (Sections 12.1 -12.5).
1. Let u = i + j
5k and v = 2i + j
Find kuk,
2015S1 PH1012: Physics A
1D Kinematics
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Weeks 2 and 3
"The man who does not read good books has no advantage over the man who cannot read
them."
- Mark
2015S1 PH1012: Physics A
Basics and Fluids
Dr Ho Shen Yong
Lecturer, School of Physical and Mathematical Sciences
Nanyang Technological University
Weeks 1 and 2
Giancoli Chap 13.1 13.7
"The true sign of intelligence is not knowledge but imagination."
- Al
MA2009: Introduction to Electrical Circuit
& Electronic Devices Part II
Logic Function & Algebra
Zhou Yufeng (Assist. Prof.)
Email: yfzhou@ntu.edu.sg, Office: N3.2-01-25
1
Review
1. I-V characteristics of MOSFET
2. CMOS as a switch
3. FET gates
NOT
NOR
NA
MA2009: Introduction to Electrical Circuit
& Electronic Devices Part II
BJT and Amplification
Zhou Yufeng (Assist. Prof.)
Email: yfzhou@ntu.edu.sg, Office: N3.2-01-25
1
Review of Diode
Three types of diodes:
Ideal diode
Offset diode
Zener diode
Two typ
MA2009: Introduction to Electrical Circuit
& Electronic Devices Part II
FET and Logic Gate
Zhou Yufeng (Assist. Prof.)
Email: yfzhou@ntu.edu.sg, Office: N3.2-01-25
1
Review
1. Active filters using OpAmps
Low pass filter (LPF)
High pass filter (HPF)
Band p
MA2009: Introduction to Electrical Circuit
& Electronic Devices Part II
Operational Amplifier
Zhou Yufeng (Assist. Prof.)
Email: yfzhou@ntu.edu.sg, Office: N3.2-01-25
1
Review
1. BJT working regions
2. BJT in active region
VBE = V
IC = IB
IE = IB + IC = (
MA2009: Introduction to Electrical Circuit
& Electronic Devices Part II
Applications of Op-Amp
Zhou Yufeng (Assist. Prof.)
Email: yfzhou@ntu.edu.sg, Office: N3.2-01-25
1
Review
For negative feedback ideal Op-Amp
Inverting
Noninverting
2
Applications of Op
PH1012 Tut 9: Electric Potentials, Current of electricity and Circuits
1. [S25.8] Two spherical conductors of radii r1 and r2 are separated by a distance much greater
than the radius of either sphere. The spheres are connected by a conducting wire. When
t
2014 PH1012 Tut 1: Basics / Thermal Physics / Archimedes Principle
1. Giancoli P13.7 How The Earth is not a uniform sphere, but has regions of varying density. Consider
a simple model of the Earth divided into three regionsinner core, outer core, and mant
PH1012 Tut 11 (B): Equilibrium
1. [G12.4] A tower crane must always be carefully balanced so
that there is no net torque tending to tip it. A particular crane
at a building site is about to lift a 2800-kg air-conditioning
unit. The cranes dimensions are s
Qn
1
Part
ai.
aii.
aiii.
aiv.
Answer
Car A: (0 + 0 ) 2
Car B: (0 + 2 ) 2
(4 + 3 )
3.25
When there is collision, two objects must be at the same space at the same time.
(Two linear non-parallel lines can only meet in space at only 1 position.)
1
4
The pa