Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
1.A Function
Definition
Let D and R be any two sets
A function f from D to R is a mapping that assigns to
each member of D one member of R
MATHEMATICS
I
f :D R
D = domain of f
R = range of f
Let x be values in D, y be the values in R
f ( x) = y
x = in
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE 3601 Engineering Fundamentals
Mechanics Tutorial 3
Question 1
A football is kicked across a level field. The ball spends 3 seconds in the air and lands 60 m from
the point where it was kicked. (Ignore air resistance.)
What is the speed of the ball at
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE 3601 Engineering Fundamentals
Tutorial 6 Friction
Question 1
C
B
A
1000 N
D
1500 N
P
Draw free body diagram for each of the blocks C and D and determine the smallest force to start the block D
moving. Block C is restrained by a cable AB. The coefficie
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE 3601 Engineering Fundamentals
Tutorial 2 Mathematics
Solutions
Question 1
If u 3i 5 j
(i)
k and v 2i 5 j 5k , find
the magnitude of u
u 3 2 5 2 ( 1) 2 35
(ii)
a unit vector in the direction of
u
1
3
5
u
u
i
j
k
u
35
35
35
(iii) the vector ( 2u 4v )
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE 3601 Engineering Fundamentals
Tutorial 1 Mathematics
Solutions
Question 1
If f ( x) 3
2 x , find f ( 4) and f (11) .
Ans: f ( 4) 3 2( 4) 11 , f (11) 3 2(11) 19
Question 2
State the domain and range of the following functions:
(A)
f ( x) 3 x 2 2 x 1
A
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
Name:
Class:
Machines
1
A simple machine raises a load of 160 kg through a distance of 1.6 m. The
effort applied to the machine is 200 N and moves through a distance of 16m.
Determine the mechanical advantage, velocity ratio and efficiency of the
machine.
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
Solution
Machines
1
A simple machine raises a load of 160 kg through a distance of 1.6 m. The
effort applied to the machine is 200 N and moves through a distance of 16m.
Determine the mechanical advantage, velocity ratio and efficiency of the
machine.
Sol
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
71316F/L2 Engineering Fundamentals
Assignment 1 2010/2011
1. Prove that
1 + cos + sin
1
=
+ tan .
1 + cos sin cos
v
v
2. For the vectors, X = 6i + 7j  k and Y = 2i + 4j  6k, find the angle between
them.
3.
r
r
For vectors a = 2i 3j + 4k and b = i + 2j
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE 3601 Engineering Fundamentals
Assignment Mechanics
[email protected]% Total 100 marks
Question 1
Figure 1 shows a L joint ABC which is pinjointed at the support B. Two wires are attached to A
and pass over frictionless pulleys. Wire SA supports a weight of 60N a
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE3601 Assignment 2 Motion
71316F 09/10
1) Robin Hood shoots an arrow vertically upward. The arrow reaches a maximum
a)
b)
c)
d)
e)
height of 90m. Neglect air resistance and take 9.8m / s 2 .
What is the velocity of the arrow at the highest point?
What i
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
Tutorial 5
Class
Name
(
)
EEE3601
Moment
1
Find the turning moment about P in each of the following diagrams. State also
the direction of moment.
a
8 cm
3N
P
b
2N
7 cm
P
c
3m
P
7N
1
Basic Mechanics
Tutorial 5
Class
Name
(
)
EEE3601
d
P
30
8N
1.2 m
e
10 N
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
Solution
Moment
1
Find the turning moment about P in each of the following diagrams. State also
the direction of moment.
a
8 cm
3N
P
Moment = 3 x 0.08 = 0.24 Nm (clockwise)
b
2N
7 cm
P
Moment = 2 x 0.07 = 0.14 Nm (anticlockwise)
c
3m
P
7N
Moment = 7 x 3 =
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE3601 Engineering Fundamentals
Tutorial 4 Mechanics
Question 1
Find the components of the 500 N force in rectangular coordinates
y
500N
147
x
(Ans.419.3 N, 272.3 N)
Question 2
A force vector has the components 45 N and 72 N in rectangular coordinates,
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
I.A Motion
Distance
scalar quantity which refers to "how much ground
an object has covered" during its motion.
MECHANICS
I
Exercise
Start here
Displacement s
vector quantity which refers to "how far out of
place an object is"; it is the object's ch
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
2.A Scalars and vectors
Two kinds of physical quantities
Scalar quantities ():
Has magnitude only
Example: length, mass, time, density, etc
MATHEMATICS
II
Vector quantities ():
Has both magnitude and direction
Example: force, velocity, acceleration
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
III.A. Unit Vector
A vector of length 1 unit is called a unit vector
unit vector of v : v =
MATHEMATICS
III
v
v
i represents a unit vector in the direction of positive xaxis
j represents a unit vector in the direction of positive yaxis
k represents a u
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
MECHANICS
II
II.A Equilibrium
A body is in Equilibrium if it moves with constant
velocity.
A body at rest is a special case of constant velocity
i.e. v = 0 = constant.
For a body to be in equilibrium, the resultant
force (meaning the vector addition of
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
MECHANICS
V
V.A Simple Machine
What is a machine
A machine is an device by means of which a force
(effort) applied at one point can be used to overcome
another force (load) at some other point.
Examples of machines in daily life:
Scissors, pliers, leve
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
MECHANICS
III
III.A Types of Beam Supports
Simply supported on points or knife edges
A diagrammatic view of a
Simply supported beam
Pin joint supported by a roller
Force perpendicular
to surface only.
Pin Joint supported by a roller
Ry
Roller: free hor
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
Engineering
Fundamentals
FUNDAMENTALS OF SOUND
& ITS APPLICATION
Section 1:Nature of sound wave &
Section 2: Characteristics of sound
Section 1:Nature of sound wave
1.
2.
Sound is longitudinal wave
Know the terms:
Wave length
Frequency
Period
Pitch
loudne
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
MECHANICS
IV
IV.A Types of Friction
Dry Friction (Coulomb Friction)
Occurs when there is a relative motion between two
rough surfaces without any lubrication.
Fluid Friction (Viscous Friction)
Develops between layers of fluid moving at different
veloc
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE 3601 Engineering Fundamentals
Tutorial 2 Mathematics
Question 1
v
v
If u = 3i + 5 j k and v = 2i 5 j 5k , find
v
(i)
the magnitude of u
(ii)
a unit vector in the direction of u
(iii)
the vector ( 2u + 4v )
v
v
v
v
v
the vector (u 5v ) .
(iv)
Question
Hong Kong Institute of Vocational Education (Tsing Yi)
Engineering Fundamentals
ENG EEE3601

Fall 2011
EEE 3601 Engineering Fundamentals
Tutorial 1 Mathematics
Question 1
If f ( x) = 3 2 x , find f (4) and f (11) .
Question 2
State the domain and range of the following functions:
(A)
f ( x) = 3x 2 2 x + 1 ,
(B)
g ( x) =
1
x
Question 3
In rightangled trian