Upload
dekya-ismile
View
221
Download
0
Embed Size (px)
Citation preview
8/8/2019 S_Kuliah03 - 2 Dimension
1/27
Engineering Mechanics :STATICS
BDA1023Lecture #03
SRI YULIS BT M. AMIN
University Tun Hussein Onn Malaysia (UTHM),
Faculty of Mechanical and Manufacturing,Department of Mechanical Engineering
8/8/2019 S_Kuliah03 - 2 Dimension
2/27
8/8/2019 S_Kuliah03 - 2 Dimension
3/27
3
2D VECTOR ADDITION
Todays Objective:
Students will be able to :
a) Resolve a 2-D vector into components
b) Add 2-D vectors using Cartesian vector
notations. Learning topics:
Application of adding forces Parallelogram law Resolution of a vector using
Cartesian vector notation (CVN)Addition using CVN
8/8/2019 S_Kuliah03 - 2 Dimension
4/27
4
READING QUIZ
1. Which one of the following is a scalar quantity?A) Force B) Position C) Mass D) Velocity
2. For vector addition you have to use ______ law.
A) Newtons Second
B) the arithmetic
C) PascalsD) the parallelogram
8/8/2019 S_Kuliah03 - 2 Dimension
5/27
5
APPLICATION OF VECTOR ADDITION
There are four
concurrent cable forces
acting on the bracket.How do you determine
the resultant force
acting on the bracket ?
8/8/2019 S_Kuliah03 - 2 Dimension
6/27
6
SCALARS AND VECTORS (Section 2.1)
Scalars Vectors
Examples: mass, volume force, velocity
Characteristics: It has a magnitude It has a magnitude
(positive or negative) and direction
Addition rule: Simple arithmetic Parallelogram law
Special Notation: None Bold font, a line or
an arrow
8/8/2019 S_Kuliah03 - 2 Dimension
7/27
7
VECTOR OPERATIONS(Section 2.2)
Scalar Multiplicationand Division
8/8/2019 S_Kuliah03 - 2 Dimension
8/27
8/8/2019 S_Kuliah03 - 2 Dimension
9/27
9
RESOLUTION OF A VECTOR
Resolution of a vector is breaking up a vector into components. It
is kind of like using the parallelogram law in reverse.
8/8/2019 S_Kuliah03 - 2 Dimension
10/27
10
CARTESIAN VECTOR NOTATION (Section 2.4)
Each component of the vector is
shown as a magnitude and a
direction.
We resolve vectors intocomponents using the x and y axes
system
The directions are based on the x and y axes. We use theunit vectors iandj to designate the x and y axes.
8/8/2019 S_Kuliah03 - 2 Dimension
11/27
11
For example,
F =Fxi + Fyj or F' =F'xi - F'yj
The x and y axes are always perpendicular to each
other. Together,they can be directed at any inclination.
8/8/2019 S_Kuliah03 - 2 Dimension
12/27
12
ADDITION OF SEVERAL VECTORS
Step 1 is to resolve each force
into its components
Step 2 is to add all the x
components together and add allthe y components together. These
two totals become the resultant
vector.
Step 3 is to find the magnitude andangle of the resultant vector
8/8/2019 S_Kuliah03 - 2 Dimension
13/27
8/8/2019 S_Kuliah03 - 2 Dimension
14/27
14
You can also represent a 2-D vector with a magnitude
(Theorem Pythagoras) and angle (trigonometry).
8/8/2019 S_Kuliah03 - 2 Dimension
15/27
15
EXAMPLE
Given: Three concurrent forces
acting on a bracket.Find: The magnitude and
angle of the resultant
force.
Plan:
a) Resolve the forces in their x-y components.
b) Add the respective components to get the resultant vector.
c) Find magnitude and angle from the resultant components.
8/8/2019 S_Kuliah03 - 2 Dimension
16/27
16
EXAMPLE(continued)
F1= { 15 sin 40 i+ 15 cos 40j} kN
= { 9.642 i+ 11.49j} kN
F2 = { -(12/13)26 i + (5/13)26j} kN
= { -24 i+ 10j} kNF3 = { 36 cos 30 i 36 sin 30j} kN
= { 31.18 i 18j } kN
8/8/2019 S_Kuliah03 - 2 Dimension
17/27
17
EXAMPLE(continued)
Summing up all the i and j components respectively, we get,FR= { (9.642 24 + 31.18) i+ (11.49 + 10 18)j } kN
= { 16.82 i + 3.49j} kN
x
y
FRFR = ((16.82)2 + (3.49)2)1/2 = 17.2 kN
= tan-1(3.49/16.82) = 11.7
8/8/2019 S_Kuliah03 - 2 Dimension
18/27
18
IN CLASS TUTORIAL (GROUP PROBLEM
SOLVING)
Given: Three concurrentforces acting on a
bracket
Find: The magnitude and
angle of theresultant force.
Plan:
a) Resolve the forces in their x-y components.
b) Add the respective components to get the resultant vector.
c) Find magnitude and angle from the resultant components.
8/8/2019 S_Kuliah03 - 2 Dimension
19/27
19
F1 = { (4/5) 850 i - (3/5) 850 j } N
= { 680 i - 510 j } N
F2 = { -625 sin(30) i - 625 cos(30)j } N
= { -312.5 i - 541.3 j } N
F3 = { -750 sin(45) i + 750 cos(45) j } N
{ -530.3 i + 530.3 j } N
GROUP PROBLEM SOLVING(continued)
8/8/2019 S_Kuliah03 - 2 Dimension
20/27
20
GROUP PROBLEM SOLVING(continued)
Summing up all the i andj components respectively, we get,
FR = { (680 312.5 530.3) i + (-510 541.3 + 530.3)j }N
= { - 162.8 i - 521 j } N
FR = ((162.8)2 + (521)2) = 546 N
= tan1 (521/162.8) = 72.64 or
From Positive x axis = 180 + 72.64 = 253
y
x
FR
8/8/2019 S_Kuliah03 - 2 Dimension
21/27
21
ATTENTION QUIZ
1. Resolve Falong x and y axes and write it in
vector form. F = { ___________ } N
A) 80 cos (30) i - 80 sin (30) j
B) 80 sin (30) i + 80 cos (30) j
C) 80 sin (30) i - 80 cos (30) jD) 80 cos (30) i + 80 sin (30) j
2. Determine the magnitude of the resultant (F1 + F2)
force in N when F1 = { 10 i + 20 j } N and
F2 = { 20 i + 20 j } N .
A) 30 N B) 40 N C) 50 N
D) 60 N E) 70 N
30
xy
F = 80 N
8/8/2019 S_Kuliah03 - 2 Dimension
22/27
22
HOMEWORK TUTORIAL
Q1(2-32) :Determine the magnitude of the resultant force and its direction,
measured clockwise from the positivex axis.
Given:
F1= 70N
F2= 50N
F3= 65N
= 30
= 45
8/8/2019 S_Kuliah03 - 2 Dimension
23/27
23
HOMEWORK TUTORIAL (continued)
Q2 (2-33):
Determine the magnitude of the resultant force and its directionmeasured counterclockwise from the positivex axis.
Given:
F1 = 50N
F2 = 35N = 120
= 25
8/8/2019 S_Kuliah03 - 2 Dimension
24/27
24
HOMEWORK TUTORIAL (continued)
Q3 (2-35) :
Three forces act on the bracket. Determine the magnitude and direction ofF1 so that the resultant force is directed along the positivex' axis
and has a magnitude ofFR.
Units Used:
kN = 1000NGiven:
FR= 1kN
F2= 450N
F3= 200N
= 45
= 30
8/8/2019 S_Kuliah03 - 2 Dimension
25/27
25
HOMEWORK TUTORIAL (continued)
Q4 (2.26) :
MemberBD exerts on memberABCa force P directed along line BD.
Knowing that P must have a 960-N vertical component, determine
(a)The magnitude of the force P,
(b) its horizontal component.
8/8/2019 S_Kuliah03 - 2 Dimension
26/27
26
Q5 (2.35):
Knowing that = 35, determine the resultant and the direction ofthe three forces shown.
HOMEWORK TUTORIAL (continued)
8/8/2019 S_Kuliah03 - 2 Dimension
27/27
27
Narrated By Ibn Abbas: (The Prophet said), Healing is in three things :A gulp of honey, cupping, and branding with fire (cauterising). But I forbid
my followers to use (cauterisation) branding with fire.
Vol. 7, Book 71. Medicine
Hadith 584 (Shahi Bukhari)