MECHANICS, UNITS, NUMERICAL CALCULATIONS &
GENERAL PROCEDURE FOR ANALYSIS
Today’s Objectives:
Students will be able to:
In-Class activities:
a) Explain mechanics / statics.
• Reading Quiz
b) Work with two types of units.
c) Round the final answer appropriately. • What is Mechanics
• System of Units
d) Apply problem-solving strategies.
• Numerical Calculations
• Concept Quiz
• Problem-Solving Strategy
• Attention Quiz
Some Important Points
• Studio course (combined lesson & problem
session)
• Sessions do not require laptops
• Important tools: syllabus, textbook (listed in syllabus),
pencil and paper, Web site of course
• Website: http://lms.rpi.edu/
• http://www.rpi.edu/dept/coreeng/WWW/IEA for back exams
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Course format
• Mini lectures
• In class activities
• 3 mid term exams: 50% *
* Highest exam will be worth 20%
* The other two exam will each be worth 15 %
• 1 final exam: 25%
• Assigned problems:
HW: 20%
CA: 5%
Mobile Devices: not permitted
• All mobile devices (cell/smart phones,
computers, pagers, etc.) must be stored
securely away during lectures and not
used.
• Use of (or ANY interaction with) a
mobile device during an exam will be
interpreted as the illicit transfer of exam
data, will be considered an act of
cheating and will be treated as such.
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WHAT IS MECHANICS?
Study of what happens to a “thing” (the technical name is
“BODY”) when FORCES are applied to it.
Either the body or the forces can be large or small.
BRANCHES OF MECHANICS
Mechanics
Rigid Bodies
(Things that do not change shape)
Statics
Dynamics
Deformable Bodies
(Things that do change shape)
Fluids
Incompressible
Compressible
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UNITS OF MEASUREMENT
(Section 1.3)
Four fundamental physical quantities (or dimensions).
• Length
• Mass
• Time
• Force
Newton’s 2nd Law relates them: F = m * a
We use this equation to develop systems of units.
Units are arbitrary names we give to the physical quantities.
UNIT SYSTEMS
Force, mass, time and acceleration are related by Newton’s
2nd law. Three of these are assigned units (called base units)
and the fourth unit is derived. Which one is derived varies by
the system of units.
We will work with two unit systems in statics:
• International System (SI)
• U.S. Customary (USCS)
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Table 1-1 in the textbook summarizes these unit systems.
COMMON CONVERSION FACTORS
Work problems in the units given unless otherwise instructed!
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THE INTERNATIONAL SYSTEM OF UNITS
(Section 1.4)
• No plurals (e.g., m = 5 kg, not kgs )
• Separate units with a •
(e.g., meter second = m • s )
• Most symbols are in lowercase.
• Some exceptions are N, Pa, M and G.
• Exponential powers apply to units, e.g., cm • cm = cm2
• Compound prefixes should not be used.
• Table 1-3 in the textbook shows prefixes used in the SI
system
NUMERICAL CALCULATIONS
(Section 1.5)
Must have dimensional “homogeneity.” Dimensions have to
be the same on both sides of the equal sign, (e.g. distance =
speed × time.)
Use an appropriate number of significant figures (3 for
answer, at least 4 for intermediate calculations). Why?
Be consistent when rounding off.
- greater than 5, round up (3528  3530)
- smaller than 5, round down (0.03521  0.0352)
- equal to 5, see your textbook for an explanation.
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PROBLEM SOLVING STRATEGY
IPE: A 3 Step Approach
1. Interpret: Read carefully and determine what is given and
what is to be found/ delivered. Ask, if not clear. If
necessary, make assumptions and indicate them.
2. Plan:
Think about major steps (or a road map) that you will
take to solve a given problem. Think of
alternative/creative solutions and choose the best one.
3. Execute: Carry out your steps. Use appropriate diagrams and
equations. Estimate your answers. Avoid simple
calculation mistakes. Reflect on and then revise
your work, if necessary.
Scalar and vectors
• A scalar quantity is completely described
by a magnitude (number).
-Examples: mass, density, length, speed, time,
temperature.
• A vector quantity has a magnitude and
direction and obeys the parallelogram law
of addition.
-Examples: force, moment, velocity, acceleration.
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Vector
Terminal point
Β
Α
Initial point
Direction of arrow
direction of vector
Length of arrow
magnitude of vector
The sum of two vectors –
geometrical representation
• Two vectors can be added vectorially using
the parallelogram law.
F1
R
F2
•Position vector F1 so that its initial point
coincides with the initial point of F2. The
vector F1+F2 is represented by the vector R.
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Vectors in rectangular coordinate
systems- two dimensional
y
(v1,v2)
V
x
(v1,v2) are the terminal points of vector V
V = v1 i + v2 j
The sum of two vectors – analytic
representation (two dimensional )
y
v2
(v1+w1,v2+w2)
(w1,w2)
w
w2
v
v1
(v1,v2)
w1
x
v + w = (v1 + w1, v2 + w2)
v + w = (v1 + w1 )i + (v2 + w2 ) j
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The sum of two vectors – rectangular
components (Three dimensional )
z
(a1,a2,a3)
a
y
b
(b1,b2,b3)
x
a + b = (a1 + b1, a2 + b2, a3 + b3)
a + b = (a1 + b1 )i + (a2 + b2 ) j + (a3 + b3 ) k
Vectors with initial point not at the
origin
z
P1(x1 ,y1 ,z1)
P2(x2 ,y2 ,z2)
w
v
y
x
w + P1P2 = v
P1P2 = v – w
= (x2i + y2j + z2k) – (x1i + y1j+ z1k)
= (x2-x1) i + (y2-y1) j + (z2-z1) k
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Example
Find the components of the vector having
initial point P1 and terminal point P2
P1(-1,0,2), P2(0,-1,0)
Solution:
V = (0 + 1, -1 - 0, 0 - 2) = (1,-1,-2)
READING QUIZ
1. The subject of mechanics deals with what happens to a body
when ______ is / are applied to it.
A) a magnetic field
B) heat
D) neutrons
E) lasers
C) forces
2. ________________ still remains the basis of most of today’s
engineering sciences.
A) Newtonian Mechanics
B) Relativistic Mechanics
C) Greek Mechanics
C) Euclidean Mechanics
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Class Assignment
Find the components of the vector having
initial point P1 and terminal point P2
P1(3, -2, 5), P2(-1, -3, 8)
ENGR-110 (IEA)
Fall-2015
CA 1 Solution
Find the components of the vector having initial point P1 and
terminal point P2:
P1 (3, -2, 5), P2 (-1, -3, 8)
P1P2 = (-1, -3, 8) - (3, -2, 5)
= (-4, -1, 3)
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