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Lecture

# ECOR1101 - Lecture 1.pdf

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Carleton University

Engineering Common Core Courses

ECOR 1101

Jack Vandenberg

Winter

Description

Lecture 1
ECOR1101 Mechanics I
ECOR1101 –Mechanics I 1 What is Mechanics?
• Study of the state of rest or motion of bodies
when acted upon by forces
• Either the bodies or the forces can be large
ECOR1101 –Mechanics I 2 Branches of Mechanics
Mechanics
Deformable
Rigid Body Body Fluid
Statics Dynamics Compressible Incompressible
At rest or with
constant V Variable V (a)
ECOR1101 –Mechanics I 3 Fundamental Units
(Dimensions)
• Four fundamental physical quantities
(dimensions)
–Length: to locate a body in space and
measure dimension of bodies (m, inch)
–Mass: measure of a quantity of matter in a
body (kg, lb)
–Time: measure of succession of events (s)
–Force: a “push” or “pull” exerted by one
body on another (N, lbf)
ECOR1101 –Mechanics I 4 Systems of Units
• We will work with two (2) systems of units in
mechanics (statics and dynamics)
–International System (SI – Système
International d’Unités)
–US Customary (imperial units)
• Both systems have 3 base units and 1 derived
ECOR1101 –Mechanics I 5 Base and Derives Units
=m·g
=F/g
ECOR1101 –Mechanics I 6 Conversion of Units
ECOR1101 –Mechanics I 7 Dimensional Analysis
• Unit conversions are easily solved through
the process of dimensional analysis
• Facts of dimensional analysis
–Conversion factor is a statement of equal
relations
–Conversion factor in ratio form = 1
–Units cancel out like variables
ECOR1101 –Mechanics I 8 Dimensional Homogeneity
• The terms of all equations must be
dimensionally homogeneous.
–Dimension of LHS = Dimension of RHS
• Consider the kinematic equation:
v v at
f i
m m m
2 s
s s s
ECOR1101 –Mechanics I 9 Models and Idealizations
• Models and idealizations are often used in
mechanics to simplify problems
• Particle: has mass but negligible size. For
example, the earth can be considered a particle
with negligible size when viewed with respect to
its orbit or other celestial bodies
• Rigid body: A rigid body can be considered as a
collection of particles but all particles remain
fixed with respect to one another under load
• Concentrated force: when the area of load
application is small with respect to the size of the
body
ECOR1101 –Mechanics I 10 Newton’s Laws of Motion
• Engineering mechanics is formulated on
Newton’s Laws of Motion
–The laws were postulated based on
experimental observation
–The laws apply to the motion of a particle
with reference to a non-accelerating
reference frame
ECOR1101 –Mechanics I 11 Newton’s Laws of Motion
st
• 1 Law: A particle at rest or in motion will
continue in its state of rest or motion unless
acted upon by an unbalanced system of
forces
ECOR1101 –Mechanics I 12 Newton’s Laws of Motion
• 2ndLaw: A particle of mass (m) acted upon
by an unbalanced system of forces (F)
experiences an acceleration (a) in the same
direction as the force and with a magnitude
proportional to the force.
F =m ·a
ECOR1101 –Mechanics I 13 Newton’s Laws of Motion
rd
• 3 Law: For every action, there is an equal
and opposite reaction.
ECOR1101 –Mechanics I 14 Newton’s Law of
Gravitational Attraction
• States that two bodies ar

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