Transcript Lecture Outline - Mechanical and Industrial Engineering

Statics & Dynamics
University of Ontario
Institute of Technology
ENGR 2020
Lecture Outline
• Introductory details
• Fundamentals
• Definitions
• Solution Style and Technique
• Vectors
Contact Details
• Dr. Jean-Claude (John) Stranart
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416-738-4403 (emergency or occasional evening)
[email protected] [email protected]
Subject: UOIT: xxxxx
Web site / Web CT
fax: 416-978-5741
Dr. Jean-Claude (John) Stranart
• Background
• Ph.D. University of Toronto
• M.A.Sc. University of Toronto
• B.A.Sc. Waterloo
• Research in mechanics, finite elements,
fatigue/fracture, smart structures
Subject Matter/Overview
• Statics
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Equilibrium of a Particle
Force System Resultants
Equilibrium of a Rigid Body
Structural Analysis
Centre of Gravity/Centroid
Friction
Subject Matter/Overview
• Dynamics
• Kinematics of a Particle
• Kinetics of a Particle
• Force, Acceleration
• Work, Energy
• Impulse, Momentum
• Kinematics of a Rigid Body
• Kinetics of a Rigid Body
• Force, Acceleration
• Work, Energy
• Impulse, Momentum
Textbook
• Engineering Mechanics: Statics and Dynamics
• R.C. Hibbler, 10th Edition
• Work book/Study Pack
Lectures
• 9:10 –11:00 Wednesday & Friday
• Room UA 1240
• 10 minute break ~ 10:00
• Available for questions after class
• If something is not clear, bring it up, don’t wait
• Room change on May 13 (only)
– UA 1120 or UA 1140
Tutorial
• Wednesday
• 12 – 2 pm
• Room UA 2120
• Is everyone available ? (Midterms)
Office Hours
• UA 3045
• To be determined
Marks/grading
• Problem Sets (5)
• Project
25%
5%
– 10-15 hours, details to follow
• Midterm Test 1
10%
– June 1
• Midterm Test 2
20%
– July 6
• Final Exam
40%
Problem Sets
• Due at the beginning of class on:
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May 20
June 3
June 17
July 8
July 22
• Assigned from Hibbler
• ~ 20 questions, ONLY 2 marked
• Est. 6 hours/set
Students
• What is your background?
• Why are you taking the course?
• What do see as the biggest challenges?
• What is your learning style?
• What software do you know ?
• Excel, MatLab, MathCad, Maple
Fundamentals
• Mechanics
• Rigid-body mechanics, deformable-body
mechanics, fluid mechanics
• Rigid body mechanics
• Statics – equilibrium of bodies
• ie at rest or constant velocity
• Dynamics
• Accelerated motion of bodies
• Include turning, curving,
Fundamentals
• Basic quantities
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Length
Time
Mass
Force
• SI
• length [m], time [s], mass [kg]
• force is derived [N = kg m s-2 ]
• US customary
• length [ft], time [s], force [lb, lbf]
• mass is derived [m=W/g, 32.2 lb/ 32.2 ft/s2 = 1.0 slug]
Fundamentals
Name
Length
Time
Mass
Force
SI
meter
[m]
second
[s]
kilogram
[kg]
newton
[N]
 kg  m 
 s 2 
US
foot
[ft]
second
[s]
slug
 lb  s 2 


 ft 
pound
[lb, lbf]
Fundamentals
• Idealisations
• Particle: has mass but size can be neglected
• simplifies analysis
• ie earth w.r.t. its orbit
• Rigid body
• Application of load does not change geometry of the
body
• Concentrated force
• Loading is assumed to act on a point
• Area over which load is applied is small w.r.t. size of
body
Newton’s Three Laws of Motion
• Basis of rigid body mechanics
• Assumes non-accelerating frame of reference
• 1) a particle at rest, or moving in a straight
line with constant velocity, will remain in that
state provided the particle is not subjected to
an unbalanced force
Newton’s Three Laws of Motion
• 2) a particle subjected to an unbalanced
experiences an acceleration that has the
same direction as the force and a magnitude
that is proportional to the force*


F  ma
 d  d

F  p  mv 
dt
dt
Newton’s Three Laws of Motion
• 3) for every force acting on a particle, the
particle exerts an equal, opposite and colinear
reaction
Analysis Procedure
• Read problem carefully and relate the physical
situation to the applicable theory
• Draw necessary diagrams, tabulate problem
data
• Apply the relevant principles(mathematical
expression)
• Solve the equations
• Check unit consistency
• Check significant digits
Analysis Procedure (continued)
• Evaluate the answer
• Judgement, common sense
• Is it reasonable
• Can the solution be validated by another
method?
Solution Style
• Two aspects to any engineering solution
• Technical solution that is correct
• Communication of the solution to others
• As essential as technical accuracy
• Solution must be clearly presented and able to be
followed
Solution Style
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Statement of the problem
Free body diagram
Assumptions, relevant principles
Applicable equations
Solution
Concluding statement
• Boxed/highlighted
Free Body Diagram
• Sketch of the particle/body/system isolated
from the surrounding system
• ALL forces which the surroundings exert on
the particle/body/system are sketched on the
body
Free Body Diagram: Procedure
1) Draw/sketch the particle isolated from its
surrounding
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Include co-ordinate axes
2) Indicate ALL forces that act on the body
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Active/applied forces – ie loads, weight,
magnetic, electrostatic
Reactive forces – constraints, supports
3) Known forces are labeled with magnitudes
and directions
Free Body Diagram: Procedure
4) Unknown forces represented by letters and
arrows (assumed direction)
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In solution, if ‘negative’ force is obtained, minus
sign indicates that the force is in the opposite
direction of that originally assumed
Examples