Transcript ME 221 Statics

ME 221 Statics
Summer 2004
Mr. Hinds
3523 EB
[email protected]
Administrative Details
• Syllabus will be posted on the web
– www.angel.msu.edu (Angel)
• Lecture attendance
– Web will be used for announcements but not all
important announcements given in class may be posted
on the web
– Bring books to class for example problems
• Sample problems will be an integral part of lecture
ME221
Lecture 1
2
Administrative Details cont.
• Exams
– Dates set and given on syllabus
– Format
• closed book, closed notes, calculator
– Excused absences: See syllabus
– Philosophy
• Most problems like HW; some problems conceptually
same as HW but somewhat different
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Lecture 1
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Administrative Details cont.
• Homework & quizzes
– solutions will be posted
– all or partial problems will be graded
– lecture quizzes used as “scrimmages”
• quizzes in the last 10-15 minutes of lecture
• similar to assigned homework
• generally announced - some unannounced
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Announcements
• HW#1 Due on Friday, May 21
Chapter 1 - 1.1, 1.3, 1.4, 1.6, 1.7
Chapter 2 – 2.1, 2.2, 2.11, 2.15, 2.21
• Quiz #1 on Friday, May 21
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Announcements
• ME221 TA’s and Help Sessions
• Chad Stimson – [email protected]
• Homework grading & help room
• Tuesdays & Thursdays – 8am to 1pm – 1522EB
• Jimmy Issa – [email protected]
• Quiz & exam grading & help room
• Tuesdays & Thursdays – 1pm to 5pm – 2415EB
• Will begin on Tuesday, May 18
• Hours also posted on Angel
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Administrative Details cont.
Questions??
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Problem Solving Strategy
1 - Modeling of physical problem (free body diagram)
2 - Expressing the governing physical laws in
mathematical form
3 - Solving the governing equations
4 - Interpretation of the results
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Mechanics Reform
• Textbook offers a departure from past standards
– recognizes the power of computer software in solving
problems
• MatLab, MathCAD, Maple, Mathmatica, VB, etc.
• calculators may be effectively utilized as well
– before using the software, the problem must be
properly posed
• posing the problem will be emphasized in this class
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Mechanics Reform cont.
• Software helps us with:
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trigonometry
units conversion
systems of equations
iterative processes for design problems
• Software does not help with:
• envisioning the physical system
• applying the proper laws of physics
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Mechanics
• Broadly defined as the study of bodies that
are acted upon by forces.
• Types of bodies
– particles (considered rigid bodies)
– rigid bodies - relative distance between any two
points remains constant throughout motion
– deformable bodies
– fluids
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Mechanics Overview
Statics
Mech Matl
Rigid
Static
Deformable
Static
Dynamics
Rigid
Dynamic
Fluid Dyn
Deformable
Dynamic
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And now ...
Statics
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Chapter 1: Measurement
•Newton’s Laws of Motion
•Space and Events
•Vectors and Scalars
•SI Units (Metric)
•U.S. Customary Units
•Unit Conversion
•Scientific Notation
•Significant Figures
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Basics: Newton’s Laws
• Every body or particle continues in a state of rest or of
uniform motion in a straight line, unless it is compelled
to change that state by forces acting upon it (1st Law).
(Law of Inertia)
• The change of motion of a body is proportional to the
net force imposed on the body and is in the direction of
the net force (2nd Law).
F=ma
• If one body exerts a force on a second body, then the
second body exerts a force on the first that is equal in
magnitude, opposite in direction, and collinear (3rd Law).
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Basics
• Space -- we need to know the position of particles
y
mi
x
z
• Event -- position at a given time
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Basics cont.
• Two broad quantities
– scalars have no direction associated with them
• e.g., temperature, mass, speed, angle
– vectors must have direction specified
• e.g., velocity, force, acceleration
• Mass -- a scalar that characterizes a body’s
resistance to motion
• Force -- (vector) the action of one body on
another through contact or acting at a distance
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International System of Units:The SI system
Length
meters
m
Time
seconds
s
Mass
kilogram
kg
Force
Newton
N
1 kg m/s2
See table 1-1 for prefixes
Compound units
Remember: Speed = distance/time
so in SI units, speed is measured in m/s
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U.S. Customary Units
Length
foot
ft
Time
seconds
s
Mass
slug
slug
Force
pound
lb
slug ft/s2
*Remember: W= mg
where g = 32.17 ft/s2
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Numerical Answers
• Significant figures
– Use 3 significant digits
– If first digit is 1, then use next 3
• Rounding off the last significant digit
– less than 5: all digits after it are dropped
– equal 5: then all digits after it are dropped
– greater than 5 or equal 5 followed by a nonzero
digit: round up
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Vectors; Vector Addition
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•
Define scalars and vectors
Vector addition, scalar multiplication
2-D trigonometry
Vector components
Law of cosines
Law of sines
Problems
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Scalars and Vectors
• Scalar is a quantity that is represented by a
single number
– examples: mass, temperature, angle
• Vectors have both magnitude and direction
– Examples: velocity, acceleration, force
– Acceleration due to gravity is down not up!
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VECTORS
Line of Action
Magnitude
y
Vector
A or A

Direction
x
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Vectors
• Vectors are equal when they have the same
magnitude and direction
B
A
=
• Vectors add by the parallelogram rule
A
+
ME221
B
A
=
Lecture 1
B
C
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More on Vectors
• Vectors are communative
A+B=B+A
B
A
C
A
B
• Vectors are associative
(A + B) + C = A + (B + C)
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Subtraction of Vectors
In order to subtract vectors, first we must understand that if we
multiply a vector by (-1) we get a vector equal in length but exactly
opposite in direction.
A
-A
Then we see that B - A = B + (-A)
B
A
So if we have D = B - A
D
This looks like this:
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-A
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Adding More Than Two Vectors
B
A
A
B
A+B

C
D
C
D = A+B+C
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Law of Cosines
This will be used often in balancing forces
g
b
a
b
a
c
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Law of Sines
Again, used throughout this and other classes
Start with the same triangle:
g
b
a
b
a
c
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Example
Determine by trigonometry the
magnitude and direction of the
resultant of the two forces shown
25o
200 lb
ME221
45o 300 lb
Lecture 1
Note: resultant of two
forces is the vectorial
sum of the two vectors
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