Statics of Rigid bodies

1. ME 221 Statics
Summer 2004
Mr. Hinds
3523 EB
hinds@msu.edu

2. ME221 Lecture 1 2
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

3. ME221 Lecture 1 3
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

4. ME221 Lecture 1 4
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

5. ME221 Lecture 1 5
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

6. ME221 Lecture 1 6
Announcements
• ME221 TA’s and Help Sessions
• Chad Stimson – stimson1@msu.edu
• Homework grading & help room
• Tuesdays & Thursdays – 8am to 1pm – 1522EB
• Jimmy Issa – jimmy@msu.edu
• Quiz & exam grading & help room
• Tuesdays & Thursdays – 1pm to 5pm – 2415EB
• Will begin on Tuesday, May 18
• Hours also posted on Angel

7. ME221 Lecture 1 7
Administrative Details cont.
Questions??

8. ME221 Lecture 1 8
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

9. ME221 Lecture 1 9
Mechanics Reform
• Textbook offers a departure from past standards
– recognizes the power of computer software in solving
problems
– before using the software, the problem must be
properly posed
• posing the problem will be emphasized in this class
• MatLab, MathCAD, Maple, Mathmatica, VB, etc.
• calculators may be effectively utilized as well

10. ME221 Lecture 1 10
Mechanics Reform cont.
• Software does not help with:
• Software helps us with:
• envisioning the physical system
• applying the proper laws of physics
• trigonometry
• units conversion
• systems of equations
• iterative processes for design problems

11. ME221 Lecture 1 11
Mechanics
• Broadly defined as the study of bodies that
are acted upon by forces.
– deformable bodies
• Types of bodies
– particles (considered rigid bodies)
– rigid bodies - relative distance between any two
points remains constant throughout motion
– fluids

12. ME221 Lecture 1 12
Mechanics Overview
Statics Rigid Static
Mech Matl Deformable Static
Dynamics Rigid Dynamic
Fluid Dyn Deformable Dynamic

13. ME221 Lecture 1 13
And now ...
Statics

14. ME221 Lecture 1 14
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

15. ME221 Lecture 1 15
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).

16. ME221 Lecture 1 16
Basics
• Space -- we need to know the position of particles
• Event -- position at a given time
x
z
y mi

17. ME221 Lecture 1 17
Basics cont.
– 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
• Two broad quantities
– scalars have no direction associated with them
• e.g., temperature, mass, speed, angle

18. ME221 Lecture 1 18
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

19. ME221 Lecture 1 19
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

20. ME221 Lecture 1 20
Numerical Answers
– equal 5: then all digits after it are dropped
• 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
– greater than 5 or equal 5 followed by a nonzero
digit: round up

21. ME221 Lecture 1 21
Vectors; Vector Addition
• Define scalars and vectors
• Vector addition, scalar multiplication
• 2-D trigonometry
• Vector components
• Law of cosines
• Law of sines
• Problems

22. ME221 Lecture 1 22
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!

23. ME221 Lecture 1 23
VECTORS
Line of Action
 Direction
Vector
A or A
x
y
Magnitude

24. ME221 Lecture 1 24
Vectors
• Vectors are equal when they have the same
magnitude and direction
=
A B
• Vectors add by the parallelogram rule
A B
+
B
=
A
C

25. ME221 Lecture 1 25
More on Vectors
• Vectors are communative
A + B = B + A B
A
C
B
A
• Vectors are associative
(A + B) + C = A + (B + C)

26. ME221 Lecture 1 26
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.
Subtraction of Vectors
Then we see that B - A = B + (-A)
So if we have D = B - A
This looks like this:
A
-A
A
-A
B
D

27. ME221 Lecture 1 27
A
B
A+B
C
D
Adding More Than Two Vectors
A
B
C

D = A+B+C

28. ME221 Lecture 1 28
Law of Cosines
This will be used often in balancing forces
c
b
a
g
b
a

29. ME221 Lecture 1 29
Law of Sines
Again, used throughout this and other classes
Start with the same triangle:
b
a
g
c
b
a

30. ME221 Lecture 1 30
300 lb
200 lb
45o
25o
Example
Determine by trigonometry the
magnitude and direction of the
resultant of the two forces shown
Note: resultant of two
forces is the vectorial
sum of the two vectors