ME 221 StaticsSummer 2004

Mr. Hinds

3523 EB

hinds@msu.edu

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

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

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

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

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

ME221 Lecture 1 7

Administrative Details cont.

Questions??

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

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

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

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

ME221 Lecture 1 12

Mechanics Overview

Statics Rigid Static

Mech Matl Deformable Static

Dynamics Rigid Dynamic

Fluid Dyn Deformable Dynamic

ME221 Lecture 1 13

And now ...

Statics

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

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).

ME221 Lecture 1 16

Basics• Space -- we need to know the position of particles

• Event -- position at a given time

xz

y mi

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

ME221 Lecture 1 18

International System of Units:The SI systemLength meters m

Time seconds s

Mass kilogram kg

Force Newton N 1 kg m/s2

See table 1-1 for prefixesCompound units

Remember: Speed = distance/time

so in SI units, speed is measured in m/s

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

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

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

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!

ME221 Lecture 1 23

VECTORS

Line of Action

Direction

VectorA or A

x

yMagnitude

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

ME221 Lecture 1 25

More on Vectors• Vectors are communative

A + B = B + A BA

C

B

A

• Vectors are associative(A + B) + C = A + (B + C)

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

ME221 Lecture 1 27

A

B

A+B C

D

Adding More Than Two Vectors

A

B

C

D = A+B+C

ME221 Lecture 1 28

Law of CosinesThis will be used often in balancing forces

c

b

a

180 2 2 2 2 cosa b c bc 2 2 2 2 cosb a c ac 2 2 2 2 cosc a b ab

ME221 Lecture 1 29

Law of SinesAgain, used throughout this and other classes

Start with the same triangle:

c

ba

sin sin sin

a b c

ME221 Lecture 1 30

300 lb200 lb

45o25o

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