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

2. ME221Lecture 12 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. ME221Lecture 13 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. ME221Lecture 14 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. ME221Lecture 15 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. ME221Lecture 16 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. ME221Lecture 17 Administrative Details cont. Questions??

8. ME221Lecture 18 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. ME221Lecture 19 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. ME221Lecture 110 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. ME221Lecture 111 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. ME221Lecture 112 Mechanics Overview Statics RigidStatic Mech Matl Deformable Static Dynamics Rigid Dynamic Fluid Dyn Deformable Dynamic

13. ME221Lecture 113 And now... Statics

14. ME221Lecture 114 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. ME221Lecture 115 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 (1 st 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 (2 nd 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 (3 rd Law).

16. ME221Lecture 116 Basics Space -- we need to know the position of particles Event -- position at a given time x z y mimi

17. ME221Lecture 117 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. ME221Lecture 118 International System of Units:The SI system Lengthmetersm Timesecondss Masskilogramkg ForceNewtonN1 kg m/s 2 See table 1-1 for prefixes Compound units Remember: Speed = distance/time so in SI units, speed is measured in m/s

19. ME221Lecture 119 U.S. Customary Units Lengthfootft Timesecondss Massslugslug Forcepoundlbslug ft/s 2 *Remember: W= mg where g = 32.17 ft/s 2

20. ME221Lecture 120 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. ME221Lecture 121 Vectors; Vector Addition Define scalars and vectors Vector addition, scalar multiplication 2-D trigonometry Vector components Law of cosines Law of sines Problems

22. ME221Lecture 122 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. ME221Lecture 123 VECTORS Line of Action  Direction Vector A or A x y Magnitude

24. ME221Lecture 124 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. ME221Lecture 125 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. ME221Lecture 126 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 B D

27. ME221Lecture 127 A B A+B C D Adding More Than Two Vectors A B C  D = A+B+C

28. ME221Lecture 128 Law of Cosines This will be used often in balancing forces c    b a

29. ME221Lecture 129 Law of Sines Again, used throughout this and other classes Start with the same triangle:    c b a

30. ME221Lecture 130 300 lb 200 lb 45 o 25 o 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