ME 221 Statics Summer 2004

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

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 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 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 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 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 Lecture 1

7. Administrative Details cont. Questions?? 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 Lecture 1

9. 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 Lecture 1

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

11. 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 Lecture 1

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

13. And now ... Statics 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 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). Lecture 1

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

17. Basics cont. • vectors must have direction specified • e.g., velocity, force, acceleration • scalars have no direction associated with them • e.g., temperature, mass, speed, angle • Two broad quantities • 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 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 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 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 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 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! Lecture 1

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

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

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

26. 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: -A Lecture 1

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

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

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

30. 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 25o 45o 300 lb 200 lb Lecture 1