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ME 221 Statics Summer 2004. Mr. Hinds 3523 EB hinds@msu.edu. 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.
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ME 221 StaticsSummer 2004 Mr. Hinds 3523 EB hinds@msu.edu
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
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
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
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
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
Administrative Details cont. Questions?? Lecture 1
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
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
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
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
Rigid Static Statics Static Deformable Mech Matl Dynamic Rigid Dynamics Dynamic Fluid Dyn Deformable Mechanics Overview Lecture 1
And now ... Statics Lecture 1
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
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
y mi x z Basics • Space -- we need to know the position of particles • Event -- position at a given time Lecture 1
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
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
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
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
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
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
Line of Action Magnitude y Vector A or A Direction x VECTORS Lecture 1
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
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
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
B A A A+B C B D C Adding More Than Two Vectors D = A+B+C Lecture 1
g b a b a c Law of Cosines This will be used often in balancing forces Lecture 1
g b a b a c Law of Sines Again, used throughout this and other classes Start with the same triangle: Lecture 1
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