MECHANICS, UNITS, NUMERICAL CALCULATIONS & GENERAL PROCEDURE FOR ANALYSIS Today s Objectives: Students will be able to: In-Class activities: a) Explain mechanics / statics. b) Work with two types of units. Reading Quiz c) Round the final answer appropriately. What is Mechanics d) Apply problem-solving strategies. System of Units Numerical Calculations Concept Quiz Problem-Solving Strategy Attention Quiz
Some Important Points Studio course (combined lesson & problem session) Sessions do not require laptops Important tools: syllabus, textbook (listed in syllabus), pencil and paper, Web site of course Website: http://lms.rpi.edu/ http://www.rpi.edu/dept/core-eng/ WWW/IEA for back exams
Course format Mini lectures In class activities 3 mid term exams: 3x15% = 50% * *Highest exam will be worth 20% 1 final exam: 25% Assigned problems: HW: 20% CA: 5%
WHAT IS MECHANICS? Study of what happens to a thing (the technical name is BODY ) when FORCES are applied to it. Either the body or the forces can be large or small.
BRANCHES OF MECHANICS M e c h a n i c s R i g i d B o d i e s ( T h i n g s t h a t d o n o t c h a n g e s h a p e ) D e f o r m a b l e B o d i e s ( T h i n g s t h a t d o c h a n g e s h a p e ) F l u i d s S t a t i c s D y n a m i c s I n c o m p r e s s i b l e C o m p r e s s i b l e
UNITS OF MEASUREMENT (Section 1.3) Four fundamental physical quantities (or dimensions). Length Mass Time Force Newton s 2 nd Law relates them: F = m * a We use this equation to develop systems of units. Units are arbitrary names we give to the physical quantities.
UNIT SYSTEMS Force, mass, time and acceleration are related by Newton s 2 nd law. Three of these are assigned units (called base units) and the fourth unit is derived. Which one is derived varies by the system of units. We will work with two unit systems in statics: International System (SI) U.S. Customary (USCS)
Table 1-1 in the textbook summarizes these unit systems.
COMMON CONVERSION FACTORS Work problems in the units given unless otherwise instructed!
THE INTERNATIONAL SYSTEM OF UNITS (Section 1.4) No plurals (e.g., m = 5 kg, not kgs ) Separate units with a (e.g., meter second = m s ) Most symbols are in lowercase. Some exceptions are N, Pa, M and G. Exponential powers apply to units, e.g., cm cm = cm 2 Compound prefixes should not be used. Table 1-3 in the textbook shows prefixes used in the SI system
NUMERICAL CALCULATIONS (Section 1.5) Must have dimensional homogeneity. Dimensions have to be the same on both sides of the equal sign, (e.g. distance = speed time.) Use an appropriate number of significant figures (3 for answer, at least 4 for intermediate calculations). Why? Be consistent when rounding off. - greater than 5, round up (3528 3530) - smaller than 5, round down (0.03521 0.0352) - equal to 5, see your textbook for an explanation.
PROBLEM SOLVING STRATEGY IPE: A 3 Step Approach 1. Interpret: Read carefully and determine what is given and what is to be found/ delivered. Ask, if not clear. If necessary, make assumptions and indicate them. 2. Plan: Think about major steps (or a road map) that you will take to solve a given problem. Think of alternative/creative solutions and choose the best one. 3. Execute: Carry out your steps. Use appropriate diagrams and equations. Estimate your answers. Avoid simple calculation mistakes. Reflect on and then revise your work, if necessary.
Scalar and vectors A scalar quantity is completely described by a magnitude (number). -Examples: mass, density, length, speed, time, temperature. A vector quantity has a magnitude and direction and obeys the parallelogram law of addition. -Examples: force, moment, velocity, acceleration.
Vector Terminal point Direction of arrow Length of arrow Initial point direction of vector magnitude of vector
The sum of two vectors geometrical representation Two vectors can be added vectorially using the parallelogram law. F 1 R Position vector F so that its initial point 1 coincides with the initial point of F. The 2 vector F +F is represented by the vector R. 1 2 F 2
Vectors in rectangular coordinate systems- two dimensional y V (v 1,v 2 ) x (v 1,v 2 ) are the terminal points of vector V V = v 1 i + v 2 j
The sum of two vectors analytic representation (two dimensional ) y (v v 1 +w 1,v 2 +w 2 ) 2 (w 1,w 2 ) w 2 w v (v 1,v 2 ) v 1 w 1 x v + w = (v 1 + w 1, v 2 + w 2 ) v + w = (v 1 + w 1 )i + (v 2 + w 2 ) j
The sum of two vectors rectangular components (Three dimensional ) z a (a 1,a 2,a 3 ) y x b (b 1,b 2,b 3 ) a + b = (a 1 + b 1, a 2 + b 2, a 3 + b 3 ) a + b = (a 1 + b 1 )i + (a 2 + b 2 ) j + (a 3 + b 3 ) k
Vectors with initial point not at the z P 1 (x 1,y 1,z 1 ) w v origin P 2 (x 2,y 2,z 2 ) y x w + P 1 P 2 = v P 1 P 2 = v w = (x 2 i + y 2j + z 2 k) (x 1 i + y 1 j+ z 1 k) = (x 2 -x 1 ) i + (y 2 -y 1 ) j + (z 2 -z 1 ) k
Example Find the components of the vector having initial point P 1 and terminal point P 2 Solution: P 1 (-1,0,2), P 2 (0,-1,0) V = (0 + 1, -1-0, 0-2) = (1,-1,-2)
READING QUIZ 1. The subject of mechanics deals with what happens to a body when is / are applied to it. A) a magnetic field B) heat C) forces D) neutrons E) lasers 2. still remains the basis of most of today s engineering sciences. A) Newtonian Mechanics B) Relativistic Mechanics C) Greek Mechanics C) Euclidean Mechanics
Class Assignment Find the components of the vector having initial point P 1 and terminal point P 2 P 1 (3, -2, 5), P 2 (-1, -3, 8)
ENGR-110 (IEA) Fall-2015 CA 1 Solution Find the components of the vector having initial point P 1 and terminal point P 2 : P 1 (3, -2, 5), P 2 (-1, -3, 8) P 1 P 2 = (-1, -3, 8) - (3, -2, 5) = (-4, -1, 3)