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STATICS, UNITS, CALCULATIONS & PROBLEM SOLVING

STATICS, UNITS, CALCULATIONS & PROBLEM SOLVING. Today’s Objectives : Students will be able to: a) Identify what is mechanics / statics. b) Work with two types of units. c) Round the final answer appropriately. d) Apply problem solving strategies. In-Class activities :

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STATICS, UNITS, CALCULATIONS & PROBLEM SOLVING

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  1. STATICS, UNITS, CALCULATIONS & PROBLEM SOLVING Today’s Objectives: Students will be able to: a) Identify what is mechanics / statics. b) Work with two types of units. c) Round the final answer appropriately. d) Apply problem solving strategies. • In-Class activities: • Sample reading quiz • What is mechanics • System of units • Numerical calculations • Sample concept quiz • Problem solving strategy • Sample attention quiz

  2. SAMPLE READING QUIZ 1. The subject of mechanics deals with what happens to a body when ______ is / are applied to it. 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) Euclidean Mechanics C) Greek Mechanics

  3. 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 could be large or small.

  4. BRANCHES OF MECHANICS

  5. What may happen if static's is not applied properly?

  6. SYSTEMS OF UNITS (Section 1.3) • Four fundamental physical quantities. • Length, mass, time, force. • One equation relates them, F = m * a • We use this equation to develop systems of units • Units are arbitrary names we give to the physical quantities.

  7. UNIT SYSTEMS • Define 3 of the units and call them the base units. • Derive the 4th unit (called the derived unit) using F = m * a. • We will work with one unit system in static’s: SI.

  8. Table 1-1 in the textbook summarizes these unit systems.

  9. RULES FOR USING SI SYMBOLS (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 exception are N, • Pa, M and G) • Exponential powers apply to units , e.g., cm2 = cm • cm • Other rules are given in your textbook

  10. 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.

  11. SAMPLE CONCEPT QUIZ 1. Evaluate the situation, in which mass(kg), force (N), and length(m) are the base units and recommend a solution. A) A new system of units will have to be formulated B) Only the unit of time have to be changed from second to something else C) No changes are required. D) The above situation is not feasible

  12. SAMPLE CONCEPT QUIZ (continued) 2. Give the most appropriate reason for using three significant figures in reporting results of typical engineering calculations. A) Historically slide rules could not handle more than three significant figures. B)Three significant figures gives better than one-percent accuracy. C) Telephone systems designed by engineers have area codes consisting of three figures. D) Most of the original data used in engineering calculations do not have accuracy better than one percent

  13. 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 / revise your work.

  14. SAMPLE ATTENTION QUIZ 1. For a static’s problem your calculations show the final answer as 12345.6 N. What will you write as your final answer? A) 12345.6 N B) 12.3456 kN C) 12 kN D) 12.3 kN E) 123 kN 2. In three step IPE approach to problem solving, what does P stand for A) Position B) Plan C) Problem D) Practical E) Possible

  15. 2–D VECTOR ADDITION Today’s Objective: Students will be able to : a) Resolve a 2-D vector into components b) Add 2-D vectors using Cartesian vector notations. • In-Class activities: • Check homework • Reading quiz • Application of adding forces • Parallelogram law • Resolution of a vector using • Cartesian vector notation (CVN) • Addition using CVN • Attention quiz

  16. READING QUIZ 1. Which one of the following is a scalar quantity? A) Force B) Position C) Mass D) Velocity 2. For vector addition you have to use ______ law. A) Newton’s Second B) the arithmetic C) Pascal’s D) the parallelogram

  17. APPLICATION OF VECTOR ADDITION There are four concurrent cable forces acting on the bracket. How do you determine the resultant force acting on the bracket ?

  18. SCALARS AND VECTORS (Section 2.1) ScalarsVectors Examples: mass, volume force, velocity Characteristics: It has a magnitude It has a magnitude (positive or negative) and direction Addition rule: Simple arithmetic Parallelogram law Special Notation: None Bold font, a line, an arrow or a “carrot”

  19. VECTOR OPERATIONS(Section 2.2) Scalar Multiplication and Division

  20. VECTOR ADDITION USING EITHER THE PARALLELOGRAM LAW OR TRIANGLE Parallelogram Law: Triangle method (always ‘tip to tail’): How do you subtract a vector? How can you add more than two concurrent vectors graphically ?

  21. RESOLUTION OF A VECTOR “Resolution” of a vector is breaking up a vector into components. It is kind of like using the parallelogram law in reverse.

  22. CARTESIAN VECTOR NOTATION (Section 2.4) • We ‘ resolve’ vectors into components using the x and y axes system • Each component of the vector is shown as a magnitude and a direction. • The directions are based on the x and y axes. We use the “unit vectors” i and j to designate the x and y axes.

  23. For example, F = Fx i + Fy j or F' = F'x i + F'y j The x and y axes are always perpendicular to each other. Together,they can be directed at any inclination.

  24. ADDITION OF SEVERAL VECTORS • Step 1 is to resolve each force into its components • Step 3 is to find the magnitude and angle of the resultant vector. • Step 2 is to add all the x components together and add all the y components together. These two totals become the resultant vector.

  25. Example of this process,

  26. You can also represent a 2-D vector with a magnitude and angle.

  27. EXAMPLE Given: Three concurrent forces acting on a bracket. Find: The magnitude and angle of the resultant force. Plan: a) Resolve the forces in their x-y components. b) Add the respective components to get the resultant vector. c) Find magnitude and angle from the resultant components.

  28. EXAMPLE (continued) F1 = { 15 sin 40° i + 15 cos 40° j } kN = { 9.642 i + 11.49 j } kN F2 = { -(12/13)26 i + (5/13)26 j } kN = { -24 i + 10 j } kN F3 = { 36 cos 30° i– 36 sin 30° j } kN = { 31.18 i– 18 j } kN

  29. y FR  x EXAMPLE (continued) Summing up all the i and j components respectively, we get, FR = { (9.642 – 24 + 31.18) i + (11.49 + 10 – 18) j } kN = { 16.82 i + 3.49 j } kN FR = ((16.82)2 + (3.49)2)1/2 = 17.2 kN  = tan-1(3.49/16.82) = 11.7°

  30. 1. Can you resolve a 2-D vector along two directions, which are not at 90° to each other? A) Yes, but not uniquely. B) No. C) Yes, uniquely. 2. Can you resolve a 2-D vector along three directions (say at 0, 60, and 120°)? A) Yes, but not uniquely. B) No. C) Yes, uniquely. CONCEPT QUIZ

  31. GROUP PROBLEM SOLVING Given: Three concurrent forces acting on a bracket Find: The magnitude and angle of the resultant force. Plan: a) Resolve the forces in their x-y components. b) Add the respective components to get the resultant vector. c) Find magnitude and angle from the resultant components.

  32. GROUP PROBLEM SOLVING (continued) F1 = { (4/5) 850 i - (3/5) 850 j } N = { 680 i - 510 j } N F2 = { -625 sin(30°) i - 625 cos(30°) j } N = { -312.5 i - 541.3 j } N F3 = { -750 sin(45°) i + 750 cos(45°) j } N { -530.3 i + 530.3 j } N

  33. y x  FR GROUP PROBLEM SOLVING (continued) Summing up all the i and j components respectively, we get, FR = { (680 – 312.5 – 530.3) i + (-510 – 541.3 + 530.3) j }N = { - 162.8 i - 521 j } N • FR = ((162.8)2 + (521)2)½ = 546 N • = tan–1(521/162.8) = 72.64° or From Positive x axis  = 180 + 72.64 = 253 °

  34. y x 30° F = 80 N ATTENTION QUIZ 1. Resolve Falong x and y axes and write it in vector form. F = { ___________ } N A) 80 cos (30°) i - 80 sin (30°) j B) 80 sin (30°) i + 80 cos (30°) j C) 80 sin (30°) i - 80 cos (30°) j D) 80 cos (30°) i + 80 sin (30°) j 2. Determine the magnitude of the resultant (F1 + F2) force in N when F1 = { 10 i + 20 j } N and F2 = { 20 i + 20 j } N . A) 30 N B) 40 N C) 50 N D) 60 N E) 70 N

  35. End of the Lecture Let Learning Continue

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