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MECHANICS, UNITS, NUMERICAL CALCULATIONS &
GENERAL PROCEDURE FOR ANALYSIS
Today’s Objectives: Students will be able to: a) Explain mechanics / statics. b) Work with two types of units. c) Round the final answer appropriately. d) Apply problem-solving strategies.
READING QUIZ
- 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
- ________________ still remains the basis of most of today’s engineering sciences. A) Newtonian Mechanics B) Relativistic Mechanics C) Greek Mechanics C) Euclidean Mechanics
BRANCHES OF MECHANICS
Statics Dynamics Rigid Bodies (Things that do not change shape) Deformable Bodies (Things that do change shape) Incompressible Compressible Fluids Mechanics
UNITS OF MEASUREMENT (Section 1.3)
- Four fundamental physical quantities (or dimensions).
- 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.
Table 1-1 in the textbook summarizes these unit systems.
COMMON CONVERSION FACTORS
- Example: Convert a torque value of 47 in • lb into SI units.
- Answer is 5.31026116 N • m?
- Work problems in the units given unless otherwise instructed!
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.)
- 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.
- Use an appropriate number of significant figures (3 for answer, at least 4 for intermediate calculations). Why?
CONCEPT QUIZ
- 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.
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.
ATTENTION QUIZ
- In three step IPE approach to problem solving, what does P stand for? A) Position B) Plan C) Problem D) Practical E) Possible
- 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
