INTRODUCTION

1. INTRODUCTION THE BEGINNING ENERGY & MATTER SPACETIME MECHANICS FLUIDS & THEIR MECHANICS DIMENSIONS & UNITS ACCURACY & PRECISION ENGINEERING PROBLEMS KK's FLM 221 - WK1: INTRO

2. THE BIG BANG • Energy – concentrated by the UNIFIED force at only point in existence (Appr. 13.7 to 15X109 years ago) • No space, no time (as we know them now) existed then • Rapid expansion scatters energy to CREATE both space & time as one entity, SPACETIME • Out of SPACETIME come two ‘original’ quantities: Length – or distance (L) and Time (t) • Unified force splits into Gravity, Nuclear (weak & strong) and electromagnetic forces • GRAVITY concentrates some of the scattered energy to occupy some of the SPACETIME. • The concentrated energy occupying some SPACETIME forms one other ‘original’ quantity: MATTER - or Mass (M) KK's FLM 221 - WK1: INTRO

3. MECHANICS I – Newton’s laws of motion (1.1) • Change of position in space is displacement(s) The change takes time (t). Big ‘s’ in a small ‘t’, means faster displacement or higher velocity (v). • When matter is being displaced, its mass (m) and velocity (v) form a new quantity called Momentum (H). The bigger each of ‘m’ and ‘v’, the bigger ‘H’ becomes. • MATTER always wants to keep its momentum constant . It resists change of its state of motion. It thus has INERTIA (In) (Newton’s 1st law). Big ‘m’ means big ‘In’. • To change Matter’s momentum, we have to use Force (F). The change depends on BOTH the Force and the time (t) it takes when acting on the Matter. This ‘F’ and ‘t’ make an other quantity called Impulse (I). • Impulse ‘I’ changes Matter’s momentum. Big ‘I’ means big Momentum change (mv2 – mv1) or H2-H1. • When velocity changes, a new quantity. Acceleration (a) is formed. Big velocity change ‘v2 – v1’ in small time ‘t’ means big ‘a’ We find that Force ‘F’ directly depends on ‘m’ (hence inertia) and ‘a’ (Newton’s 2nd law) • When Force ‘F’ acts on Matter through whatever means, the latter ‘retaliates’ on those means with an equal, opposing Reaction ‘R’. (Newton’s 3rd law) (1.2) (1.3) (1.4) (1.5) (1.6) (1.7) (1.8) KK's FLM 221 - WK1: INTRO

4. MECHANICS II – Matter in Equilibrium • No Momentum change • No NETT external force or Moment • If external forces exist, each ‘harasses’ Matter individually – creating Stresses within. • Constituents of the Matter may shift within creating internal Strains . KK's FLM 221 - WK1: INTRO

5. SOLIDS & FLUIDS KK's FLM 221 - WK1: INTRO

6. FLUIDS – LIQUIDS & GASES KK's FLM 221 - WK1: INTRO

7. DIMENSIONS What are they – and where do they originate? • Statements describing or characterising a physical quantity to show how the quantity is related to initial ones from the big bang • All physical quantities have an origin from what was available at the big bang PRIMARY – the first quantities to emerge from the big bang and to which all others’ origin, can be traced. Otherwise, called Fundamental dimensions: see Table 1 SECONDARY – or Derived: see Table 2 KK's FLM 221 - WK1: INTRO

8. TABLE 1 – FUNDAMENTAL DIMENSIONS KK's FLM 221 - WK1: INTRO

9. UNITS • The magnitudes assigned to the dimensions of a quantity • Several systems of units but the SI units and their derivatives are the only internationally accepted ones. • In the SI system, ‘M’ is expressed in kilo grams (kg), ‘L’ in metres (m) and ‘t’ in seconds (s). • Derived dimensions have units directly related to those of the fundamental quantities from which they originate • Dimensional analysis of a given quantity helps establish its relationship with the fundamental ones – and hence, can be used to describe the quantity’s unit • Quantities of same dimensions have similar units though not necessarily identical (eg Work and Moment – ‘J’ and ‘Nm’) • Smaller or bigger quantities are expressed in multiples of 10 and suitable prefixes are used before the normal SI unit. See Table 3. KK's FLM 221 - WK1: INTRO

10. ENGINEERINGPROBLEMS • Solution of Mankind’s problems using laws of the physical sciences and mathematics • Three methods of solution: • Experimental – Most accurate; expensive; slow; often times not possible • Analytical – makes simplifying assumptions; models problem - often mathematically; cheapest; faster; often times only feasible method; subject to errors depending on validity of assumptions • Combined – Begins with analytical, makes experimental model of analytical solution, revises the analysis from results on model: More reliable than ii) and less expensive than i) KK's FLM 221 - WK1: INTRO

11. ACCURACY, PRECISION & SIGNIFICANT DIGITS • Accuracy – how close to the true value of the quantity is the result? (Errors are repeatable and appr. fixed) • Precision – how close to each other are the repeated results? (Errors are random) • Significant digits – how relevant are all the digits shown in a result? (In most engineering problems, 3 digits are standard) Precise, inaccurate Accurate, imprecise KK's FLM 221 - WK1: INTRO