Transcript Chapter-1
Engineering Mechanics: Statics in SI Units, 12e 1 General Principles Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Objectives • • • • Basic quantities and idealizations of mechanics Newton’s Laws of Motion and Gravitation Principles for applying the SI system of units Standard procedures for performing numerical calculations • General guide for solving problems Copyright © 2010 Pearson Education South Asia Pte Ltd Chapter Outline 1. 2. 3. 4. 5. 6. Mechanics Fundamental Concepts Units of Measurement The International System of Units Numerical Calculations General Procedure for Analysis Copyright © 2010 Pearson Education South Asia Pte Ltd 1.1 Mechanics • Mechanics can be divided into 3 branches: - Rigid-body Mechanics - Deformable-body Mechanics - Fluid Mechanics • Rigid-body Mechanics deals with - Statics - Dynamics Copyright © 2010 Pearson Education South Asia Pte Ltd 1.1 Mechanics • Statics – Equilibrium of bodies At rest Move with constant velocity • Dynamics – Accelerated motion of bodies Copyright © 2010 Pearson Education South Asia Pte Ltd 1.2 Fundamentals Concepts Basic Quantities 1. Length - locate the position of a point in space 2. Mass - measure of a quantity of matter 3. Time - succession of events 4. Force - a “push” or “pull” exerted by one body on another Copyright © 2010 Pearson Education South Asia Pte Ltd 1.2 Fundamentals Concepts Idealizations 1. Particles - has a mass and size can be neglected 2. Rigid Body - a combination of a large number of particles 3. Concentrated Force - the effect of a loading Copyright © 2010 Pearson Education South Asia Pte Ltd 1.2 Fundamentals Concepts Newton’s Three Laws of Motion • First Law “A particle originally at rest, or moving in a straight line with constant velocity, will remain in this state provided that the particle is not subjected to an unbalanced force” Copyright © 2010 Pearson Education South Asia Pte Ltd 1.2 Fundamentals Concepts Newton’s Three Laws of Motion • Second Law “A particle acted upon by an unbalanced force F experiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force” F ma Copyright © 2010 Pearson Education South Asia Pte Ltd 1.2 Fundamentals Concepts Newton’s Three Laws of Motion • Third Law “The mutual forces of action and reaction between two particles are equal and, opposite and collinear” Copyright © 2010 Pearson Education South Asia Pte Ltd 1.2 Fundamentals Concepts Newton’s Law of Gravitational Attraction F G m1 m 2 r2 F = force of gravitation between two particles G = universal constant of gravitation m1,m2 = mass of each of the two particles r = distance between the two particles mM e Weight: W G 2 r 2 Letting g GM e / r yields W mg Copyright © 2010 Pearson Education South Asia Pte Ltd 1.3 Units of Measurement SI Units • • • • Stands for Système International d’Unités F = ma is maintained only if – 3 of the units, called base units, are defined – 4th unit is derived from the equation SI system specifies length in meters (m), time in seconds (s) and mass in kilograms (kg) Force unit, Newton (N), is derived from F = ma Copyright © 2010 Pearson Education South Asia Pte Ltd 1.3 Units of Measurement Name Length Time Mass International Systems of Units (SI) Meter (m) Second (s) Kilogram (kg) Newton (N) Copyright © 2010 Pearson Education South Asia Pte Ltd Force kg .m 2 s 1.3 Units of Measurement • • • At the standard location, g = 9.806 65 m/s2 For calculations, we use g = 9.81 m/s2 Thus, W = mg (g = 9.81m/s2) • Hence, a body of mass 1 kg has a weight of 9.81 N, a 2 kg body weighs 19.62 N Copyright © 2010 Pearson Education South Asia Pte Ltd 1.4 The International System of Units Prefixes • For a very large or small numerical quantity, units can be modified by using a prefix • Each represent a multiple or sub-multiple of a unit Eg: 4,000,000 N = 4000 kN (kilo-newton) = 4 MN (mega- newton) 0.005m = 5 mm (milli-meter) Copyright © 2010 Pearson Education South Asia Pte Ltd 1.4 The International System of Units Copyright © 2010 Pearson Education South Asia Pte Ltd 1.5 Numerical Calculations Dimensional Homogeneity • • • Each term must be expressed in the same units Regardless of how the equation is evaluated, it maintains its dimensional homogeneity All terms can be replaced by a consistent set of units Copyright © 2010 Pearson Education South Asia Pte Ltd 1.5 Numerical Calculations Significant Figures • • • Accuracy of a number is specified by the number of significant figures it contains A significant figure is any digit including zero e.g. 5604 and 34.52 have four significant numbers When numbers begin or end with zero, we make use of prefixes to clarify the number of significant figures e.g. 400 as one significant figure would be 0.4(103) Copyright © 2010 Pearson Education South Asia Pte Ltd 1.5 Numerical Calculations Rounding Off Numbers • • • Accuracy obtained would never be better than the accuracy of the problem data Calculators or computers involve more figures in the answer than the number of significant figures in the data Calculated results should always be “rounded off” to an appropriate number of significant figures Copyright © 2010 Pearson Education South Asia Pte Ltd 1.5 Numerical Calculations Calculations • • • Retain a greater number of digits for accuracy Work out computations so that numbers that are approximately equal Round off final answers to three significant figures Copyright © 2010 Pearson Education South Asia Pte Ltd 1.6 General Procedure for Analysis • 1. 2. 3. 4. 5. 6. To solve problems, it is important to present work in a logical and orderly way as suggested: Correlate actual physical situation with theory Draw any diagrams and tabulate the problem data Apply principles in mathematics forms Solve equations which are dimensionally homogenous Report the answer with significance figures Technical judgment and common sense Copyright © 2010 Pearson Education South Asia Pte Ltd Example Convert to 2 km/h to m/s. Solution 2 km 1000 m 1 h 2 km/h 0.556 m/s h km 3600 s Remember to round off the final answer to three significant figures. Copyright © 2010 Pearson Education South Asia Pte Ltd