Engineering Mechanics: Statics in SI Units, 12ecivil.emu.edu.tr/courses/civl211/2016-2017spring/Statics-Chapter...Engineering Mechanics: Statics in SI Units, ... Chapter Objectives

General Principles 1

Engineering Mechanics: Statics in SI Units, 12e

Copyright © 2010 Pearson Education South Asia Pte Ltd 1

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

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Chapter Outline

1.  Mechanics 2.  Fundamental Concepts 3.  Units of Measurement 4.  The International System of Units 5.  Numerical Calculations 6.  General Procedure for Analysis

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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

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1.1 Mechanics

•  Statics – Equilibrium of bodies Ø At rest Ø Move with constant velocity •  Dynamics – Accelerated motion of bodies

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1.2 Fundamentals Concepts

Basic Quantities 1.  Length

- locate the position of a point in space 3.  Mass

- measure of a quantity of matter 4.  Time

- succession of events 5.  Force

- a “push” or “pull” exerted by one body on another

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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

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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”

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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”

maF =

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Newton’s Three Laws of Motion •  Third Law

“The mutual forces of action and reaction between two particles are equal and, opposite and collinear”

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Newton’s Law of Gravitational Attraction Me: mass of Earth

Weight: Letting yields

221

rmm

GF =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

2rmMGW e=

2/ rGMg e= mgW =

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12

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*1–13. Two particles have a mass of 8 kg and 12 kg,respectively. If they are 800 mm apart, determine the forceof gravity acting between them. Compare this result withthe weight of each particle.

01 Ch01 1-6.indd 401 Ch01 1-6.indd 4 6/12/09 8:02:56 AM6/12/09 8:02:56 AM

F = G m1m2

r2

Where G = 66.73(10–12) m3/(kg · s2)

W1 = 8(9.81) = 78.5 N Ans

W2 = 12(9.81) = 118 N Ans

F = 66.73(10–12) = 10.0(10–9) N = 10.0 nN Ans8(12)(0.8)2! "


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

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Name Length Time Mass Force

International Systems of Units (SI)

Meter (m) Second (s) Kilogram (kg) Newton (N)

⎟⎠⎞

⎜⎝⎛

2.smkg

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•  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, Ø  a body of mass 1 kg has a weight of 9.81 N, Ø  a body of mass 2 kg has a weight of 19.62 N.

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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)

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1.4 The International System of Units

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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

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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)

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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

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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

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1.6 General Procedure for Analysis

•  To solve problems, it is important to present work in a logical and orderly way as suggested:

1.  Correlate actual physical situation with theory 2.  Draw any diagrams and tabulate the problem data 3.  Apply principles in mathematics forms 4.  Solve equations which are

dimensionally homogenous 5.  Report the answer with

significance figures 6.  Technical judgment

and common sense 22

Copyright © 2010 Pearson Education South Asia Pte Ltd 23


Example

Convert to 2 km/h to m/s. Solution

m/s 556.0s 3600

h 1km

m 1000hkm 2 km/h 2 =⎟

⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛=

Remember to round off the final answer to three significant figures.

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Engineering Mechanics: Statics in SI Units, 12ecivil.emu.edu.tr/courses/civl211/2016-2017spring/Statics-Chapter...Engineering Mechanics: Statics in SI Units, ... Chapter Objectives

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