Engineering Mechanics Statics note in Si units

8/11/2019 Engineering Mechanics Statics note in Si units

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General Principles1

Engineering Mechanics:

Statics in SI Units, 12e

Copyright 2010 Pearson Education South Asia Pte Ltd


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Chapter Outline

1. Mechanics

2. Fundamental Concepts

3. Units of Measurement

4. The International System of Units5. 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

At rest

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

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


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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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Newtons Three Laws of Motion

First Law

A particle originally at rest, or moving in a straight line

with constant velocity, will remain in this stateprovided that the particle is not subjected to an

unbalanced force





Second Law

A particle acted upon by an unbalanced forceF

experiences an acceleration athat has the samedirection as the force and a magnitude that is directly

proportional to the force

maF





Third Law

The mutual forces of action and reaction between two

particles are equal and, opposite and collinear



1.3 Units of Measurement

SI Units

Stands for Systme International dUnits

F = mais maintained only if

3 of the units, called base units, are defined

4thunit 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




Name Length Time Mass Force

InternationalSystems of Units

(SI)

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

2

.

s

mkg




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


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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 zeroe.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(10

3

)


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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 theanswer than the number of significant figures in the

data

Calculated results should always be rounded offto

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 data3. Apply principles in mathematics forms

4. Solve equations which are

dimensionally homogenous

5. Report the answer withsignificance figures

6. Technical judgment

and common sense


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Example

Convert to 2 km/h to m/s.

Solution

m/s556.0s3600

h1

km

m1000

h

km2km/h2

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

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Engineering Mechanics Statics note in Si units