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General Principles11

Engineering Mechanics: Statics in SI Units, 12e

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


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


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


1.1 Mechanics

• Statics – Equilibrium of bodies At rest Move with constant velocity

• Dynamics – Accelerated motion of bodies


1.2 Fundamentals Concepts

Basic Quantities1. 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



Idealizations1. 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



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”



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



Newton’s Three Laws of Motion• Third Law

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



Newton’s Law of Gravitational Attraction

Weight:

Letting yields

221

r

mmGF

F = force of gravitation between two particlesG = universal constant of gravitationm1,m2 = mass of each of the two particlesr = distance between the two particles

2r

mMGW e

2/ rGMg e mgW


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



Name Length Time Mass Force

International Systems 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


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)


1.4 The International System of Units


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



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 figurese.g. 400 as one significant figure would be 0.4(103)



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



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


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


Example

Convert to 2 km/h to m/s.

Solution

m/s 556.0s 3600

h 1

km

m 1000

h

km 2 km/h 2

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


QUIZ

1. 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

2. ________________ still remains the basis of most of today’s engineering sciences.

A) Newtonian Mechanics B) Relativistic Mechanics

C) Greek Mechanics C) Euclidean Mechanics


QUIZ

3. 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.


QUIZ

4. Give the most appropriate reason for using three significant figures in reporting results of typical engineering calculations.

A) Historically slide rules could not handle more than three significant figures.

B) Three significant figures gives better than one-percent accuracy.

C) Telephone systems designed by engineers have area codes consisting of three figures.

D) Most of the original data used in engineering calculations do not have accuracy better than one percent.


QUIZ

5. 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

6. In three step IPE approach to problem solving, what does P stand for?

A) Position B) Plan C) Problem

D) Practical E) Possible

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