General Principles1

STATICSAssist. Prof. Dr. Cenk Üstündağ

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

Outline

1. Mechanics2. Fundamental Concepts3. Units of Measurement4. The International System of Units5. Numerical Calculations6. 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

- Length is used to locate the position of a point in space andthereby describe the size of a physical system. Once a standard unit of length is defined, one can then use it to define distances and geometric properties of a body as multiples of this unit.

2. Mass- Mass is a measure of a quantity of matter that is used to compare the action of one body with that of another. This property manifests itself as a gravitational attraction between two bodies and provides a measure of the resistance of matter to a change in velocity.

1.2 Fundamentals Concepts

Basic Quantities3. Time

- Time is conceived as a succession of events. Although the principles of statics are time independent, this quantity plays an important role in the study of dynamics.

4. Force - In general, force is considered as a “push” or “pull” exerted byone body on another. This interaction can occur when there is direct contact between the bodies, such as a person pushing on a wall, or it can occur through a distance when the bodies are physically separated. Examples of the latter type include gravitational, electrical, and magnetic forces. In any case, a force is completely characterized by its magnitude, direction, and point of application.

1.2 Fundamentals Concepts

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

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”

1.2 Fundamentals Concepts

Newton’s Three Laws of Motion• Second Law

“A particle acted upon by an unbalanced force Fexperiences an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force”

maF

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”

1.2 Fundamentals Concepts

Newton’s Law of Gravitational Attraction

Weight:

Letting yields

221

rmm

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

We can develop an approximate expression for finding the Weight W of a particle having a mass m1 = m . If we assume the earth to be a nonrotating sphere of constant density and having a mass m2 = Me , then if r is the distance between the earth’s center and the particle, we have

2rmMGW 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

1.3 Units of Measurement

Name Length Time Mass Force

International Systems of Units (SI)

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

2.

smkg

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

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 unitEg: 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

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

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

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

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 theory2. Draw any diagrams and tabulate the problem data3. Apply principles in mathematics forms4. Solve equations which are

dimensionally homogenous5. Report the answer with

significance figures6. Technical judgment

and common sense

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.