Chap1. General Principles

Objectives

  • To provide an introduction to the basic quantities and idealizations of mechanics
  • To give a statement of Newton's Laws of Motion and Gravitation
  • To review the principles for applying the SI system of units
  • To examine the standard procedures for performing numerical calculations
  • To present a general guide for solving problems

1.1 Mechanics

(1) A branch of the physical sciences that is concerned with the state of rest or motion of bodies that are subjected to the action of forces

(2) Rigid Body Mechanics & deformable-body mechanics(solid mechanics) & fluid mechanics

A. Rigid body Mechanics

a. statics : deals with the equilibrium of bodies that are either at rest or move with a constanct velocity)

  • dynamics when the acceleration is zero, remain in equilibrium

b. dynamics : concerned with the accelerated motion of bodies

1.2 Fundamental Concepts

(1) Basic quantities

A. length : locate the position of a point in space and theerby describe the size of a physical system

  • used to define distances and geometric properties as multiples of this unit

B. time : a succession of events, important in dynamics

C. mass : a measure of a quentity of matter used to compare the action of one body with that of another.

  • manifests itself as a gravitational attration between two bodies

  • a measure of the resistance of matter to a change in velocity

D. Force : a push or pull exerted by one body on another

  • occur when there is direct contact between the bodies

  • completely characterized by its magnitude, direction, and point of application.

(2) Idealizations

  • in order to simplify of the theory

A. particle : has a mass, but a size that can be neglected.

  • geometry of the body will not be involved in the analysis

B. rigid body : a combination of a large number of particles in which all the particles remain at a fixed distance from one another, both before and after applying a load.

  • body shape does not change when a load is applied, so we do not have to consider the type of material from which the body is made

C. concentrated force : the effect of loading which is assumed to act at a point on a body

  • represent a load by a concentrated force, provided the area over which the load is applied is very small compared to the overall size of the body

(3) Newton's Law of Motion

A. 1st Law : A particle originally at rest, or moving in a straight line with constant velocity, tends to remain in this state provided the particle is not subjected to an unbalanced force.

B. 2nd 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.

\[F = ma\]

C. 3rd Law : The mutual forces of action and reaction between two particles are equal, opposite, and collinear.

(4) Newton's Law of Gravitational Attration

\[F=G\frac{m_1 m_2}{r^2}\]

where

F = force of gravitation between the two particles

G = universal constant of gravitation; according to experimental evidence, \(G = 66.73(10^-12) m^3/(kg· s^2)\)

\(m_1, m_2\) = mass of each the two particles r = distance between the two particles

(5) Weight : Any two particles or bodies have a mutual attractive (gravitational) force acting between them. However, the only gravitational force having any sizable magnitude is that between the earth and the particle.

\[W = G \frac{m M_e}{r^2} = mg\]

  • Since W depends on r, it is not an absolute quantity. Its magnitude is determined from where the measurement was made

1.3 Unit of measurement

(1) SI Units : length (m), time (s), mass (kg), force \(N = \frac{kg \times m}{s^2}\)

1.4 The International System of Units

(1) prefixes : G, M, k, m, \(μ\)) , n

1.5 Numerical Calculations

(1) Dimensional homogeneity : eath term must be expressed in the same units

(2) Significant Figures : Show significant figures by using notation not 23400 but \(23.4(10^3)\)

(3) Rounding Off Numbers :

(4) Calculations : Do not round off calculations until expressing the final graph.

1.6 General Procedure for Analysis

  1. Read the problem carefully and try to correlate the actual physical situation with the theory studied.

  2. Tabulate the problem data and draw to a larger scale any necessary diagrams

  3. Apply the relevant principles, generally in mathematical form. When writing any equations, be sure they are dimensionally homogeneious.

  4. Solve the necessary equations, and report the answwer with no more than 3 significant figures

  5. Study the answer with technical judgement and common sense to determine wheter or not it seems reasonable.