Engineering Mechanics Statics - An Introduction

Engineering Mechanics

It is a branch of engineering that deals with the effects of forces on objects under the study of physical science.

History of Mechanics

Logical Divisions of Mechanics

• Statics
  It concerns the equilibrium of bodies under action of forces

• Dynamics
  It concerns the motion of bodies with respect to time.

Basic Concepts

•  Space
  Space is the geometric region occupied by bodies whose positions are described by linear and angular measurements relative to 2-dimensional and 3-dimensional coordinate systems.

• Time
  Time is the measure of succession of events and is the basic quantity in dynamics.

•  Mass
  Mass is the measure of inertia of a body which is it’s resistance to a change of velocity. OR
  Quantity of matter in a body.

•  Force
  Force is the action of one body on another. The action of a force is characterized by the magnitude, by the direction of its action and by its point of application.
  
  *Reaction is a resistance to the applied force in opposite direction. 

• Particle
  It is a body of negligible dimensions. We often choose a particle as a differential element of a body.

• Rigid Body
  A body is considered rigid when the change in distance between any two of its points is negligible. 

Newton's Laws 

• Law #1
  A particle remains at rest or continues to move with a uniform velocity (in a straight line with a constant speed) if there is no unbalanced force acting on it.

• Law #2
  The acceleration of a particle is proportional to sum of forces acting on it, and is in the direction of this vector sum.
  Mathematically;

 F ∝ a

 F = ma                                                            …….. (1)

• Law #3
  The force of action and reaction between interacting bodies are equal in magnitude, opposite in direction and collinear (they lie on the same line).

Law Of Gravitation

The mutual force of attraction between two particles is directly proportional to the ratio of the masses of the two particles to the distance between the centers of the particles.

Mathematically;

where,

F is equal to mutual force between particles,

G is the constant of Gravitation,

m₁ and m₂ is equal to masses of two particles, and,

r is equal to distance between centers of particles.

G = 6.673 x 10^-11 m³ kg^-1 s^-2 

Gravitational Attraction of the Earth

The gravitational attraction of the earth on a body (it’s weight) exists whether the body is at rest or in motion. For a body of mass “m” near the surface of the earth the gravitational attraction “F” on the body is denoted by the Equation 1. We usually denote magnitude of this gravitational force or weight with the symbol “W” because the body falls with an acceleration “g”.

Equation 1 gives,

W=mg

Where,

W is weight in Newton’s,

m is the mass in kilograms, and,

g is acceleration of gravity in m/s².

g = 9.81 m/s² = 32.2 ft/s²