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STATICS

Lecture 2

Chapter 1: Introduction to Statics

Izzuddin Zaman

Faculty of Mechanical and Manufacturing Engineering

UTHM

1

What is Statics?

• Statics is actually the application of mathematics and basic

physics (Newton’s laws) to study forces in materials, machines and structures. Forces are of interest to engineers for two reasons:

1. they cause materials to deform and break, and
2. they cause things to move.

• Statics is used to calculate forces in systems that don’t move,

or move at constant velocity. The application of physics to study

motion is known as dynamics.

Structural engineers – Design buildings and structures, Mechanical engineers – Design machinery, which may range from engines to micro electro-mechanical systems. Biomedical engineers – Design artificial organs and implants.

Fundamental Concepts

Basic Quantities

• Length - associated with the notion of the position of a point P given in terms of three coordinates measured from a reference point or origin.
• Time - definition of an event requires specification of the time and position at which it occurred
• Mass - used to characterize and compare bodies, e.g., response to earth’s gravitational attraction and resistance to changes in translational motion.
• Force - represents the action of one body on another. A force is characterized by its point of application, magnitude, and direction, i.e., a force is a vector quantity.

Fundamental Principles

• Two forces acting on a particle may be replaced by a single force, called their resultant, obtained by drawing the diagonal of the parallelogram which has sides equal to the given forces
• condition of equilibrium or of motion of a rigid body will remain unchanged if a force acting at a given point of the rigid body is replaced by a force of the same magnitude and same direction, but acting at a different point, provided that the two forces have the same line of action
  • Parallelogram Law
• Principle of Transmissibility

Parallelogram Law for the addition of forces :

Principle of Transmissibility :

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”

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”

F  ma

Newton’s Law of Gravitational

Attraction

2

1 2

r

m m F  G

F = force of gravitation between two particles

G = universal constants of gravitation

m1,m2 = mass of each of the two particles

r = distance between the two particles

Newton’s Law of Gravitational

Attraction

• The force F exerted by the earth on a particle is defined as the

weight W of the particle

M = mass of the earth

m = mass of the particle

R = radius of the earth

• The magnitude W of the weight of a particle of mass m :

R

GM g 

W  mg

Units of Measurement

At the standard location,

g = 9.806 65 m/s^2

• For calculations, we use

g = 9.81 m/s^2

Thus,

W = mg (g = 9.81m/s^2 )

Hence, a body of mass 1 kg has a weight of 9.81 N,

a 2 kg body weighs 19.62 N

Prefixes

Izzuddin-FKMP 14

For a very large or very small numerical quantity, the units can be modified by using a prefix

Each represent a multiple or sub-multiple of a unit

E.g.: 4,000,000 N = 4000 kN (kilo-newton)

= 4 MN (mega- newton)

0.005m = 5 mm (mili-meter)

Exponential Form

Prefix SI Symbol

Multiple 1 000 000 000 109 Giga G 1 000 000 106 Mega M 1 000 103 Kilo k Sub-Multiple 0.001 10 -3^ Milli m 0.000 001 10 -6^ Micro μ 0.000 000 001 10 -9^ nano n