CE 201 - Statics Lecture 1

Contents Basic Principles (Chapter 1) Force Vectors (Chapter 2) Mechanics Basic Quantities Newton’s Laws of Motion Newton’s Law of Gravitational Attraction Units of Measurement Force Vectors (Chapter 2) Scalars and Vectors

Mechanics Mechanics is the branch of the physical sciences concerned with the state of rest or motion of bodies that are subjected to the action of forces.

Subdivisions of Mechanics Deformable Bodies Rigid Bodies Fluids Statics (At Rest) Dynamics (In Motion)

Definition of Some Basic Quantities Length: is needed to locate the position of a point in space and thereby describes the size of a physical system. Time: is conceived as a succession of events. Mass: is a property of matter by which we can compare the action of one body with that of another. This property manifests itself as a gravitational attraction between two bodies and provides a quantitative measure of the resistance of matter to a change in velocity. Force: is considered as a “push” or “pull” exerted by one body on another and it is characterized by its magnitude, direction, and point of application. Particle: A particle has a mass, but has a size that can be neglected. Rigid-Body: is 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. Concentrated Force: A concentrated force represents the effect of a loading which is assumed to act at a point on a body.

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 the particle IS NOT subjected to an unbalanced external force” Balanced Forces Particle at Rest Particle in Motion (v=0, a=0) (v>0, a=0) Stay at rest Stay in 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”. If ( F ) is applied to a particle of mass (m), this law may be expressed mathematically as: F = ma

Third Law “The mutual forces of action and reaction between two particles are equal in magnitude, opposite in direction and collinear in orientation”.

Newton’s Law of Gravitational Attraction A law governing the gravitational attraction between any two particles is mathematically stated as: F = G [m1  m2 / r2] Where F = force of gravitation between the two particles G = A universal constant of gravitation; (66.73x10-12 m3/kg s2) m1 and m2 = mass of each of the two particles r = the distance between the two particles

Weight Weight is the gravitational force between the earth and the particle. If we assume that: W = weight of the particle m = m1 = is the mass of the particle m2 = is the mass of the earth r = is the distance between the earth’s center and the particle Then: W = G [m  m2 / r2] Letting: g = G  m2 / r2 Therefore, from the second law of motion ( F = ma ): W = mg Where g = the acceleration due to gravity

Units of Measurements SI Units SI is known as the International System of Units where Length is in meters (m), time is in seconds (s), and mass is in kilograms (kg) and force is in Newton (N) (1 Newton is the force required to give 1 kilogram of mass an acceleration of 1 m/s2).

US Customary System of Units (FPS) FPS is the system of units where length is in feet (ft), time is in seconds (s), and force is in pounds (lb). The unit mass is called a slug (1 pound is the force required to give one slug of mass an acceleration of 1 ft/s2).

Conversion Factors Force; 1 lb = 4.4482 N Mass; slug = 14.5938 kg Length; ft = 0.304 m

Prefixes giga = G = 109 = 1,000,000,000 mega = M = 106 = 1,000,000 kilo = k = 103 = 1,000 milli = m = 10-3 = 0.001 micro = μ = 10-6 = 0.000 001 nano = η = 10-9 = 0.000 000 001

FORCE VECTORS Scalars and Vectors Scalar A quantity identified by positive or negative number. It is characterized by its magnitude only Elementary algebra is used when mathematical operations are involved Examples include mass, length, and volume Symbolized in Italic Type

Vector A quantity by its magnitude and direction Examples include force, moment, and displacement Symbolized in boldface type

Graphical Representation of a Vector Vectors are represented by ARROWS Magnitude is represented by the length of the arrow Direction is defined by  Vector A is written as A Line of Action  Head A Tail