Statics Of Rigid Bodies Chapter 1 e6q46

Mindanao State University Iligan Institute of Technology College of Engineering

Statics of Rigid Bodies Gevelyn Bontilao Itao, MOE

MECHANICS Mechanics - a branch of physical sciences which describes and predicts the condition of ret or motion of bodies that are subjected to the action of forces. MECHANICS

Rigid-Body Mechanics

Statics gsbitao_2012

Dynamics

Deformable-Body Mechanics

Fluid Mechanics

Two Areas of Rigid-Body Mechanics

Statics  deals with equilibrium of bodies, i.e., those that are either at rest or move with constant velocity Dynamics  deals with accelerated motion of bodies

gsbitao_2012

Fundamental Concepts Four Basic Quantities: Length  is used to locate the position of a point in space and describe the size of a physical system. Time is  is conceived as a succession of events. Mass  is a measure of a quantity of matter that is used to compare the action of one body with that of another .

Force  is the action of one body on another . gsbitao_2012

Definition of Idealizations:

Particle  has a mass, but a size that can be neglected. Rigid-body is  a combination of a large number of a particles in which all the particles remain at a fixed distance from one another, both before and after applying a load..

Concentrated Force  represents the effect of a loading which is assumed to act at a point on a body. gsbitao_2012

Six Fundamental Principles

1. The Parallelogram Law for the Addition of Forces  States that the two forces acting on a particle may be replaced by a single force which is called the RESULTANT FORCE. TOPIC

gsbitao_2012

Six Fundamental Principles 2. The Principle of Transmissibility  States that the condition of equilibrium or of motion of a rigid body will remain unchanged if a force, F, acting at a given point of rigid body is replaced by a force F’ of the same magnitude and same direction, TOPIC bur acting at a different point, provided that the forces have the same line of action.

gsbitao_2012

Six Fundamental Principles Newton’s Three Laws of Motion: 3. The First Law  If the resultant force acting on a particle is zero, the particle will remain at rest (if originally at rest) or will move with constant speed in a straight line (if originally in motion), provided that the particle is not TOPIC subjected to an unbalanced force.

gsbitao_2012

Six Fundamental Principles Newton’s Three Laws of Motion: 4. The Second Law  If the resultant force acting on a particle is not equal to zero (subjected to an unbalanced force), the particle will have an acceleration proportional to the magnitude of the resultant TOPIC and in the direction of this resultant force.

gsbitao_2012

Six Fundamental Principles Newton’s Three Laws of Motion: 5. The Third Law  The mutual forces of action and reaction between two bodies in have the same magnitude, same line of action and opposite sense. TOPIC

gsbitao_2012

Six Fundamental Principles 6. The Third Law  States that two particles of mass m1 and m2 are mutually attracted with equal and opposite forces, F and –F of magnitude F given by the formula TOPIC

gsbitao_2012

Systems of Units SI Units  Base Units: Length meter Time second Mass kilogram  Derived Unit: Force Newton 1N = 1 kg •m/sec2

gsbitao_2012

US Customary  Base Units: Length feet Time second Mass pounds  Derived Unit: Force Slug slug= 1 lb •sec2 / ft

Conversion Factor

gsbitao_2012

Prefixes of Units

gsbitao_2012

Methods of Problem Solving 1. Read the problem carefully and try to correlate the actual physical situation with the concepts. 2. Draw any necessary diagrams and tabulate the problem data. 3. Apply the relevant principles, generally in is mathematical form.

gsbitao_2012

4. Solve the necessary equations algebraically as far as practical, making sure they are dimensionally homogeneous. Use a consistent set of units and complete the solution numerically. 5. Study the answer with technical judgment and common sense to determine whether or not it seems reasonable.

Numerical Accuracy

The accuracy of the solutions of the problem depends upon 1. The accuracy of the given data. is

2. The accuracy of the computations performed.

gsbitao_2012

FORCE VECTORS

What is a FORCE?  We cannot measure force, only it effects: deformation of structures, acceleration. is

 Instead we hypothesize: A force applied to a particle is a vector. Motion is determined by vector sum. A particle remains at rest only if total force acting on it is zero.

gsbitao_2012

FORCE VECTORS Scalar  a quantity characterized by a positive or negative number  have magnitude but no direction, represented by plain numbers. is Vector  represented by a letter with an arrow over it (A). Graphically,  the length of an arrow (magnitude)  the angle between a reference axis and arrows line of action (direction)  indicated by the arrow head (sense) gsbitao_2012

Vector Operations

1. Vector Addition: A + B = R (Resultant Force) Methods of Vector Addition: a. Parallelogram Method TOPIC

gsbitao_2012

Vector Operations

1. Vector Addition: A + B = R (Resultant Force) Methods of Vector Addition: b. Head-to-Tail Method TOPIC

gsbitao_2012

Vector Operations

2. Vector Subtraction: A - B = R (Resultant Force) Methods of Vector Addition: a. Parallelogram Method TOPIC

gsbitao_2012

Vector Operations

3. Multiplication and Division of Vector by a Scalar: a x A = a A (Vector) If a is positive: the sense is the same as A TOPIC =is-1opposite to A If a is negative: the sense

Example: A = 2 a. If a = 2 b. If a = -1

gsbitao_2012

Vector Operations

4. Resolution of Vector - A vector maybe resolved into two components having known line of action using the parallelogram method. TOPIC

gsbitao_2012

Vector Operations

Law of SINE and COSINE:

TOPIC

gsbitao_2012

Vector Addition of Forces in Coplanar System

Example 1: The screw eye is subjected to two forces F1 and F2. Determine the magnitude and direction of the resultant force. is

gsbitao_2012

Vector Addition of Forces in Coplanar System Example 2: The forces F acting on the frame has a magnitude of 500N and is to be resolved into two components acting along AB and AC. Determine the angle Ө, measured below the horizontal, so that the isfrom A towards C and has a component FAC is directed magnitude of 400N. Determine also FAB .

gsbitao_2012

Addition of a System of Coplanar System Cartesian Unit Vectors - Used to designate the direction of the known axes in coplanar system is

gsbitao_2012

Addition of a System of Coplanar System Scalar Notation - The scalar component of F with respect to Ө, can be express as Is wit Fx = F cos Ө Fy = F sinH Ө

- And the direction of the force F can be obtained by

tan Ө = Fy /Fx - The magnitude of the force is then

F2 = Fx2 + Fy2 gsbitao_2012

Addition of a System of Coplanar System - For two or more forces

R = F1 + F 2 + F3 + … Fn = (Fx1i+Fy1j)+(Fx2i+F Isy2 witj)+(Fx3i+Fy3j)+…+(Fxni+Fynj) R = ΣFx i+ ΣFy j H

- And the direction of the resultant force R is then

tan Ө = ΣFy /ΣFx - The magnitude of the resultant force R is then

R2 = (ΣFx)2 + (ΣFy)2 gsbitao_2012

Addition of a System of Coplanar System

Example 1: The screw eye is subjected to two forces F1 and F2. Determine the magnitude and direction of the resultant force. is

gsbitao_2012

Addition of a System of Coplanar System Example 2: Determine the magnitude of the component force F and the magnitude of the resultant force FR if FR is directed along the positive is y axis.

gsbitao_2012