statics

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STATICS TUTORIAL 2 UNIT 1 Force and
Equilibrium Chapter 3 Equilibrium of a Particle
Ir Dr Kanesan Muthusamy EBXS3103 Statics Jan 2005
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SEQUENCE OF CHAPTER 3

• Introduction
• Objectives
• 3.1 Condition for the Equilibrium of a particle
• 3.2 Free Body Diagram
• 3.2.1 Procedure for Drawing FBD
• 3.3 Coplanar Force Systems
• 3.3.1 Scalar Notation
• 3.3.2 Procedure for Analysis
• Summary

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Introduction

• In the proceeding sections, we have discussed the
  methods for determining the resultant of several
  forces acting on a particle.
• In some cases, we may find that the resultant of
  the forces acting on the particle is zero.
• In such cases the net effect of the given forces
  is zero and the particle is said to be in
  equilibrium.
• when the resultant of all the forces acting on
  the particle is zero, the particle is said to be
  in equilibrium

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Objectives

• At the end of this chapter, you should be able to
  
• 1. Introduce the concept of a free body diagram
  for a particle
• 2. Show how to solve the equilibrium problems for
  a particle using the equations of equilibrium.

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3.1 Condition for the Equilibrium of A Particle

• A particle is said to be in equilibrium if the
  particle
• is at rest (if originally at rest) or
• has a constant velocity (if originally in
  motion).
• Normally, however, the term equilibrium of more
  precisely static equilibrium is used to
  describe an object at rest. To maintain
  equilibrium, it is necessary to satisfy Newtons
  first law of motion.
• Newtons first law of motion requires that the
  resultant force acting on a particle to be equal
  to zero. This condition may be expressed as

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3.1 Condition for the Equilibrium of A Particle

• Newtons first law of motion requires that the
  resultant force acting on a particle to be equal
  to zero. This condition may be expressed as
• ?F 0
• where ? F is the vector sum of all the forces
  acting on a particle.

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3.2 Free Body Diagram (FBD)

• The equation of equilibrium can only be applied
  if all the known and unknown forces acting on the
  particles are taken into account.
• The best possible way to do this is to draw the
  particles free-body diagram.
• This diagram is simply a sketch which shows the
  particle free from its surrounding with all the
  forces acting on it.

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3.2.1 Procedure for Drawing FBD

• To construct a free-body diagram, the following
  steps are necessary
• Draw Outline Shape
• Imagine that the particle is cut free from its
  surroundings or isolated by drawing the outline
  shape of the particle only
• Show All Forces
• Show on this sketch all the forces acting on
  the particle. There are two class of forces that
  act on the particle. They can be active forces,
  which tend to set the particle in motion, or
  they can be reactive forces which are the
  results of the constraints or supports that tend
  to prevent motion.
• Identify Each Force
• The forces that are known should be labeled
  complete with their magnitudes and directions.
  Letters are used to represent the magnitudes and
  directions of forces that are not known.

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3.3 Coplanar Force Systems

• In the case of a particle subjected to a system
  of coplanar forces that lie in the x-y plane as
  shown in Figure 3.1, then each and every force
  can be resolved into its own i and j components.

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3.3 Coplanar Force Systems

• For equilibrium condition, the equation can be
  written as
• ?F 0
• ?Fx i ?Fy j 0
• For both of these vector equations above to be
  valid, then both the x and y components must be
  equal to zero. Hence,
• ?Fx 0 F1x F2x ..
• ?Fy 0 F1y F2y ..
• The scalar equations of equilibrium shown above
  require that the algebraic sum of the x and y
  components of all the forces acting on the
  particle must be equal to zero.

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3.3.1 Scalar Notation

• Since each of these two equilibrium equations
  requires the resolution of vector components
  along the specified x and y axes, the scalar
  notation will be used to represent the components
  when applying these equations
• Consider the free-body diagram of the particle
  subjected to the two forces shown in Figure 3.2.
  Here, initially we can assumed that the unknown
  force F acts to the right to maintain
  equilibrium. Applying the equation of equilibrium
  along the x axis,

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3.3.1 Scalar Notation

• ?Fx 0 F 10N 0
• Both terms are positive since both forces act in
  the positive x direction.
• When this equation is solved, we will get F -10
  N. Here the negative sign indicates that F must
  act to the left to hold the particle in
  equilibrium (Figure 3.2).

??
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3.3.2 Procedure for Analysis

• Coplanar force equilibrium problems for a
  particle can be analyzed using the following
  procedure.
• 1. Free-Body Diagram
• 2. Establish the x and y axes is any suitable
  orientation
• 3. Label all the known and unknown force
  magnitudes and directions on the diagram.
• 4. The sense of a force having an unknown
  magnitude can be initially assumed.
• 5. Equations Of Equilibrium
• Apply the equations of equilibrium ?Fx 0 and
  ?Fy 0 .
• Components are positive if they are directed
  along a positive axis and negative if they are
  directed along the negative axis.
• 6. If the solution gives a negative result, this
  indicates that the sense of the force is
  reverse of that shown on the free-body diagram.

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Example 3.1

• Determine the tension in cables AB and AD for
  equilibrium of the 2500 N engine shown in Figure
  Example 1 (a).

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Example 3.1

• In order to solve this problem, we will
  investigate the equilibrium of the ring at A
  because this particle is subjected to forces of
  both cables AB and AD.
• There are three concurrent forces acting on the
  ring.
• The forces TB and TD have unknown magnitudes but
  known directions and cable CA exerts a downward
  force on A equal to 2500 N.

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Example 3.1

• The two unknown magnitudes TB and TD can be
  obtained from the two scalar equations for
  equilibrium
• ?FX 0 and ?FY 0.

• To apply these equations, the x and y axes are
  established on the free-body diagram and TB must
  be resolved into its x and y components.

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Example 3.1

• ?Fx 0 TB cos 30 TD 0
• ?Fy 0 TB sin 30 2500 0
• Solving the above two equations, yields,
• TB 4900 N
• TD 4250 N

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Summary

• This chapter has summarized on the aspect below
• concept of equilibrium of a particle.
• method of isolating the body under the action of
  system of forces using the concept of free-body
  diagram (FBD).
• procedure for solving the problems involving the
  particle using the equations of equilibrium.

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• Thank You