SlideShare une entreprise Scribd logo
1  sur  7
Télécharger pour lire hors ligne
Chapter Objectives
•Develop the equations of equilibrium for a
rigid body
•Concept of the free-body diagram for a
rigid body
•Solve rigid-body equilibrium problems
using the equations of equilibrium
When all the forces that act upon an object are balanced, then the object is said to be in a state of
equilibrium.
If an object is at equilibrium, then the forces are balanced. Balanced is the key word that is used
to describe equilibrium situations. Thus, the net force is zero and the acceleration is 0 m/s/s.
Objects at equilibrium must have an acceleration of 0 m/s/s. This extends from Newton's first
law of motion. But having an acceleration of 0 m/s/s does not mean the object is at rest. An
object at equilibrium is either ...
 at rest and staying at rest, or
 in motion and continuing in motion with the same speed and direction.
If an object is at rest and is in a state of equilibrium, then we would say that the object is at
"static equilibrium." "Static" means stationary or at rest.
The state of the object is analyzed in terms of the forces acting upon the object. The object is a
point on a string upon which three forces were acting. See diagram at right. If the object is at
equilibrium, then the net force acting upon the object should be 0 Newton. Thus, if all the forces
are added together as vectors, then the resultant force (the vector sum) should be 0 Newton.
(Recall that the net force is "the vector sum of all the forces" or the resultant of adding all the
individual forces head-to-tail.) Thus, an accurately drawn vector addition diagram can be
constructed to determine the resultant. Sample data for such a lab are shown below.
Force A Force B Force C
Magnitude 3.4 N 9.2 N 9.8 N
Direction 161 deg. 70 deg. 270 deg
Another way of determining the net force (vector sum of all the forces) involves using the
trigonometric functions to resolve each force into its horizontal and vertical components. Once
the components are known, they can be compared to see if the vertical forces are balanced and if
the horizontal forces are balanced. The diagram below shows vectors A, B, and C and their
respective components. For vectors A and B, the vertical components can be determined using
the sine of the angle and the horizontal components can be analyzed using the cosine of the
angle. The magnitude and direction of each component for the sample data are shown in the table
below the diagram.
The data in the table above show that the forces nearly balance. An analysis of the horizontal
components shows that the leftward component of A nearly balances the rightward component
of B. An analysis of the vertical components show that the sum of the upward components of A
+ B nearly balance the downward component of C. The vector sum of all the forces is (nearly)
equal to 0 Newton. But what about the 0.1 N difference between rightward and leftward forces
and the 0.2 N difference between the upward and downward forces? Why do the components of
force only nearly balance? The sample data used in this analysis are the result of measured data
from an actual experimental setup. The difference between the actual results and the expected
results is due to the error incurred when measuring force A and force B. We would have to
conclude that this low margin of experimental error reflects an experiment with excellent results.
We could say it's "close enough for government work."
The equilibrium of a body is expressed as
FR=∑F=0 , (∑MR)o=∑Mo=0
Consider summing moments about some
other point, such as point A, we require
∑MA= r X FR +(MR)O=0
For equilibrium of a rigid body in 2D,
ΣFx= 0; ΣFy= 0; ΣMO= 0
•ΣFxand ΣFyrepresent sums of x and y
components of all the forces
•ΣMOrepresents the sum of the couple
moments and moments of the force
components
Free Body Diagrams- Support
Reactions :
• If a support prevents the translation of a
body in a given direction, then a force is
developed on the body in that direction.
• If rotation is prevented, a couple moment
is exerted on the body.
Free Body Diagrams-Internal
Forces:
•External and internal forces can act on a
rigid body
•For FBD, internal forces act between
particles which are contained within the
boundary of the FBD, are not represented
•Particles outside this boundary exert
external forces on the system
Weight and Center of Gravity
•Each particle has a specified weight
•System can be represented by a single
resultant force, known as weight Wof the
body
•Location of the force application is known
as the center of gravity
Procedure for Drawing a FBD:
1. Draw Outlined Shape
•Imagine body to be isolated or cut free
from its constraints
2. Show All Forces and Couple Moments
•Identify all external forces and couple
moments that act on the body
Procedure for Analysis
Equations of Equilibrium
•Apply ΣMO= 0 about a point O
•Unknowns moments of are zero about O
and a direct solution the third unknown can
be obtained
•Orient the x and y axes along the lines that
will provide the simplest resolution of the
forces into their x and y components
•Negative result scalar is opposite to that
was assumed on the FBD

Contenu connexe

Tendances

Engineering Mechanice Lecture 06
Engineering Mechanice Lecture 06Engineering Mechanice Lecture 06
Engineering Mechanice Lecture 06Self-employed
 
Basics and statics of particles unit i - GE6253 PPT
Basics and statics of particles   unit i - GE6253 PPTBasics and statics of particles   unit i - GE6253 PPT
Basics and statics of particles unit i - GE6253 PPTTHANGA KASI RAJAN S
 
Presentation on Equilibrium and Equilibrium equation 2D
Presentation on Equilibrium and Equilibrium equation 2DPresentation on Equilibrium and Equilibrium equation 2D
Presentation on Equilibrium and Equilibrium equation 2DToufiq Rifath
 
Equilibrium & equation of equilibrium in 3D
Equilibrium & equation of equilibrium in 3DEquilibrium & equation of equilibrium in 3D
Equilibrium & equation of equilibrium in 3Dimoinul007
 
Presentation on free body diagram 10.01.03.119
Presentation on free body diagram 10.01.03.119Presentation on free body diagram 10.01.03.119
Presentation on free body diagram 10.01.03.119Safa Rahman
 
(2) equilibrium
(2) equilibrium(2) equilibrium
(2) equilibriumphysics101
 
Mechanical Equilibrium acloutier copyright 2011
Mechanical Equilibrium acloutier copyright 2011Mechanical Equilibrium acloutier copyright 2011
Mechanical Equilibrium acloutier copyright 2011Annie C. Cloutier
 
Equilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2DEquilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2Drasel2211
 
COPLANNER & NON-CONCURRENT FORCES
COPLANNER & NON-CONCURRENT FORCESCOPLANNER & NON-CONCURRENT FORCES
COPLANNER & NON-CONCURRENT FORCESAkash Patel
 
G9 asp. 2.3 position time graph
G9 asp.  2.3 position time graphG9 asp.  2.3 position time graph
G9 asp. 2.3 position time graphMajed Allah
 
Engineering mechanics fundamentals 2018 ghaffar sir
Engineering mechanics fundamentals 2018 ghaffar sirEngineering mechanics fundamentals 2018 ghaffar sir
Engineering mechanics fundamentals 2018 ghaffar sirabdul ghaffar
 
Engineering Mechanice Lecture 02
Engineering Mechanice Lecture 02Engineering Mechanice Lecture 02
Engineering Mechanice Lecture 02Self-employed
 
Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)
Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)
Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)Fariya Rahman Moho
 
Fundamentals of statics
Fundamentals of statics Fundamentals of statics
Fundamentals of statics sujay762
 
Study of free body diagram
Study of free body diagramStudy of free body diagram
Study of free body diagramHafiz Talha
 
6161103 5.3 equations of equilibrium
6161103 5.3 equations of equilibrium6161103 5.3 equations of equilibrium
6161103 5.3 equations of equilibriumetcenterrbru
 
Concurrent Forces
Concurrent ForcesConcurrent Forces
Concurrent Forcesguestb54490
 

Tendances (18)

Engineering Mechanice Lecture 06
Engineering Mechanice Lecture 06Engineering Mechanice Lecture 06
Engineering Mechanice Lecture 06
 
Basics and statics of particles unit i - GE6253 PPT
Basics and statics of particles   unit i - GE6253 PPTBasics and statics of particles   unit i - GE6253 PPT
Basics and statics of particles unit i - GE6253 PPT
 
Presentation on Equilibrium and Equilibrium equation 2D
Presentation on Equilibrium and Equilibrium equation 2DPresentation on Equilibrium and Equilibrium equation 2D
Presentation on Equilibrium and Equilibrium equation 2D
 
Equilibrium & equation of equilibrium in 3D
Equilibrium & equation of equilibrium in 3DEquilibrium & equation of equilibrium in 3D
Equilibrium & equation of equilibrium in 3D
 
Presentation on free body diagram 10.01.03.119
Presentation on free body diagram 10.01.03.119Presentation on free body diagram 10.01.03.119
Presentation on free body diagram 10.01.03.119
 
(2) equilibrium
(2) equilibrium(2) equilibrium
(2) equilibrium
 
Mechanical Equilibrium acloutier copyright 2011
Mechanical Equilibrium acloutier copyright 2011Mechanical Equilibrium acloutier copyright 2011
Mechanical Equilibrium acloutier copyright 2011
 
Free body diagram
Free body diagramFree body diagram
Free body diagram
 
Equilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2DEquilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2D
 
COPLANNER & NON-CONCURRENT FORCES
COPLANNER & NON-CONCURRENT FORCESCOPLANNER & NON-CONCURRENT FORCES
COPLANNER & NON-CONCURRENT FORCES
 
G9 asp. 2.3 position time graph
G9 asp.  2.3 position time graphG9 asp.  2.3 position time graph
G9 asp. 2.3 position time graph
 
Engineering mechanics fundamentals 2018 ghaffar sir
Engineering mechanics fundamentals 2018 ghaffar sirEngineering mechanics fundamentals 2018 ghaffar sir
Engineering mechanics fundamentals 2018 ghaffar sir
 
Engineering Mechanice Lecture 02
Engineering Mechanice Lecture 02Engineering Mechanice Lecture 02
Engineering Mechanice Lecture 02
 
Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)
Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)
Equilibrium & Equation of Equilibrium : 2 D (ID no:10.01.03.014)
 
Fundamentals of statics
Fundamentals of statics Fundamentals of statics
Fundamentals of statics
 
Study of free body diagram
Study of free body diagramStudy of free body diagram
Study of free body diagram
 
6161103 5.3 equations of equilibrium
6161103 5.3 equations of equilibrium6161103 5.3 equations of equilibrium
6161103 5.3 equations of equilibrium
 
Concurrent Forces
Concurrent ForcesConcurrent Forces
Concurrent Forces
 

En vedette (6)

Week 1 - WWI and Treaty of Versailles
Week 1 - WWI and Treaty of VersaillesWeek 1 - WWI and Treaty of Versailles
Week 1 - WWI and Treaty of Versailles
 
2 gaia
2 gaia2 gaia
2 gaia
 
Sample2
Sample2Sample2
Sample2
 
Pp -wk two-- 5593--
Pp -wk two-- 5593--Pp -wk two-- 5593--
Pp -wk two-- 5593--
 
Proyecto Comenius Sports For Peace
Proyecto Comenius  Sports For PeaceProyecto Comenius  Sports For Peace
Proyecto Comenius Sports For Peace
 
Similarities & differences
Similarities & differencesSimilarities & differences
Similarities & differences
 

Similaire à Weebly

How to Prepare Rotational Motion (Physics) for JEE Main
How to Prepare Rotational Motion (Physics) for JEE MainHow to Prepare Rotational Motion (Physics) for JEE Main
How to Prepare Rotational Motion (Physics) for JEE MainEdnexa
 
Engineering Mechanics Chapter 5 Equilibrium of a Rigid Body
Engineering Mechanics  Chapter 5  Equilibrium of a Rigid BodyEngineering Mechanics  Chapter 5  Equilibrium of a Rigid Body
Engineering Mechanics Chapter 5 Equilibrium of a Rigid BodyAhmadHajasad2
 
Equilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2DEquilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2Drasel2211
 
Engineering Mechanics.pptx
Engineering Mechanics.pptxEngineering Mechanics.pptx
Engineering Mechanics.pptxYogesh Kulkarni
 
Momento en estructuras
Momento en estructurasMomento en estructuras
Momento en estructurasRol D
 
4 intro to fbd chap3.1and3.2
4  intro to fbd chap3.1and3.24  intro to fbd chap3.1and3.2
4 intro to fbd chap3.1and3.2VigneshN59
 
System Isolation and the Free-Body Diagram
System Isolation and the Free-Body DiagramSystem Isolation and the Free-Body Diagram
System Isolation and the Free-Body DiagramShahzaib Farooq
 
Engineering Mechanics - Intro to Statics.pdf
Engineering Mechanics - Intro to Statics.pdfEngineering Mechanics - Intro to Statics.pdf
Engineering Mechanics - Intro to Statics.pdfYogesh Kulkarni
 
moments couples and force couple systems by ahmad khan
moments couples and force couple systems by ahmad khanmoments couples and force couple systems by ahmad khan
moments couples and force couple systems by ahmad khanSelf-employed
 

Similaire à Weebly (20)

How to Prepare Rotational Motion (Physics) for JEE Main
How to Prepare Rotational Motion (Physics) for JEE MainHow to Prepare Rotational Motion (Physics) for JEE Main
How to Prepare Rotational Motion (Physics) for JEE Main
 
Engineering Mechanics Chapter 5 Equilibrium of a Rigid Body
Engineering Mechanics  Chapter 5  Equilibrium of a Rigid BodyEngineering Mechanics  Chapter 5  Equilibrium of a Rigid Body
Engineering Mechanics Chapter 5 Equilibrium of a Rigid Body
 
4773390
47733904773390
4773390
 
Applied mechanics
Applied mechanicsApplied mechanics
Applied mechanics
 
Applied mechanics
Applied mechanicsApplied mechanics
Applied mechanics
 
Ctm 154[1]
Ctm 154[1]Ctm 154[1]
Ctm 154[1]
 
Me211 1
Me211 1Me211 1
Me211 1
 
Equilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2DEquilibrium and Equation of Equilibrium:2D
Equilibrium and Equation of Equilibrium:2D
 
Engineering Mechanics.pptx
Engineering Mechanics.pptxEngineering Mechanics.pptx
Engineering Mechanics.pptx
 
12475602.ppt
12475602.ppt12475602.ppt
12475602.ppt
 
12475602.ppt
12475602.ppt12475602.ppt
12475602.ppt
 
Momento en estructuras
Momento en estructurasMomento en estructuras
Momento en estructuras
 
MECHANICS OF SOLID
MECHANICS OF SOLIDMECHANICS OF SOLID
MECHANICS OF SOLID
 
4 intro to fbd chap3.1and3.2
4  intro to fbd chap3.1and3.24  intro to fbd chap3.1and3.2
4 intro to fbd chap3.1and3.2
 
System Isolation and the Free-Body Diagram
System Isolation and the Free-Body DiagramSystem Isolation and the Free-Body Diagram
System Isolation and the Free-Body Diagram
 
EQUILIBRIUM-TOPIC.pdf
EQUILIBRIUM-TOPIC.pdfEQUILIBRIUM-TOPIC.pdf
EQUILIBRIUM-TOPIC.pdf
 
KMCH Basic Biomechanics.ppt
KMCH Basic Biomechanics.pptKMCH Basic Biomechanics.ppt
KMCH Basic Biomechanics.ppt
 
Engineering Mechanics - Intro to Statics.pdf
Engineering Mechanics - Intro to Statics.pdfEngineering Mechanics - Intro to Statics.pdf
Engineering Mechanics - Intro to Statics.pdf
 
moments couples and force couple systems by ahmad khan
moments couples and force couple systems by ahmad khanmoments couples and force couple systems by ahmad khan
moments couples and force couple systems by ahmad khan
 
Physics
PhysicsPhysics
Physics
 

Weebly

  • 1. Chapter Objectives •Develop the equations of equilibrium for a rigid body •Concept of the free-body diagram for a rigid body •Solve rigid-body equilibrium problems using the equations of equilibrium When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium. If an object is at equilibrium, then the forces are balanced. Balanced is the key word that is used to describe equilibrium situations. Thus, the net force is zero and the acceleration is 0 m/s/s. Objects at equilibrium must have an acceleration of 0 m/s/s. This extends from Newton's first law of motion. But having an acceleration of 0 m/s/s does not mean the object is at rest. An object at equilibrium is either ...  at rest and staying at rest, or  in motion and continuing in motion with the same speed and direction. If an object is at rest and is in a state of equilibrium, then we would say that the object is at "static equilibrium." "Static" means stationary or at rest. The state of the object is analyzed in terms of the forces acting upon the object. The object is a point on a string upon which three forces were acting. See diagram at right. If the object is at equilibrium, then the net force acting upon the object should be 0 Newton. Thus, if all the forces are added together as vectors, then the resultant force (the vector sum) should be 0 Newton. (Recall that the net force is "the vector sum of all the forces" or the resultant of adding all the individual forces head-to-tail.) Thus, an accurately drawn vector addition diagram can be constructed to determine the resultant. Sample data for such a lab are shown below.
  • 2. Force A Force B Force C Magnitude 3.4 N 9.2 N 9.8 N Direction 161 deg. 70 deg. 270 deg Another way of determining the net force (vector sum of all the forces) involves using the trigonometric functions to resolve each force into its horizontal and vertical components. Once the components are known, they can be compared to see if the vertical forces are balanced and if the horizontal forces are balanced. The diagram below shows vectors A, B, and C and their respective components. For vectors A and B, the vertical components can be determined using the sine of the angle and the horizontal components can be analyzed using the cosine of the angle. The magnitude and direction of each component for the sample data are shown in the table below the diagram.
  • 3. The data in the table above show that the forces nearly balance. An analysis of the horizontal components shows that the leftward component of A nearly balances the rightward component of B. An analysis of the vertical components show that the sum of the upward components of A + B nearly balance the downward component of C. The vector sum of all the forces is (nearly) equal to 0 Newton. But what about the 0.1 N difference between rightward and leftward forces and the 0.2 N difference between the upward and downward forces? Why do the components of force only nearly balance? The sample data used in this analysis are the result of measured data from an actual experimental setup. The difference between the actual results and the expected results is due to the error incurred when measuring force A and force B. We would have to conclude that this low margin of experimental error reflects an experiment with excellent results. We could say it's "close enough for government work." The equilibrium of a body is expressed as FR=∑F=0 , (∑MR)o=∑Mo=0 Consider summing moments about some other point, such as point A, we require
  • 4. ∑MA= r X FR +(MR)O=0 For equilibrium of a rigid body in 2D, ΣFx= 0; ΣFy= 0; ΣMO= 0 •ΣFxand ΣFyrepresent sums of x and y components of all the forces •ΣMOrepresents the sum of the couple moments and moments of the force components Free Body Diagrams- Support Reactions : • If a support prevents the translation of a body in a given direction, then a force is developed on the body in that direction. • If rotation is prevented, a couple moment is exerted on the body.
  • 5. Free Body Diagrams-Internal Forces: •External and internal forces can act on a rigid body •For FBD, internal forces act between particles which are contained within the boundary of the FBD, are not represented •Particles outside this boundary exert external forces on the system Weight and Center of Gravity •Each particle has a specified weight
  • 6. •System can be represented by a single resultant force, known as weight Wof the body •Location of the force application is known as the center of gravity Procedure for Drawing a FBD: 1. Draw Outlined Shape •Imagine body to be isolated or cut free from its constraints 2. Show All Forces and Couple Moments •Identify all external forces and couple moments that act on the body Procedure for Analysis Equations of Equilibrium •Apply ΣMO= 0 about a point O •Unknowns moments of are zero about O and a direct solution the third unknown can be obtained
  • 7. •Orient the x and y axes along the lines that will provide the simplest resolution of the forces into their x and y components •Negative result scalar is opposite to that was assumed on the FBD