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PHILIPPINE STATE COLLEGE OF AERONAUTICS

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

1|P a g e

LEARNING

MODULE 02:–

Resultant of Force

System

AMT 3102-

ENGINEERING MECHANICS

Prepared by:

ENGR. CARMELITA C. ARBOZO

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

1|P a g e

LEARNING

MODULE 02:–

Resultant of Force

System

AMT 3102-

ENGINEERING MECHANICS

Prepared by:

ENGR. CARMELITA C. ARBOZO

PHILIPPINE STATE COLLEGE OF AERONAUTICS

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

2|P a g e

TABLE OF CONTENTS

TitlePageAllotted time

Introduction410minutes

Resultant of Two Forces4,515minutes

➢Example Solved Problems6,7,8,930minutes

➢Problem Solving Activity No.No.21026.14minutes

Resultant of Concurrent Force System11,1215minutes

➢Example Solved Problems13,14,1540 minutes

➢Problem Solving Activity No.31630minutes

Moment of a Force17,18,1915minutes

➢Example Solved Problems20,21,2240 minutes

➢Problem Solving Activity No.42330 minutes

Resultant of Parallel Forces2415minutes

➢Example Solved Problems25,26,27,2830 minutes

➢Problem SolvingActivity No.52930minutes

Couples3015minutes

➢Example Solved Problems31,32,3340minutes

➢Problem Solving Activity No.63430minutes

Resultant of Non-Concurrent Forces3515minutes

➢Example Solved Problems36,3740minutes

➢Problem SolvingActivity No.73830minutes

441.24 minutes

TABLES OF REFERENCES

ReferencesNo.

Materials (textbooks, references, journals, online)1

Singer, Ferdinand L., Engineering Mechanics: Statics and Dynamics2

Mcgill, David J., EngineeringMechanics: Statics and an Intro to Dynamics3

Singer, F.L (1954). Engineering Mechanics (2nd Ed.) New York: Harpens

and Row, Publishers, Inc.4

Hibbeler, R.C. (2010) Engineering Mechanics (12th Ed.) New Jersey:

Pearson Prentice Hall5

Beer,F.P.& Johnston, Jr.E.R.(2016) Vector Mechanics for Engineers Static

(11thEd.) New York: McGraw-Hill Education6

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

2|P a g e

TABLE OF CONTENTS

TitlePageAllotted time

Introduction410minutes

Resultant of Two Forces4,515minutes

➢Example Solved Problems6,7,8,930minutes

➢Problem Solving Activity No.No.21026.14minutes

Resultant of Concurrent Force System11,1215minutes

➢Example Solved Problems13,14,1540 minutes

➢Problem Solving Activity No.31630minutes

Moment of a Force17,18,1915minutes

➢Example Solved Problems20,21,2240 minutes

➢Problem Solving Activity No.42330 minutes

Resultant of Parallel Forces2415minutes

➢Example Solved Problems25,26,27,2830 minutes

➢Problem SolvingActivity No.52930minutes

Couples3015minutes

➢Example Solved Problems31,32,3340minutes

➢Problem Solving Activity No.63430minutes

Resultant of Non-Concurrent Forces3515minutes

➢Example Solved Problems36,3740minutes

➢Problem SolvingActivity No.73830minutes

441.24 minutes

TABLES OF REFERENCES

ReferencesNo.

Materials (textbooks, references, journals, online)1

Singer, Ferdinand L., Engineering Mechanics: Statics and Dynamics2

Mcgill, David J., EngineeringMechanics: Statics and an Intro to Dynamics3

Singer, F.L (1954). Engineering Mechanics (2nd Ed.) New York: Harpens

and Row, Publishers, Inc.4

Hibbeler, R.C. (2010) Engineering Mechanics (12th Ed.) New Jersey:

Pearson Prentice Hall5

Beer,F.P.& Johnston, Jr.E.R.(2016) Vector Mechanics for Engineers Static

(11thEd.) New York: McGraw-Hill Education6

PHILIPPINE STATE COLLEGE OF AERONAUTICS

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

3|P a g e

Course Learning Outcomes [CLO]

CLO1.Applytheknowledgeof

mathematicstosolvecomplex

mechanicsproblems;

CLO2.Utilizescientificconcepts,laws

andtheoriesinsolvingproblemsrelated

totheirfieldofspecialization;

CLO3.Conveyageneralunderstanding

ofengineeringmechanicsasawayto

associatetheirknowledgeintheir

chosencourse;

CLO10.Demonstratehonestyindoing

individual/groupworkonthiscourse.

Module Learning Outcomes [MLO]

MLO01.Solveproblemsofthreeormore

concurrentforcesbyusingtherectangular

componentsofavectortodetermine

magnitudeanddirection.

MLO02.Fofrmulatethemomentofaforce

aboutasecifiedaxisthroughhands-on

problemsolving.

MLO03.Determineresultantsofparallel

forcesbydemosntartingtheproper

procedures.

MLO04.Computingresolutionofforceinto

aforceandacouplethroughsample

problems

Topic Learning Outcomes [TLO]

TLO04.Resolveforcesintotheir

rectangularcomponentsandrepresent

theneteffectofdifferentforcesystems

intoaresultantthroughproblems

solving.

TLO05.Computemomentofforce

aboutaspecifiedaxisbydemonstrating

thepropermethod.

TLO06.Solveresultantforceofnon-

concurrentforcesthroughpractice

problems.

This module discussesForce and Components,Resultant of Coplanar Concurrent

Force System,Moment of a Force,Resultant of ParallelForces,Couples,Resultant

of Non-Concurrent Forces.

LEARNING OUTCOMES

HONESTY CLAUSE

As a state college, students are expected to uphold and integrity, principle and self-

respect, using their knowledge and skills for theenhancement of human welfare and

environment; being honest and fair in their class activity, requirements and other

projects will not engage in cheating or plagiarism. The institution undertakes as a

modestandnominalidealofbehaviorsinacademicmattersthatstudentsbe

straightforward and that they distribute for deposit solely the produce of their particular

efforts.

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

3|P a g e

Course Learning Outcomes [CLO]

CLO1.Applytheknowledgeof

mathematicstosolvecomplex

mechanicsproblems;

CLO2.Utilizescientificconcepts,laws

andtheoriesinsolvingproblemsrelated

totheirfieldofspecialization;

CLO3.Conveyageneralunderstanding

ofengineeringmechanicsasawayto

associatetheirknowledgeintheir

chosencourse;

CLO10.Demonstratehonestyindoing

individual/groupworkonthiscourse.

Module Learning Outcomes [MLO]

MLO01.Solveproblemsofthreeormore

concurrentforcesbyusingtherectangular

componentsofavectortodetermine

magnitudeanddirection.

MLO02.Fofrmulatethemomentofaforce

aboutasecifiedaxisthroughhands-on

problemsolving.

MLO03.Determineresultantsofparallel

forcesbydemosntartingtheproper

procedures.

MLO04.Computingresolutionofforceinto

aforceandacouplethroughsample

problems

Topic Learning Outcomes [TLO]

TLO04.Resolveforcesintotheir

rectangularcomponentsandrepresent

theneteffectofdifferentforcesystems

intoaresultantthroughproblems

solving.

TLO05.Computemomentofforce

aboutaspecifiedaxisbydemonstrating

thepropermethod.

TLO06.Solveresultantforceofnon-

concurrentforcesthroughpractice

problems.

This module discussesForce and Components,Resultant of Coplanar Concurrent

Force System,Moment of a Force,Resultant of ParallelForces,Couples,Resultant

of Non-Concurrent Forces.

LEARNING OUTCOMES

HONESTY CLAUSE

As a state college, students are expected to uphold and integrity, principle and self-

respect, using their knowledge and skills for theenhancement of human welfare and

environment; being honest and fair in their class activity, requirements and other

projects will not engage in cheating or plagiarism. The institution undertakes as a

modestandnominalidealofbehaviorsinacademicmattersthatstudentsbe

straightforward and that they distribute for deposit solely the produce of their particular

efforts.

PHILIPPINE STATE COLLEGE OF AERONAUTICS

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

4|P a g e

INTRODUCTION

The forceis an important factor in the field of Mechanics, which maybebroadly

*defined as an agentwhichproducesor tends to produce, destroys ortendsto destroy

motion. e.g., a horse applies force to pull a cart and to set it in motion. Force is also

required towork on a bicycle pump. In this case, the force issupplied by the muscular

power of our arms andshoulders.

Resultant of Two Forces

•Force action of one body on another,

characterizedbyitspointof

application, magnitude, line of action

and sense.

•Experimentalevidenceshowsthat

thecombinedeffectoftwoforces

mayberepresentedbyasingle

resultant force.

•Theresultantisequivalenttothe

diagonalofaparallelogramwhich

contains the two forces in adjacent

legs.

•Force is a vector quantity.

Figure2.0(©Ferdinand P. Beer & E.

Russell Johnston, Jr.)

Vectors

•Vector: parameters possessing magnitude and direction

whichaddaccordingtotheparallelogramlaw.

Examples: displacements, velocities, accelerations

•Scalar:parameterspossessingmagnitudebutnot

direction. Examples: mass, volume, temperature.

•Vectorclassifications:

✓Fixedorboundvectorshavewelldefinedof

application that cannot be changed without affecting

an analysis.

✓Free vectors may be freely moved in space without

changing their effect on an analysis.

✓Sliding vectors may be appliedanywhere along their

line of action without affecting an analysis.

•Equal vectors have the same magnitude and direction.

•Negativevectorofagivenvectorhasthesame

magnitude and the opposite direction.Figure

2.1(©Ferdinand P.

Beer & E. Russell

Johnston, Jr.)

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

4|P a g e

INTRODUCTION

The forceis an important factor in the field of Mechanics, which maybebroadly

*defined as an agentwhichproducesor tends to produce, destroys ortendsto destroy

motion. e.g., a horse applies force to pull a cart and to set it in motion. Force is also

required towork on a bicycle pump. In this case, the force issupplied by the muscular

power of our arms andshoulders.

Resultant of Two Forces

•Force action of one body on another,

characterizedbyitspointof

application, magnitude, line of action

and sense.

•Experimentalevidenceshowsthat

thecombinedeffectoftwoforces

mayberepresentedbyasingle

resultant force.

•Theresultantisequivalenttothe

diagonalofaparallelogramwhich

contains the two forces in adjacent

legs.

•Force is a vector quantity.

Figure2.0(©Ferdinand P. Beer & E.

Russell Johnston, Jr.)

Vectors

•Vector: parameters possessing magnitude and direction

whichaddaccordingtotheparallelogramlaw.

Examples: displacements, velocities, accelerations

•Scalar:parameterspossessingmagnitudebutnot

direction. Examples: mass, volume, temperature.

•Vectorclassifications:

✓Fixedorboundvectorshavewelldefinedof

application that cannot be changed without affecting

an analysis.

✓Free vectors may be freely moved in space without

changing their effect on an analysis.

✓Sliding vectors may be appliedanywhere along their

line of action without affecting an analysis.

•Equal vectors have the same magnitude and direction.

•Negativevectorofagivenvectorhasthesame

magnitude and the opposite direction.Figure

2.1(©Ferdinand P.

Beer & E. Russell

Johnston, Jr.)

PHILIPPINE STATE COLLEGE OF AERONAUTICS

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

5|P a g e

Addition of Vector

•Trapezoid rule for vector addition

•Triangle rule for vector addition

•Law of Cosines,

•Law of sines

•Vector addition is commutative,

•Vector subtraction

•Addition of three ormore vectors

through repeated application of the

triangle rule.

•The polygon rule for the addition of

three or more vectors

•Vector addition is associative,

•Multiplication of a vector by a scalar

Figure 2.2(©Ferdinand P. Beer &E.

Russell Johnston, Jr.)

INSTITUTE OF ENGINEERING AND TECHNOLOGY

AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT

LearningModule 02:Resultant of Force System

5|P a g e

Addition of Vector

•Trapezoid rule for vector addition

•Triangle rule for vector addition

•Law of Cosines,

•Law of sines

•Vector addition is commutative,

•Vector subtraction

•Addition of three ormore vectors

through repeated application of the

triangle rule.

•The polygon rule for the addition of

three or more vectors

•Vector addition is associative,

•Multiplication of a vector by a scalar

Figure 2.2(©Ferdinand P. Beer &E.

Russell Johnston, Jr.)

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