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Module 02: Resultant of Force System

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PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
AIRCRAFT MAINTANCE ANDTECHNOLOGYDEPARTMENT
LearningModule 02:Resultant of Force System
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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
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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
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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
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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.)
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