Module 02: Resultant of Force System

PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
AIRCRAFT MAINTANCE AND TECHNOLOGY DEPARTMENT
Learning Module 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 AND TECHNOLOGY DEPARTMENT
Learning Module 02: Resultant of Force System
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TABLE OF CONTENTS
Title Page Allotted time
Introduction 4 10minutes
Resultant of Two Forces 4,5 15minutes
➢ Example Solved Problems 6,7,8,9 30minutes
➢ Problem Solving Activity No. No.2 10 26.14minutes
Resultant of Concurrent Force System 11,12 15minutes
➢ Example Solved Problems 13,14,15 40 minutes
➢ Problem Solving Activity No.3 16 30minutes
Moment of a Force 17,18,19 15minutes
➢ Example Solved Problems 20,21,22 40 minutes
➢ Problem Solving Activity No.4 23 30 minutes
Resultant of Parallel Forces 24 15 minutes
➢ Example Solved Problems 25,26,27,28 30 minutes
➢ Problem Solving Activity No.5 29 30minutes
Couples 30 15minutes
➢ Example Solved Problems 31,32,33 40minutes
➢ Problem Solving Activity No.6 34 30minutes
Resultant of Non-Concurrent Forces 35 15minutes
➢ Example Solved Problems 36,37 40minutes
➢ Problem Solving Activity No.7 38 30minutes
441.24 minutes
TABLES OF REFERENCES
References No.
Materials (textbooks, references, journals, online) 1
Singer, Ferdinand L., Engineering Mechanics: Statics and Dynamics 2
Mcgill, David J., Engineering Mechanics: Statics and an Intro to Dynamics 3
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 Hall 5
Beer,F.P. & Johnston, Jr.E.R.(2016) Vector Mechanics for Engineers Static
(11th Ed.) New York: McGraw-Hill Education 6

PHILIPPINE STATE COLLEGE OF AERONAUTICS
INSTITUTE OF ENGINEERING AND TECHNOLOGY
AIRCRAFT MAINTANCE AND TECHNOLOGY DEPARTMENT
Learning Module 02: Resultant of Force System
3 | P a g e
Course Learning Outcomes [CLO]
CLO1. Apply the knowledge of
mathematics to solve complex
mechanics problems;
CLO2. Utilize scientific concepts, laws
and theories in solving problems related
to their field of specialization;
CLO3. Convey a general understanding
of engineering mechanics as a way to
associate their knowledge in their
chosen course;
CLO 10. Demonstrate honesty in doing
individual/group work on this course.
Module Learning Outcomes [MLO]
MLO 01. Solve problems of three or more
concurrent forces by using the rectangular
components of a vector to determine
magnitude and direction.
MLO 02. Fofrmulate the moment of a force
about a secified axis through hands-on
problem solving.
MLO 03. Determine resultants of parallel
forces by demosntarting the proper
procedures.
MLO 04. Computing resolution of force into
a force and a couple through sample
problems
Topic Learning Outcomes [TLO]
TLO 04.Resolve forces into their
rectangular components and represent
the net effect of different force systems
into a resultant through problems
solving.
TLO 05. Compute moment of force
about a specified axis by demonstrating
the proper method.
TLO 06. Solve resultant force of non-
concurrent forces through practice
problems.
This module discusses Force and Components, Resultant of Coplanar Concurrent
Force System, Moment of a Force, Resultant of Parallel Forces, 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 the enhancement 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
modest and nominal ideal of behaviors in academic matters that students be
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 AND TECHNOLOGY DEPARTMENT
Learning Module 02: Resultant of Force System
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INTRODUCTION
The force is an important factor in the field of Mechanics, which maybe broadly
*defined as an agent which produces or tends to produce, destroys or tends to destroy
motion. e.g., a horse applies force to pull a cart and to set it in motion. Force is also
required to work on a bicycle pump. In this case, the force is supplied by the muscular
power of our arms and shoulders.
Resultant of Two Forces
• Force action of one body on another,
characterized by its point of
application, magnitude, line of action
and sense.
• Experimental evidence shows that
the combined effect of two forces
may be represented by a single
resultant force.
• The resultant is equivalent to the
diagonal of a parallelogram which
contains the two forces in adjacent
legs.
• Force is a vector quantity.
Figure 2.0(©Ferdinand P. Beer & E.
Russell Johnston, Jr.)
Vectors
• Vector: parameters possessing magnitude and direction
which add according to the parallelogram law.
Examples: displacements, velocities, accelerations
• Scalar: parameters possessing magnitude but not
direction. Examples: mass, volume, temperature.
• Vector classifications:
✓ Fixed or bound vectors have well defined of
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 applied anywhere along their
line of action without affecting an analysis.
• Equal vectors have the same magnitude and direction.
• Negative vector of a given vector has the same
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 AND TECHNOLOGY DEPARTMENT
Learning Module 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 or more 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.)