BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Lesson title: Resultant of Concurrent Force System
Lesson Objectives:
At the end of the module you will be able to:
1. Show how to add forces and resolve them into components using
the parallelogram law.
2. Express force and position in Cartesian vector form and explain
how to determine the vector’s magnitude and direction
3. Determine the resultant of multiple forces acting on a particle.
.
Class number: _______
Date:_______________
Materials:
Canon F-789SGA, Pen and
Notebook
Reference
1. Engineering Mechanics Statics
(Metric Edition) by Andrew Pytel &
Jaan Kiusalaas
2. Simplified Engineering
Mechanics by Dela Fuente,
Racines, Ocampo,Siapno &Olleta
3. Engineering Mechanics
Besavilla
4. MATHalino.com
Productivity Tip:
Study like there’s no tomorrow because
if you keep putting off your studies for
tomorrow, you’ll probably too late.
A. LESSON PREVIEW/REVIEW
1) Introduction (2 mins)
Last meeting, we resolved the vector into its components then
compute the resultant of two vectors applying analytical
method such as cosine law and sine law. In this module we
will discuss, express, and determine the magnitude and
position of concurrent force system.
Force, in the ordinary sense , is a push or a pull exerted on a
body ( or by an “unseen constant influence”, as in the force of
gravity or the electrostatic magnetic force. Force is a vector
quantity, and possesses both magnitude and direction.
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
 External force exerted by a body on a rigid body; will cause it either to: remain at rest or in motion.
 At rest (stationary), if these external or action force are balanced or in a state of
equilibrium.
 In motion, if these forces are unbalanced.
 On the other hand, internal forces hold together the parts making up, and causes deformation
to the rigid body.
2) Activity 1: What I Know Chart, part 1 (3 mins)
What I Know
Questions:
What I Learned (Activity 4)
1. What are Concurrent forces?
1. 2. How do you determine the
resultant force acting on the
object?
3Why do we need to find the
resultant force?
B.MAIN LESSON
1) Activity 2: Content Notes (13 mins)
Force Systems:
A force system constitute two or more forces acting on a body or a set of bodies.
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
2 Categories of Force System
1. Coplanar (2- dimensional) when all the forces lie or act along one plane.
2. Non-coplanar (3 dimensional) also called spatial force system when all forces do not lie or act in one
plane.
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
Classification of force system as to the line of action of individual force.
(i) Concurrent force system is one where the forces act at the same point on the body.
\
(ii) Parallel force system when the forces are all parallel( lines of action do not intersect.)
(iii) General force system when the forces are non-parallel and non-concurrent.
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
RESULTANT OF THREE OR MORE CONCURRENT FORCE SYSTEM
The determination of the resultant of two forces has been mentioned in lesson 1 by parallelogram and
triangle laws. The magnitude and direction of the resultant were solved analytically by the use of basic
mathematical relations.
In a related manner, the resultant of three or more forces maybe obtained by the used of analytical
method.
Analytical Solution:
Example Problems:
1. Plot and compute the magnitude and position of the resultant of the given concurrent forces.
F1= 400 N; along (+) x- axis
F2= 200 N; -210˚
F3= 300 N; 240˚
F4= 300 N; S 30˚E
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
2. Compute the magnitude and position of the resultant of the four concurrent forces shown in the figure.
3. The resultant of the concurrent forces in the figure below is 300 N pointing up along y- axis. Compute the
values of F and Ө to give this resultant.
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
2) Activity 3: Skill-building Activities (with answer key) (18 mins + 2 mins checking)
Exercises: Solve the following problems then place and show your complete solution in a short coupon
bond in a landscape orientation without erasures.
1. For the forces as shown in the figure compute the magnitude of the equilibrant.
2. The force of 500 N is the resultant of the forces P and 250 N acting as shown in the figure. Compute the
following:
a)the angle Ө that the 500 N makes with the horizontal, (b)the value of  and (c) the value of P.
3) Activity 4: What I Know Chart, part 2 (2 mins)
What I Know
Questions:
2. What are Concurrent forces?
What I Learned (Activity 4)
2. 2. How do you determine the
resultant force acting on the object?
3. 3. Why do we need to find the
resultant force?
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
4) Activity 5: Check for Understanding (5 mins)
Student Engagement (SE) Think-Pair-Share
Problem Solving:
Solve the problem with complete solution in landscape orientation by placing it in a short coupon bond
and avoid erasures.
1. The resultant R= 1,350 N of the three concurrent forces in the figure points vertically down along Yaxis. Find the magnitude and direction of the unknown force F1.
5) Activity 6: Assessment for Student Learning
Classroom Assessment Technique (CAT) 3-2-1
Three things you learned:
1.
2.
3.
Two things that you would like to learn more about:
1.
2.
One question you still have:
1.
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BES 025: Statics of Rigid Bodies
Student Activity Sheet #2
Name:_____________________________________________________________
Section: ____________Schedule:_______________________________________
Class number: _______
Date:_______________
C. LESSON WRAP-UP
1) Activity 6: Thinking about Learning (5 mins)
1. Where/when and how else can you use what you’ve learned?
FAQs
Q: If all the forces acting on a rigid body are in the same plane (coplanar), what is the direction of the resultant
force vector?
A: What we know for certain is that the resultant force would also be in the same plane. However, its direction
depends upon the directions of the forces in the group. If all the forces happen to be parallel, then the resultant
force would also be parallel to these forces; otherwise, we have to rely on vector algebra to determine its exact
direction.
Q:Can I represent a distributed force acting on a rigid body by its resultant?
A: Yes you can, but you must be careful that the resultant is in the same direction as the distributed force and
it is placed at the centroid of the distributed area.
KEY TO CORRECTIONS
Activity 3:
1. R=35.36 N
2. θ=53.13O
α=83.16O
P=503.79 KN
Activity 5:
1.
Ө=74.13˚ and F1= 2,873.743 N
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