The document discusses coplanar non-concurrent force systems where multiple forces act in the same plane but at different points. It defines moment as the product of a force and its perpendicular distance from the point of interest. A couple is formed by two equal and opposite forces that rotate a body without translating it. Varignon's principle states that the sum of the moments of individual forces equals the moment of the resultant force about any point. Conditions for equilibrium of coplanar non-concurrent forces on a body are also presented. An example problem finds the resultant and location of a non-concurrent force system.
INTRODUCTION TO ENGINEERING MECHANICS - SPP.pptxSamirsinh Parmar
Engineering Mechanics, Mechanics, Scalars, Vectors, Force system, Measurment units, Concept of force, system of forces, Idealized Mechanics, Fundamental Concepts, Scalar and vector Operations, Accuracy of Engineering Calculation, Problem Solving Approach
INTRODUCTION TO ENGINEERING MECHANICS - SPP.pptxSamirsinh Parmar
Engineering Mechanics, Mechanics, Scalars, Vectors, Force system, Measurment units, Concept of force, system of forces, Idealized Mechanics, Fundamental Concepts, Scalar and vector Operations, Accuracy of Engineering Calculation, Problem Solving Approach
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
In Engineering Mechanics the static problems are classified as two types: Concurrent and Non-Concurrent force systems. The presentation discloses a methodology to solve the problems of Concurrent and Non-Concurrent force systems.
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Definition of force,types of forces,law of forces,system of forces, moment of a force, couple,moment of a couple,types of moments,features of couple and principle of moments.
If a body is subjected to many forces on its plane at a single point then they are called as Coplanar Concurrent Forces. The effect of the forces acting on the body is unknown. It is necessary to determine the resultant force of the coplanar forces to know this effect. Copy the link given below and paste it in new browser window to get more information on Law Of Polygon:-
http://www.transtutors.com/homework-help/mechanical-engineering/force-systems-and-analysis/law-of-polygon.aspx
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
In Engineering Mechanics the static problems are classified as two types: Concurrent and Non-Concurrent force systems. The presentation discloses a methodology to solve the problems of Concurrent and Non-Concurrent force systems.
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Definition of force,types of forces,law of forces,system of forces, moment of a force, couple,moment of a couple,types of moments,features of couple and principle of moments.
If a body is subjected to many forces on its plane at a single point then they are called as Coplanar Concurrent Forces. The effect of the forces acting on the body is unknown. It is necessary to determine the resultant force of the coplanar forces to know this effect. Copy the link given below and paste it in new browser window to get more information on Law Of Polygon:-
http://www.transtutors.com/homework-help/mechanical-engineering/force-systems-and-analysis/law-of-polygon.aspx
This slide show accompanies the learner guide "Mechanical Technology Grade 10" by Charles Goodwin, Andre Lategan & Daniel Meyer, published by Future Managers Pty Ltd. For more information visit our website www.futuremanagers.net
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Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
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Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
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Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
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Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
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3. Coplanar Non-concurrent Force System:-
This is the force system in which lines of action of
individual forces lie in the same plane but act at different
points of application.
COPLANAR NON - CONCURRENT
FORCE SYSTEM
F2
F1
F3
F1 F2
F5
F4
F3
3
4. Moment Of A Force :-
The moment of a force is equal to the product of the force
and the perpendicular distance of line of action of force from
the point about which the moment is required.
M = P x X
Here, M = moment
P = Force
X = Perpendicular distance between the line of action of
force and the point about which moment is required.
Unit of moment is N.m. or kN,m.
Examples of moment are :-
i) To tight the nut by spanner
ii) To open or close the door
Sign for moment:-
Generally, clockwise moment is taken as positive and anticlockwise
moment is taken as negative.
6. Couple:-
To equal and opposite forces whose lines of action are
different form a couple. Resultant or net force of couple is zero.
Hence, couple acting on a body do not create any translatory
motion of the body. Couple produces only rotational motion of
the body.
• Types of couple:
There are two types of couple.
i ) Clockwise couple
ii) Anticlockwise couple
Clockwise couple:-
It rotates the body in
clockwise direction.
It is taken as positive.
Anticlockwise couple:-
It rotates the body in anticlockwise direction.
It is taken as negative.
7. Arm of couple :-
The perpendicular distance between the lines of action of
two forces forming couple is know as the arm of couple.
Moment of couple :-
Moment of couple = Forces x arm of couple
M = P x a
unit of couple is N.M. Or KN.M
Example of couple are :-
I. Forces applied to the key of a lock, while locking or
unlocking it.
II. Forces applied on the steering wheel of a car by two
hands to steer the car towards left or right.
III.To open or close wheel valve of a water supply pipe line.
8. CHARACTERISTICS OF A COUPLE :-
I. The algebraic sum of the forces, forming the couple is zero.
II. The algebric sum of the moment of the forces, forming the
couple, about any point is the same and equal to the moment of the
couple itself.
Moment of couple M = P.a
Now, taking moment @ 0,
Mo = P ( a + x ) – P.x
= P.a + P.x – P.x
= P.a
III. A couple cannot be balanced by a single force, but can be balanced
only by a couple, but of opposite nature.
IV. If number of coplanar couples are acting on the body, the they can
be reduced to a single couple, whose magnitude will be equal to the
algebraic sum of moment of all the couples.
9. DIFFRENCE:-
MOMENT COUPLE
Moment = Force x Perpen-
dicular distance
M = P.x
It is produced by a single
Force not passing through C.G.
of the body.
The force move the body in
the direction of force and rotate
the body.
To balance the force causing
moment, equal and opposite
forces is required
Two equal and opposite
forces whose lines of action are
different form a couple.
It is produced by two equal
and opposite parallel, non-
collinear forces.
Resultant force of couple is
zero. Hence, body does not
move, but rotate only.
Couple can not be balance by
a single force. It can be balance
by a couple only.
10. Example :-
Replace the couple and force by a single force – couple applied
at a for the lever shown in figure. Also find the distance of a point
C from A where only a single force can replace the force-couple
System.
Solution:- Moment of couple of 250 kN force is
= 250 × 120
= 30000N.mm
11. Single force to replace the force couple system :
Let, 500 N is applied at distance x from A at point C.
Moment of force and couple at b from
= (250×120) + 500 × (200cos 60̇ )
= 30000 + 50000
= 80000 N.mm …..( i )
Moment of force 500 N at C @ B,
= 500× (200 + x) cos60̇
= 250 (200 + x)
= 50000 + 250 x …..( ii )
Equating ( i ) and ( ii )
50000 + 250 x = 80000
250 x = 30000
x = 120 mm.
12. VARIGNON’S PRINCIPLE OF MOMENTS
It states,
‘If number of coplanar forces are acting simultaneously on
a particle, the algebraic sum of the moments of all the forces about
any point is equal to the moment of their resultant force about the
same point.
13. Proof:-
Consider two forces P and Q acting at a point a represented
in magnitude and direction by AB and AC as shown in figure.
let, O be the point, about which
the moments are taken. Through O,
draw a line CD parallel to the
direction of force P, to meet the line
of action of Q at C. Now with AB and AC as two adjacent sides,
complete parallelogram ABCD. Join the diagonal AD of the
parallelogram and OA and OB, diagonal AD represents in
magnitude and direction the resultant of two forces P and Q.
Now, taking moment of forces P,Q and R about O.
Moment of force P about O
= 2 × Area of triangle AOB ….. ( i )
Similarly, moment of force Q, about O,
= 2 × Area of triangle AOC …..( ii )
O C D
R
Q
A P B
14. Moment of resultant R, about O,
= 2 × Area of triangle AOD …..( iii )
Now, from the geometry of the figure,
Area of ∆ AOD = Area of ∆ AOC + Area of ∆ ACD
But area of ∆ACD = Area of ∆ ADB
= Area of ∆ AOB
Therefore, Area of ∆ AOD = Area of ∆ AOC + Area of ∆ AOB
Multiplying both sides by 2,
2 × Area of ∆ AOD = 2 × Area of ∆ AOC + 2 × Area of ∆ AOB
Therefore, moment of force P and O = moment of force P and O
+ moment of force Q and O
( Here, we have considered only two forces. But this principle can
be exerted for any number of forces.)
15. If the body is acted upon by a number of co-planar
non-concurrent forces. It may have one of the following stats:
I. The body may move in any one direction.
II. The body may rotate about itself without moving.
III. The body may move in any one direction, and at the
same time it may also rotate about itself.
IV. The body may be completely at rest.
CONDITION OF EQUILIBRIUM FOR COPLANER
NON – CONCURRENT FORCES:-
16. Example :-
Determine the resultant and locate the same with respect to point
‘A’ of a non-concurrent force system shown in figure.
Solution:-
∑H = 0.5 cos60̇ + 1.2 –
2.1 cos45̇
= 0.25 + 1.2 – 1.485
= - 0.035kN (←)
∑V = 1.1 C 0.5 sin60̇ +
2.1 sin45̇
= 1.1 + 0.433 + 1.485
= 3.02kN (↑)
R = √(∑H)2 + (∑V)2
= √(-0.035)2+ (3.02)2
= 3.02kN
17. tanθ = = = 86.28
∑V
∑H
3.02
0.035
θ = 89.33̇
∑H = -Ve
∑V = +Ve
Therefore, R will be in 2
quadrant.
Location of resultant:
Let R is at perpendicular
distance x from A.
Taking moment @ A.
R.x + (1.2×1.5) + 0.5sin60̇ × 2 = 4.0 +2.1cos45̇ × 1.54
3.02 x + 1.8 + 0.866 = 4 + 2.23
3.02 x = 3.564
x = 1.18 m .