ENGR221 Lecture 2

8/8/2019 ENGR221 Lecture 2

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Concurrent Force SystemsConcurrent Force Systems

ENGR 221

January 15, 2003


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Lecture Goals

Lecture Goals

2.1 Introduction

2.2 Forces and their Characteristics 2.4 Resultant of Three or more concurrent Forces

2.5 Resolution of a Force into Components


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IntroductionIntroduction -- DefinitionDefinition

Concurrent Force Systems:

A concurrent force system contains forces whose

lines-of action meet at some one point.

Forces may be tensile (pulling)


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IntroductionI

ntroduction -- DefinitionDefinitionConcurrent Force Systems:A concurrent force system contains forces whose

lines-of action meet at some one point.

Forces may be compressive (pushing)


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IntroductionI

ntroduction -- DefinitionDefinitionForce exerted on a body has two effects:

The external effect, which is tendency to

change the motion of the body or to develop

resisting forces in the body

The internal effect, which is the tendency to

deform the body.


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IntroductionI

ntroduction -- DefinitionDefinitionIf the force system acting on a body produces

no external effect, the forces are said to be in

balance and the body experience no change inmotion is said to be in equilibrium.

The process of reducing a force system to a simpler

equivalent stem is called a reduction. The processof expanding a force or a force system into a less

simple equivalent system is called a resolution.


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IntroductionI

ntroduction -- DefinitionDefinitionAforce is a vector quantity that, when applied to

some rigid body, has a tendency to produce translation

(movement in a straight line) or translation androtation of body. When problems are given, a force

may also be referred to as a load or weight.

Characteristics of force are the magnitude,

direction(orientation) andpoint of application.


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IntroductionI

ntroduction -- DefinitionDefinitionScalar Quantity has magnitude only (not direction)

and can be indicated by a point on a scale. Examples

are temperature, mass, time and dollars.

Vector Quantities have magnitude and direction.

Examples are wind velocity, distance between to

points on a map and forces.


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IntroductionI

ntroduction -- DefinitionDefinitionCollinear: If several forces lie along the same line-of

action, they are said to be collinear.

CoplanarWhen all forces acting on a body are in the

same plane, the forces are coplanar.


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IntroductionI

ntroduction -- DefinitionDefinitionType of Vectors

Free Vector- is vector which may be freely moved

creating couples in space.

Sliding Vector- forces action on a rigid body are

represented by vectors which may move or slid along

their line of action.

Bound Vector or Fixed Vector- can not be moved

without modifying the conditions of the problem.


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IntroductionI

ntroduction -- DefinitionDefinitionPrinciple of Transmissibility

The principle of transmissibility states that the

condition of equilibrium or of motion of a rigid body

will remain unchanged if aforce Faction at a given

point of the rigid body is replace by aforce Fof the

same magnitude and the same direction, but acting at

a different point, provided that the two forces have the

same line of action.


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IntroductionI

ntroduction -- DefinitionDefinitionPrinciple of Transmissibility

Line of action


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IntroductionI

ntroduction -- DefinitionsDefinitions

1. Point loads - concentratedforces exerted at point or

location

2. Distributed loads - a force

applied along a length or

over an area. The

distribution can be uniform

or non-uniform.

Types of Forces(Loads)


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IntroductionI


Resultant Forces

If two forcesP

and Q acting ona particleA may be replaced by

a single forceR, which has the

same effect on the particle.


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IntroductionI


Resultant Forces

This force is called the resultantof the forces P and Q and may be

obtained by constructing a

parallelogram, using P and Q as

two sides of the parallelogram.The diagonal that pass through A

represents the resultant.


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IntroductionI


Resultant Forces

This is known as theparallelogram law for the

addition of two forces. This law

is based on experimental

evidence,; it can not be provedor derived mathematically.


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IntroductionI


Resultant Forces

For multiple forces action on a point, the forces canbe broken into the components of x and y.


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VectorsVectorsThe vectors can be solved by

1. Law of sine and law of cosines (two forces)

2. Graphically

3. Equilibrium

a) Table

b) Sum of values

0F !


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Homework (Due 1/22/03)

Homework (Due 1/22/03)

Problems:

2-3, 2-5, 2-8, 2-14, 2-15, 2-29,2-37


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Example

Problems

Example

Problems

1. Determine the magnitude and

direction of the resultant of the twoforces.


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Example

Problems

Example

Problems

2. Two structural members B and C are

riveted to the bracketA

. Knowingthat the tension in member B is 6 kN

and the tension in C is 10 kN,

determine the magnitude and

direction of the resultant force acting

on the bracket.


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Example ProblemsExample Problems3. Determine the magnitude and direction ofP

so that the resultant ofP and the 900-N force

is a vertical force of 2700-N directed

downward.


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Example ProblemsExample Problems4. A cylinder is to be lifted by two cables. Knowing

that the tension in one cable is 600 N, determine

the magnitude and direction of the force so that the

resultant of the vertical force of 900 N.


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Example ProblemsExample Problems5. Determine the force in each supporting wire.


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Example ProblemsExample Problems6. The stoplight is supported by two wires. The light

weighs 75-lb and the wires make an angle of 10o with

the horizontal. What is the force in each wire?


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Example ProblemsExample Problems7. In a ship-unloading operation, a

3500-lb automobile is supported by

a cable. A rope is tied to the cable

at A and pulled in order to center the

automobile over its intendedposition. The angle between the

cable and the vertical is 2o, while

the angle between the rope and the

horizontal is 30o. What is the

tension in the rope?


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Example ProblemsExample Problems8. The barge B is pulled by two tugboatsA and C. At a given

instant the tension in cable AB is 4500-lb and the tension in

cable BC is 2000-lb. Determine the magnitude and direction

of the resultant of the two forces applied at B at that instant.


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Example ProblemsExample Problems9. Determine the resultant of the forces on the bolt.


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Example ProblemsExample Problems10. Determine which set of force system is in equilibrium. For

those force systems that are not in equilibrium, determine

the balancing force required to place the body in

equilibrium.


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Example ProblemsExample Problems11. Two forces P and Q of magnitude P=1000-lb and

Q=1200-lb are applied to the aircraft connection.

Knowing that the connection is in equilibrium,

determine the tensions T1 and T2.


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Example ProblemsExample Problems

12. Determine the forces in each of the four wires.


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13. The blocks are at rest on a frictionless incline. Solve for

the forces F1 and F2 required for equilibrium.


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14. LengthA= 5 ft, and length B =10 ft and angle E = 30o.

Determine the angle F of the incline in order to maintain

equilibrium.


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15. Solve for the resisting force at pinA to maintain equilibrium.

ENGR221 Lecture 2

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