introduction to statics. forces in equilibrium tall buildings are an impressive example of...

Introduction to Statics

Forces in Equilibrium

Tall buildings are an impressive example of equilibrium, or the balancing of forces.

A modern office tower is constructed of steel and concrete beams that are carefully designed to provide reaction forces to balance against wind, gravity, and people.

All forces acting on the building must add up to zero.

Statics

The study of forces and their effects on a system in a state of rest or uniform motion

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Equilibrium

• The concept of equilibrium is important to the design of bridges, buildings and virtually any technology invented by humans.

• In order for a bridge to stay in place, ALL the forces acting on the bridge must add up to produce a net force of zero.

Statics Principles

Newton’s First Law of Motion (law of inertia):

An object in a state of rest or uniform motion will continue to be so unless acted upon by another force.

If the net force of an object is zero (equilibrium), an object at rest will stay at rest and an object in motion will stay in motion with constant speed and direction.

Statics Principles

Newton’s Second Law of Motion:

The acceleration of an object is proportional to the net force acting on the object and inversely proportional to the object’s mass

Force = Mass x Acceleration

The acceleration of an object in equilibrium is zero because the net force acting on the object is zero. Zero acceleration means neither the speed or the direction of motion can change.

Statics PrinciplesNewton’s Second Law of Motion:

Any object at rest is in equilibrium and has a net force of zero acting on it.

Imagine a book sitting on a table. Gravity pulls the book downward with a force equal

to the books weight.

But what force balances the weight?

The table exerts an upward force on the book called the Normal Force.

In mathematics, Normal means perpendicular. The force the table exerts is perpendicular to the table’s surface.

Statics Principles

Newton’s Third Law of Motion:

For every action force, there is an equal and opposite reaction force

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Statics PrinciplesNewton’s Third Law of Motion:The third law explains why normal forces exist.

The book pushes down on the table, so the table pushes up on the book. The book’s force on the table is the action force, and the table’s force on the book is the reaction

force.

These forces are equal in strength. If the book is at rest, these forces must be equal but opposite in direction.

EquilibriumStatic Equilibrium:

A condition where there are no net external forces acting upon a particle or rigid body and the body remains at rest or continues at a constant velocity

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Equilibrium

Translational Equilibrium:

The state in which there are no unbalanced forces acting on a body

x

y

F =0

F =0

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Balanced Unbalanced

Equilibrium

Rotational Equilibrium:The state in which the sum of all the clockwise moments equals the sum of all the counterclockwise moments about a pivot point

M=0©iStockphoto.com

Remember Moment = F x D

Statics Principles

Scalar Quantities:A physical quantity that has magnitude only

Examples: Mass, length, time, volume, temperature, pressure, and speed

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Scalars• Scalars have Magnitude• A scalar is a quantity that can be completely

described by a single value called a magnitude.

• Magnitude means the size or amount and always includes units of measurement

• Temperature is a good example of a scalar quantity. If you use a thermometer to check your temperature and it shows 101 F. The magnitude of your temperature is 101, degrees Fahrenheit is the unit of measurement.

O

Statics Principles

Vector Quantities:A physical quantity that has both a magnitude and direction

Examples: Position, velocity, force, and moment

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Vectors• Vectors have direction

• If you are giving someone directions to your house, you could not just say drive 5 miles. You must also add the direction to drive those 5 miles.

• A force vector has units of Newtons, like all forces; the force vector also includes the direction of the force.

What Is a Force?

A vector quantity defined by its known magnitude, direction, and point of application

A

45 lbf

21.8°NE

The pushing or pulling interaction of objects

A force vector is drawn as an arrow.

Force Units

British System of Units Pound-force (lbf)

International System of Units Newton (N)

Conversions between Unit Systems1lbf = 4.448 N

1N = 0.2248 lbf

Static Equilibrium Force Principles

Forces always occur in pairs.

Force pairs act in opposite directions and have the same magnitude.

Force Components

A single force can be replaced by component forces if their combination produces the same effect as the original force.

a

F a

Fay

Fax

a

Resultant Force

A single force that has the same effect as two or more concurrent forces

2lbf5lbf

5lbf

2lbf

7lbf

Resultant

3lbf

Resultant

=

=

Free Body DiagramVisual representation of force and object interactions

Individual objects or members are isolated from their environment or system, illustrating all external forces acting upon them

Free Body Diagram Components

Vector quantity has direction and magnitude

ForceA straight line push or pull acting upon an object

Direction is illustrated by arrowhead

Magnitude is illustrated by length of line segment and is the amount of push or pull

Free Body Diagram Components

The twisting effort about a point or axis when a force is applied at a distance

Arc with an arrowhead acting about a point indicating direction of CW or CCW

Moment

• Distance (d) is called the moment arm. It must be measured perpendicular to the line of action of the force.

Moment Review

Line of ActionF

Point of Rotation

d

Moment (M) = Force (F) x distance (d)

Free Body Diagram Procedure

A stack of three books, each weighing 5 lb, is sitting on top of a table. Draw the Free Body Diagram (FBD) of the top book.

Free Body Diagram Procedure• 1. Sketch the isolated object.

What is the isolated object?

Top Book

Free Body Diagram Procedure• 2. Sketch the applied and norm

forces.

When an object is in contact with and is supported by a second object, the second object can be replaced with a normal force which is perpendicular to the surface of the second object.

Free Body Diagram Procedure• 2. Sketch the applied force and norm

forces.

Applied Force Weight of top book

Normal Force Reaction force pushing up on the book, causing it not to fall

Free Body Diagram Procedure• 3. Label objects and forces.

N=5 lbf

W=5 lbf

PLTW – DE book

Free Body Diagram Procedure• 4. Label dimensions.

N=5 lbf

W=5 lbf

PLTW – DE book

For more complex free body diagrams, proper dimensioning is required, including length, height, and angles.

45°

8 ft

8 ft10 ft

38.6°

Free Body Diagram Practice

Fapp

FN

W W

Ff

θ

θ

Create a FBD for the sled pictured below.

Fapp

Ff

FN

Free Body Diagram Practice

FN

W W

FN

Fapp

Fapp

F f

F f

θ

θ

Create a FBD for the refrigerator pictured below.

Free Body Diagram Practice

M1

M2

FBD of Mass 1:

FT

FBD of the movable pulley:

W1

W2 + W pulley

FT

FT

Tension Forces (FT ) are equal throughout the system.

Create a FBD for the pulley system pictured below.