Static Equilibrium

ENGR 122

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Equilibrium: a state of rest or balance due to the equal action of opposing forces.

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2. Change of motion is proportional to the moving force impressed and takes place in the direction of the straight line in which the force is impressed. F = m a∙

Newton’s Laws

1. Every body perseveres in its state of rest or uniform motion in a straight line, except when compelled to change that state by impressed forces. INTERTIA coffee wants to keep going when

you stomp on the brakes

3. Reaction is always equal and opposite to action; that is, the actions of two bodies on each other are always equal and directly opposite. FORCES COME IN PAIRS

force of ball on plane force of plane on ball

ball

FB

FP

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Equilibrium

The resultant of all forces acting on an object must be zero for the object not to move.

Thus, the resultant of all forces is zero. What does a zero vector look like?

What are the x- and y-components of a vector with zero length?

Necessary condition for static equilibrium.

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Free Body Diagrams are sketches of bodies with all Interacting bodies removed; their effect instead are represented by force vectors. Consider a barrel wedged intoa groove, with contact at points A and B.

Free Body Diagrams

barrelA

B

45°FB

FA

x

y

W45°

STEPS:1.Choose bodies to include on FBD

2. Draw the body of interest

3. Show loads exerted by interacting bodies; name the loads

4. Define a coordinate system

5. Label distances and angles

Free body diagrams (FBDs) are a necessary part of a mechanics problem solution.They are the tool we use to write equilibrium equations.

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100 lb

A

B

2D Equilibrium

Part A: The FBD

1. Choose a body or combination of bodies to be shown on the FBD.

2. Sketch the outline of the body, isolating it from interacting bodies.

3. Identify all forces exerted by interacting bodies removed in step 2. Show them as vectors on the sketch

4. Choose and label coordinate axes.

5. Label distances and angles needed to solve the problem.

x

y

BA

FBFA

W = 100 lb

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2D Equilibrium x

y

BA

FBFA

W = 100 lbPart B: The ComponentsFind the x- and y-components of all forces shown on the FBD.

Force A Force B Force W (weight)

Part C: The MathThe sum of all x-components must be zero; the sum of all y-components must be zero.

The solution of this system of equations gives the tensions in cables A and B.

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Tips for Solving Statics Problems1. Take pride in your FBDs. Use a straight edge, and write neatly.

Shameful example of a FBD.

If its messy on your paper, it will be messy in your mind.

2. Don’t draw your FBDs too small.

minimum size too small

Yes, your instructors have seen this.

It won’t do you much good if you can’t see it.

2 inches x 2 inches (5cm x 5cm) should be a minimum size

??

3. Write down all of this stuff (every time!!!).

Being systematic is the key to avoiding errors.

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Class Problem

Louisiana

LWTL

80°

AB

C

A worker is pulling an engine on a hoist to align it over a truck bed.If the worker is pulling with an 80 lb. force, determine the weightof the engine and the tension in the hoist’s cable.

Class Problem - Solution

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Uncle Fred, who weighs 200 lbs., is trying out his new zip line. Unfortunately, the bearings in his homemade zip line lock up, causing him to come to rest as shown. Determine the tension in the zip line on each side of the pulley. NOTE: The tension on each side of a frictionless pulley is ALWAYS equal, and if the pulley was frictionless, Uncle Fred would come to rest when the angles in front of him and behind him became equal. However, this pulley is NOT frictionless.

Class Problem

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Class Problem - Solution