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Static Equilibrium

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

ENGR 122

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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

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

ball 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

F B

force of ball on plane

F P

force of plane on ball

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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

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

y

A

barrel

B

45 °

F A W

45 °

F B

x

STEPS: 1.

Choose bodies to include on FBD 2.

Draw the body of interest 3.

4.

Show loads exerted by interacting bodies; name the loads 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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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.

B A

100 lb

F A

q

A

y

F B

q

B

x

W = 100 lb

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2D Equilibrium

F A

q

A

y

F B

q

B

x

Part B: The Components

Find the x- and y-components of all forces shown on the FBD.

Force A Force B Force W (weight) W = 100 lb

Part C: The Math

The 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 Problems

1. 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.

Yes, your instructors have seen this.

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

minimum size too small ??

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

2 inches x 2 inches (5cm x 5cm) should be a minimum size Being systematic is the key to avoiding errors.

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Class Problem

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 weight of the engine and the tension in the hoist’s cable.

B

80 °

C A LWTL

Louisiana 8

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Class Problem - Solution

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Class Problem

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.

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Class Problem - Solution

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