Static Equilibrium

1. living with the lab Static Equilibrium Equilibrium: a state of rest or balance due to the equal action of opposing forces. ENGR 122

2. living with the lab Newton’s Laws 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 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 FB 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 FP force of ball on plane force of plane on ball

3. living with the lab 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.

4. living with the lab 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 STEPS: Choose bodies to include on FBD Draw the body of interest barrel A FA Show loads exerted by interacting bodies; name the loads x B W Define a coordinate system FB Label distances and angles 45° 45° Free body diagrams (FBDs) are a necessary part of a mechanics problem solution. They are the tool we use to write equilibrium equations.

5. living with the lab 2D Equilibrium Part A: The FBD B A Choose a body or combination of bodies to be shown on the FBD. 100 lb Sketch the outline of the body, isolating it from interacting bodies. Identify all forces exerted by interacting bodies removed in step 2. Show them as vectors on the sketch y FA FB Choose and label coordinate axes. qA qB x Label distances and angles needed to solve the problem. W = 100 lb

6. living with the lab 2D Equilibrium Part B: The Components Find the x- and y-components of all forces shown on the FBD. Force W (weight) Force B Force A y Part C: The Math FA FB The sum of all x-components must be zero; the sum of all y-components must be zero. qA qB x The solution of this system of equations gives the tensions in cables A and B. W = 100 lb

7. living with the lab Tips for Solving Statics Problems 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. 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. 2 inches x 2 inches (5cm x 5cm) should be a minimum size too small minimum size ?? Write down all of this stuff (every time!!!). Being systematic is the key to avoiding errors.

8. living with the lab 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. C 80° B A LWTL Louisiana

9. living with the lab Class Problem - Solution

10. living with the lab 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.

11. living with the lab Class Problem - Solution