# More on Center of Gravity -More on Static Equilibrium AP Physics C Mrs. Coyle Rio-Antirio Bridge,...

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-More on Center of Gravity -More on Static Equilibrium

AP Physics CMrs. CoyleRio-Antirio Bridge, Coyle Summer 2009

Rio-Antirio Bridge, Greece Coyle, Summer 2009

Ex: Minnesota Metrodome Roof Collapse

http://www.youtube.com/watch?v=ip8sM_1tXho

Mechanical EquilibriumTranslationalSF=0 Static (v=0)

Dynamic (v=Constant)RotationalSt=0

Static(=0)

Dynamic (=constant)

Necessary Condition for EquilibriumThe net (resultant) external force must be zero.

The net (resultant) extrenal torque must be zero about any axis.

Static EquilibriumNo translationSF=0 Static (v=0)

No rotationSt=0

Static(=0)

Examples: What type of equilibrium exists?A physics book sitting on a table.A skater at constant velocity.A spinning CD.The wheel of a car traveling at constant velocity.

When objects are in equilibrium:p=0 of its center of mass.

L=0 about any axis.

Ex: Stable Equilibrium compared to Static EquilibriumWhen an object returns to static equilibrium after it undergoes a displacement it is in stable equilibrium.

Ex: A steel ball at the bottom of a bowl when moved to the side of the bowl, returns to the bottom and eventually stops.

Remember: Center of GravityThe point of the object where the force of gravity is thought to be acting.

Average location of weight.

If g is the same throughout the object then the CM coincides with the CG.

Problem Solving Strategy for Static EquilibriumDraw the free body diagram of the object. Set up the equations for: SF=0 Set up the equation for: St=0 (pick the axis with the simplest math). Solve the equations for the unknowns.

Ex: 12.2A person holds a 50N ball.Find the upward force exerted by the bicep on the forearm and acting at the joint. Neglect the weight of the forearm.

Ans: 583N

Free Body Diagram

Ex: 12.3A uniform beam is attached to a wall by a pin connection. A 600N person stands 2m from the wall. Find the tension in the cable and the magnitude and direction of the force exerted by the wall on the beam.

Ans: 313N, 580N , 71.10

Use the pivot at the wall as the axis.The beams weight acts at its CG.

Analyze forces into x and y components

Ex: 12.4A uniform ladder of mass m and length l, rests against a smooth vertical wall. If the coefficient of static friction between the ground and the ladder is 0.40, find the minimum angle at which the ladder would not slip.

Ans:510

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