-More on Center of Gravity -More on Center of Gravity -More on Static Equilibrium -More on Static Equilibrium

AP Physics CMrs. CoyleRio-Antirio Bridge, Coyle Summer

2009

Rio-Antirio Bridge, GreeceCoyle, Summer 2009

Ex: Minnesota Metrodome Roof Collapse

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

Mechanical EquilibriumMechanical Equilibrium

Translational• F=0

–Static (v=0)

–Dynamic(v=Constant)

Rotational• =0

–Static(ω=0)

–Dynamic(ω=constant)

Necessary Condition for Necessary Condition for EquilibriumEquilibrium

1. The net (resultant) external force must be zero.

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

Static EquilibriumStatic Equilibrium

No translation• F=0

–Static (v=0)

No rotation• =0

–Static(ω=0)

Examples: What type of Examples: What type of equilibrium exists?equilibrium exists?

1. A physics book sitting on a table.2. A skater at constant velocity.3. A spinning CD.4. The wheel of a car traveling at constant

velocity.

When objects are in equilibrium:When objects are in equilibrium:

• Σp=0 of its center of mass.

• ΣL=0 about any axis.

Ex: Stable Equilibrium compared Ex: Stable Equilibrium compared to Static Equilibriumto Static Equilibrium

• When 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 GravityRemember: Center of Gravity

• The 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 Problem Solving Strategy for Static EquilibriumStatic Equilibrium

1. Draw the free body diagram of the object.

2. Set up the equations for: F=0

3. Set up the equation for: =0 (pick the axis with the simplest math).

4. Solve the equations for the unknowns.

Ex: 12.2• A 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: 12.3• A 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 beam’s weight acts at its CG.

Analyze forces into x and y components

Ex: 12.4• A 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 θat which the ladder would not slip.

• Ans:510