Transcript 3 More on Static Equilibrium and Center of Gravity

-More on Center of Gravity
-More on Static Equilibrium
Rio-Antirio Bridge, Coyle Summer 2009
AP Physics C
Mrs. Coyle
Rio-Antirio Bridge, Greece
Coyle, Summer 2009
Ex: Minnesota Metrodome Roof
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• http://www.youtube.com/watch?v=ip8sM_1t
Xho
Mechanical Equilibrium
Translational
• SF=0
Rotational
• St=0
–Static (v=0)
–Static(ω=0)
–Dynamic
(v=Constant)
–Dynamic
(ω=constant)
Necessary Condition for
Equilibrium
1. The net (resultant) external force
must be zero.
2. The net (resultant) extrenal torque
must be zero about any axis.
Static Equilibrium
No translation
No rotation
• SF=0
• St=0
–Static (v=0)
–Static(ω=0)
Examples: What type of
equilibrium exists?
1.
2.
3.
4.
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:
• Σp=0 of its center of mass.
• ΣL=0 about any axis.
Ex: Stable Equilibrium compared
to 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 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 Static
Equilibrium
1. Draw the free body diagram of the object.
2. Set up the equations for: SF=0
3. Set up the equation for: St=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