Piri Reis University 2011-2012/ Physics -I
Physics for Scientists &
Engineers, with Modern
Physics, 4th edition
Giancoli
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Piri Reis University 2011-2012 Fall Semester
Physics -I
Chapter 12
Static Equilibrium; Elasticity and Fracture
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Piri Reis University 2011-2012
Lecture XII
I.The Conditions for Equilibrium
II. Solving Statics Problems
III. Applications to Muscles and Joints
IV. Stability and Balance
V. Elasticity; Stress and Strain
VI. Fracture
VII. Spanning a Space: Arches and Domes
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I. The Conditions for Equilibrium
An object with forces acting on it, but that is not moving, is said to be in
equilibrium.
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I. The Conditions for Equilibrium
The first condition for equilibrium is that
the forces along each coordinate axis
add to zero.
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I. The Conditions for Equilibrium
The second condition of equilibrium is that there be no torque around
any axis; the choice of axis is arbitrary.
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II. Solving Statics Problems
1. Choose one object at a time, and make a free-body diagram showing
all the forces on it and where they act.
2. Choose a coordinate system and resolve forces into components.
3. Write equilibrium equations for the forces.
4. Choose any axis perpendicular to the plane of the forces and write the
torque equilibrium equation. A clever choice here can simplify the
problem enormously.
5. Solve.
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II. Solving Statics Problems
The previous technique may not fully solve all statics problems, but it is a
good starting point.
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II. Solving Statics Problems
If a force in your solution comes out negative (as FA will here), it just means
that it’s in the opposite direction from the one you chose. This is trivial to fix,
so don’t worry about getting all the signs of the forces right before you start
solving.
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II. Solving Statics Problems
If there is a cable or cord in the problem, it
can support forces only along its length.
Forces perpendicular to that would cause it
to bend.
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III. Applications to Muscles and Joints
These same principles can be used to
understand forces within the body.
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III. Applications to Muscles and Joints
The angle at which this man’s back is bent
places an enormous force on the disks at the
base of his spine, as the lever arm for FM is
so small.
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IV. Stability and Balance
If the forces on an object are such that they tend to return it to its
equilibrium position, it is said to be in stable equilibrium.
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IV. Stability and Balance
If, however, the forces tend to move it away from its equilibrium point, it is
said to be in unstable equilibrium.
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IV. Stability and Balance
An object in stable equilibrium may become unstable if it is tipped so that its
center of gravity is outside the pivot point. Of course, it will be stable again
once it lands!
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IV. Stability and Balance
People carrying heavy loads automatically adjust their posture so their
center of mass is over their feet. This can lead to injury if the contortion
is too great.
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Example 1
A uniform 40.0 N board supports a father (800 N) and daughter (350 N) as
shown. The support is under the center of gravity of the board and the
father is 1.00 m from the center.
(a) Determine the magnitude of the upward force n exerted on the board by
the support.
(b) Determine where the child should sit to balance the system.
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Example 2
A diver of weight 580 N stands at
the end of a 4.5 m diving
board of negligible mass (see
Fig). The board is attached to
two pedestals 1.5 m apart.
(a) Draw a free body diagram.
(b) What are the magnitude and direction of the force on the board from
left pedestal?
(c) What are the magnitude and direction of the force on the board from
right pedestal?
(d) Which pedestal is being stretched and which is compressed?
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V. Elasticity; Stress and Strain
Hooke’s law: the change in length is
proportional to the applied force.
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V. Elasticity; Stress and Strain
This proportionality holds until the force reaches the proportional limit.
Beyond that, the object will still return to its original shape up to the
elastic limit. Beyond the elastic limit, the material is permanently
deformed, and it breaks at the breaking point
.
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V. Elasticity; Stress and Strain
The change in length of a stretched object depends not only on the
applied force, but also on its length and cross-sectional area, and the
material from which it is made.
The material factor is called Young’s modulus, and it has been
measured for many materials.
The Young’s modulus is then the stress divided by the strain.
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V. Elasticity; Stress and Strain
In tensile stress, forces tend to
stretch the object.
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Elastic properties of solids
Tension or
compression
Young’s modulus:
tensile _____
F/A
Y

tensile ______ L / Li
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Elastic properties of solids
Shear modulus:
shear _______ F / A
S

shear _______ x / h
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Elastic properties of solids
Hydraulic stress
Bulk modulus:
volume ______
F/A
P
B


volume ______ V / Vi V / Vi
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HOMEWORK
Giancoli, Chapter 12
10, 11, 13, 20, 23, 27, 29, 32, 57, 59
References
o “Physics For Scientists &Engineers with Modern Physics” Giancoli 4th edition,
Pearson International Edition
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