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```Physics Notes Ch 9
Statics
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Statics – The study of forces in
equilibrium. The net force and the net
torque on an object (or on a system)
are zero.
The object is either at rest or its center
of mass is moving at constant velocity.
Equilibrium
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Fx = 0
Fy = 0
Fz = 0
Any force acting in the negative x, y or
z direction will have a negative sign.
This is the first condition for
equilibrium.
Torque (Chapter 8, section 4)
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Torque is equal to the product of force times
the moment arm.
 = r F
 (Greek lowercase letter tau) is the symbol
for torque.
Moment arm (r) is the perpendicular
distance from the axis of rotation to the line
along which the force acts.
F is any force.
May also be written as:  = rF 
Equilibrium
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For a body to remain at rest , the net
torque acting on it must be zero.
=0
This is the second condition for
equilibrium.
Fx = 0, Fy = 0, Fz = 0 &   = 0
These are the only requirements for a
body to be in equilibrium.
Elasticity
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Any object changes shape under the
action of applied forces.
The change in length of an object is
directly related to the force applied: F
Hooke’s law (F = k L) applies to
almost any solid (iron to bone) up to a
point called the proportional limit.
Elasticity
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The change in length is also directly related
to the original length: L0
The change in length is inversely proportional
to the cross-sectional area: A
The change in length is also inversely
proportional to a measure of its elasticity
called the Elastic modulus (Young’s Modulus):
E. (There is a table of the Elastic Moduli of
various materials on page 254.
L = F L0 / EA
Elasticity
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If a greater force is applied the object will
continue to stretch and the object will return
to its original length if stretched up to the
elastic limit.
If the force continues to increase, the object
will continue to stretch (but not return to its
original length when the force is removed)
until its maximum elongation is reached at
the breaking point.
The maximum force that can be applied prior
to breaking is called the ultimate strength.
Stress & Strain
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Stress is the force per unit area.
Stress = force/area = F /A
Strain is the ratio of the change in
length to the original length.
Strain=change in length/Original Length
= L/L0
Elastic Modulus
1 F
L 
L0
E A
F/A
stress
E

L / L0 strain
```