Within the elastic region (see the graph below), there exist a relationship
between the force applied and the change in the physical state of the
object. Experiments have shown that the elastic behavior can be described
by the following relations with the condition that the change in the
physical state is small in compared to the original. It can be shown
that the stress is directly proportional to the strain within the straight
line region. This relationship is expressed by Hooke's Law in two ways.
1. The equation
F =  kx
2. The equations
of stress and strain.
In the region where
the stress is directly proportional to the strain, relationship are
obtained. The stress is directly proportional to the strain.
In tensile/
compressive we have
In the Bulk
stress/strain we have:
Since
P
= F/A then the equation simplifies to
P
= B(ΔV/V_{0})
In the Shear
stress/strain we have:
Example 1 
A
tow truck is pulling a car out of a ditch by means of a
steel cable that is 9.1 m long. and has radius of 0.50 cm.
When the car just begins to move, the tension in the cable
is 890 N. How much has the cable stretched?



Example 2 
The
pressure increases by 1.0x104 N/m2 for every meter of depth
beneath the surface of the ocean. At what depth does the
volume of a Pyrex glass tube , 1.0 x 102 m on an edge at
the ocean's surface decreases by 1.0 x 1010m3? 


Example 3 
A
copper cube, 0.3m on a side is subjected to two shearing
forces each of magnitude F = 6.0 x106 N. Find the angle
in degrees which is one measure of how the shape of the
block has been altered by shear deformation. 


