Deformation of solid
Hooke’s law
Explain force-extension graph
A
--Because we are changing the force and this
results in a change in the extension, the force
along the horizontal axis and the extension
along the vertical axis.
--But this graph has extension on the
horizontal axis and force on the vertical axis.
--Because the gradient of the straight section
of this graph turns out to be an important
quantity, known as the force constant of the
spring
--The extension x is directly proportional to
the applied force (load)
F = kx
Hooke’s low:
--A material obeys Hooke’s low if the
Extension produced in it is proportional
to the applied force (load).
--So, the force constant k of the spring is
given by the equation
k = F/x
--A stiffer spring will have a large value for
the force constant k. Beyond point A, the
graph is no longer a straight line; its gradient
changes and we can no longer use the
elastic limit & spring
constant
Elastic limit
--The force beyond which the spring becomes
permanently deformed is known as the elastic
limit.
--Explain: if you apply a small force to a spring and
then release it, it will return to its original length.
This behavior is described as ‘elastic.’ However, if
you apply a large force, the spring may not return
to its original length. It has become permanently
deformed
elastic limit & spring
constant
Spring constant
--Hooke’s low is a principle of
physics that state that the
force F needed to extend or
compress a spring by some
distance X is proportional to
that distance.
--F = kX, where the gradient k
is known as the force constant
of the spring
--F is the applied force (load)
--X is the extension
Calculation of the effective spring constant
of two spring combine in series
Consider two
springs placed
in series with a
mass on the
bottom of the
second. The
force is the
same on each
of the two
springs.
Therefore,
F = k11X11 = k22X22
Solving...