A
composite bar of lengthis made from a bar of material
1 and length
attached to a bar ofmaterial
2 and length.
(a) We have to show that the effective
coefficient of linear expansion
for this bar isgiven
by.
(b) Using steel and brass we have to design
such a composite bar whose length is 52.4 cm
and whose effective coefficient of linear
expansion is .
The
coefficients of linear expansion for steel and brass are
and .
When the
temperature of the composite material is raised by
,
length of the bar of material 1 changes by
,
and that of the bar of
material 2 changes by
.
The change in length of
the composite bar will therefore be
Therefore, the effective
linear expansion coefficient of the composite bar is
(b)
Let the bar 1
be steel and its length be
and the bar 2 be brass and its length be
.
The length of the composite bar L
is 52.4 cm. We want the linear coefficient of expansion of the
composite bar to be
.
We therefore have
Substituting
,
we find that the length of the steel bar has to be 39.3 cm and that
of the brass bar has to be 13.1 cm.
is made from a bar of material
1 and length
attached to a bar of material
2 and length
.
(a) We have to show that the effective
coefficient of linear expansion
for this bar is given
by
.
(b) Using steel and brass we have to design
such a composite bar whose length is 52.4 cm
and whose effective coefficient of linear
expansion is
.
and
.
,
length of the bar of material 1 changes by
,
.
.
,
we find that the length of the steel bar has to be 39.3 cm and that
of the brass bar has to be 13.1 cm.