# Math Help - A bimetallic rob..

1. ## A bimetallic rob..

A bimetallic rod is composed of brass and copper.
a. If the rod is subjected to a compressive force, will the rod bend toward the brass or the copper? Why?
b. Justify your answer mathematically if the compressive force is 5.00 X 104 N.

2. Can't completely answer your question, but I'm sure it would bend toward the softer metal. Doubt this helps you, sorry.

3. Originally Posted by Refujoi
A bimetallic rod is composed of brass and copper.
a. If the rod is subjected to a compressive force, will the rod bend toward the brass or the copper? Why?
b. Justify your answer mathematically if the compressive force is 5.00 X 104 N.
The ratio of the changes in length of the brass and copper is equal to the
ratio of the Young's modulus of copper to brass:

$
\frac{\Delta l_B}{\Delta l_C}=\frac{\Delta Y_C}{\Delta Y_B}\approx \frac{100}{130}
$
.

So the change (reduction) in length of the brass is less than that of the
copper, so the rod bend toward the copper.

To justify this we do not need to know the loading, just that the tensile
stress is the same in both the copper and brass, then as for each material:

$
Y=\frac{\mbox{tensile stress}}{\Delta l/l_0}
$

the result follows.

RonL