Question

A rod is made of two sections joined end to end. The sections are identical, except that one is steel and the other is brass. While one end is held fixed, the other is pulled to result in a change in length of 1.20 mm. By how much does the length of each section increase?

Answer 1

so right away we see that the E value of steel is twice that of brass.

we know this ratio

(E* delta L) of steel/ L= (E*delta L) of brass/ L

and we know that the denominator of both sides cancels because the original sections are identical in length. so we now have:

E* delta L (steel) = E* delta L (brass)

since we know the ratio of E values is 2 to 1, then the ratio of delta L values must be 1 to 2, to make the above ratio true. so we know that whatever length brass expands, steel expands by exactly half of it.

so we can divide 1.2 into three equal parts. we get

0.4

multiplying this by two gives us the expansion of brass, and the remaining 0.4 mm are the expansion of steel