How Does Young's Modulus Affect the Elongation of Composite Rods?

[notsam]

Homework Statement

The radius of a rod is 0.146 cm, the length
of aluminum part is 1.2 m and of the copper
part is 2.76 m. The rods are connected. Determine the elongation of the rod if it is
under a tension of 3140 N. Young’s modulus
for aluminum is 7 × 1010 Pa and for copper
1.1 × 1011 Pa .
Answer in units of cm.

Homework Equations

E= F*Lo/Ao*Lc
E= Young's modulus
F= Force
Lo= Original length
Ao=Area
Lc= Change in length

The Attempt at a Solution

Ok so I have the Young's Modulus for each piece of the complete rod. Those plug into "E", 3140 is my force, ect. The only unknown is the change in length, also the only thing that I have to convert to start working the problem is the radius and then my final awnser back to cm which is the units the final awnser must be in. Ok so my thinking is that even though it is a SINGLE rod with two diffrent parts you must solve each part seperatly. Soo I solve for the Aluminum side and find its change in length, and then do another equation with the Copper. After solving for each Lc I can then add them together to find the total change in length. OR is it because there is a single force acting on the whole system I have to have a single equation with the Young's modulus
numbers added together "E total", then also add the total lengths up "Lo total", and the total area of "Ao total" Aluminum and Copper?

 

[Mapes]

The first approach will work much better. (Imagine a rod of stiff steel end-to-end with a rod of compliant rubber and you'll see that adding the Young's moduli won't work at all.)