Young's Modulus for Two Materials connected

AI Thread Summary
To calculate the change in length for aluminum and steel connected as one rod, the equations for stress and strain can be set equal due to the uniform force applied. The total change in length of the rod is 1mm, with the aluminum section being twice as long as the steel section. By manipulating the equations for each material's Young's modulus, the relationship between their respective changes in length can be established. The force and area can be eliminated from the equations, simplifying the calculations. Using the given ratios and total change in length, the problem can be solved effectively.
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If Aluminum and steel are connected as one rod, and are attached to the wall and is pulled upon. How would the change in length for each material of the rod be calculated? I'm given that the Aluminum section is twice as long as the steel section, and the total change in length of the whole rod is 1mm.

So far, I've said:
F = Y(delta-L / L-naught)A + Y(delta-L / L-naught)A
*Where, the first part is for Aluminum, and the Second part is for Steel.

Manipulating this equation I got:

(2Fx)/A = (6.9E10)(delta-Laluminum) + (4E11)(delta-Lsteel)
and, delta-Aluminum + delta-steel = 0.001m
*where x = the length of steel, therefore aluminum = 2x.

This is where I'm stuck. I dont' know the Force applied, or the Area of the rod. What can i do? Thanks in advance for any help.
 
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OK another thing I've thought up is saying...

F = Y(delta-Laluminum / L-naught)A
and
F = Y(delta-Lsteel / L-naught)A

since force is equal throughout?

Then set the two equations equal to one another, where A cancels out?

Can anyone confirm this is a way of doing it?
 
Looks good to me. The stress (F/A) is the same throughout the rod. You'll also need to use the other facts given regarding total change in length and the ratio of the two original lengths.
 
awsome, thanks a lot.
 

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