# Length change for a rod of two sections

1. May 3, 2014

### Myr73

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 1.20mm. By how much does the length of each section increase ?
I understand that E (brass) = 1/2 E steel.
However first of all. when it change in length of 1.20 mm, is it talking about the complete change in length or just the one of the steel?
After that, I am unsure how to put the equation together. I understand that Change in L = 1/E (F/A) L0
But considering we don't have F and A. I know a previous explanation just took F/A out, but I cant see how that would work.
Thank you

2. May 3, 2014

### TSny

Hello, Myr73. Welcome to PF!

I think they mean the total change in length is 1.20 mm.

Can you find the ratio ΔLsteel/ΔLbrass?

3. May 3, 2014

### Myr73

Thank you,
Umm so like {(1/Esteel)(F/A)L0steel }/ {(1/Ebrass)(F/A) L0brass} ??
do F and A cancel there--> 1/Esteel L0Steel / 1/Ebrass Lobrass ?? Idk

4. May 3, 2014

### TSny

Yes, F and A cancel. Anything else cancel? Note that they said each rod is identical except for the material.

5. May 3, 2014

### Myr73

So Lo cancels as well lol.. Then ΔLsteel/ΔLbrass= 1/ESteel / 1 / Ebrass.. Would I cancel the 1's as well? = ESteel/Ebrass?
Does ΔLsteel/ΔLbrass=2 ?

6. May 3, 2014

### TSny

$$\frac{\Delta L_{steel}}{\Delta L_{brass}} = \frac{ \frac{1}{E_{steel}}}{\frac{1}{E_{brass}}}$$

Be careful when you simplify this. Do you remember rules for dividing by a fraction?

7. May 3, 2014

### Myr73

umm.. ΔLsteel/ΔLbrass= Ebrass/Esteel.= 0.5 ?

8. May 3, 2014

Yes.

9. May 3, 2014

### Myr73

hugh..nice thanks.. however I don't know what to do next.

10. May 3, 2014

### TSny

You have two unknowns. What are they?

To solve for two unknowns you need two equations that relate the unknowns. Can you write down two equations that you could use to solve for the unknowns?

11. May 3, 2014

### Myr73

The two unknowns are Delta L (brass) and (steel). Or do you mean the F and A.. I am sorry I honestly don't know. on-line classes sometimes leaves me with a shortage of information.

12. May 3, 2014

### TSny

Yes, your two unknowns are ΔLsteel and ΔLbrass.

You have found the ratio of these and that gives you one equation to work with.

You will need another relation between ΔLsteel and ΔLbrass. Can you write down a second relation (or equation) based on what's given in the problem?

13. May 3, 2014

### Myr73

ok,
Let's see I have --> L0(brass)= L0(Steel) , L = 2L0(b)=2L0(s) or = L0(b) + L0(s)
Delta L = Lfb-L0b + Lfs-L0s ( although I can't see how I can use that)
Delta L= 1.2mm
ok umm --> 1.2mm = Delta L (brass) + Delta L (S)
and 0.5 Delta L Brass= Delta L Steel
--> 1.2=1.5 Delta L (Brass)
--> 1.2/1.5=0.8mm = Delta L (Brass)
1.2-0.8= 0.4mm= Delta L( Steel)
Is that right, or am I way off ? lol

14. May 3, 2014

### TSny

That looks correct. Good work!

15. May 3, 2014

### Myr73

Thank you :).. You help me alot , I appreciate your kindness

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