Deformation of a dicomponent rod under tension

[Woopydalan]

Homework Statement

Homework Equations

The Attempt at a Solution

For this problem, my thinking was that since the top of the rod is fixed, then the only part that is elongating is the bottom, so I found the part elongating at AB and said that was the total elongation. I am not sure if this reasoning is sound. I suppose the other possibility would be to add up AB and BC to get the total, but then I don't know what the deformation at point B means. I am interpreting that as the elongation of BC.

 

[haruspex]

Yes, you need to add them for the total deformation, and the deflection of B is the change in length of BC (since C appears to be a fixed point). I haven't checked the arithmetic but your equations look right.

 

[Woopydalan]

Wouldn't that mean that you need the answer to part b to solve part a? That is why I am confused I think

 

[haruspex]

Wouldn't that mean that you need the answer to part b to solve part a? That is why I am confused I think

Yes, the questions are asked in reverse of the logical order.

 

[Woopydalan]

Here is my attempt 2. How does it look?

 

[haruspex]

Looks about right.