Young's Modulus Question: stretch of a wire

[DanT]

Homework Statement

A force stretches a wire by 2mm. A second wire of the same material and with the same area of cross-section and twice the length is also stretched by the same force. What will its stretch be?

Homework Equations

F= (YA/L)ΔL

The Attempt at a Solution

F, Y, and A are all equal

First wire:
F =(YA/L₁)*2 mm

Second wire:
F =(YA/2L₁)ΔL

1. I set them equal to each other to solve for ΔL
(YA/2L₁)ΔL = (YA/L₁)*2

2. I canceled out YA
ΔL/2L₁ = 2/L₁

3. I multiplied both sides by 2L₁ to isolate ΔL

ΔL = 4 mmDid I do this correctly? I'm unsure because I've received notes from a friend and they got a different answer for the same problem. Thanks in advance.

 

[haruspex]

You did it right.
An easier route to the answer considers the longer wire as two copies of the first wire end to end. Each copy is subject to the same tension as the original, so each stretches 2mm.