Young's Modulus Question: stretch of a wire

  • #1
1
0

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 cancelled out YA
ΔL/2L1 = 2/L1

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

ΔL = 4 mm


Did 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.
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,536
6,432
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.
 
  • Like
Likes DanT

Related Threads on Young's Modulus Question: stretch of a wire

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
3
Views
10K
  • Last Post
Replies
3
Views
893
  • Last Post
Replies
4
Views
8K
  • Last Post
Replies
15
Views
7K
  • Last Post
Replies
2
Views
18K
  • Last Post
Replies
1
Views
1K
Replies
11
Views
19K
Replies
7
Views
30K
Top