# isaac physics B9.7

a wire of natural length 50cm, diameter 1.5mm and young modulus 3.2 GPa is stretched to a new length of 54.2 cm, which is below the limit of proportionality. how much work was done in order for this to happen?
Original post by Rehan1337!
a wire of natural length 50cm, diameter 1.5mm and young modulus 3.2 GPa is stretched to a new length of 54.2 cm, which is below the limit of proportionality. how much work was done in order for this to happen?

3.3
Original post by Rehan1337!
a wire of natural length 50cm, diameter 1.5mm and young modulus 3.2 GPa is stretched to a new length of 54.2 cm, which is below the limit of proportionality. how much work was done in order for this to happen?

We can assume wholly Elastic Response.
Given:
Work done is defined as:
W=Fd (after integrating) (1)

d is defined in the Question.
F can be obtained given the definition of Young's Modulus:
E=σ/ε=Fdu/AU (2)

Here I define du as the Change in Length and U as the original Length.

Solving for F by rearranging (2) and substituting it into (1) provides the solution.
Original post by Bleu_
3.3

"3.3" doesn't mean anything.
Original post by Joseph McMahon
We can assume wholly Elastic Response.
Given:
Work done is defined as:
W=Fd (after integrating) (1)

d is defined in the Question.
F can be obtained given the definition of Young's Modulus:
E=σ/ε=Fdu/AU (2)

Here I define du as the Change in Length and U as the original Length.

Solving for F by rearranging (2) and substituting it into (1) provides the solution.

Can you explain why you have to integrate my head is stuck
Original post by Bryson199
Can you explain why you have to integrate my head is stuck

This was a while ago: I think I was being overly specific about the definition of work i.e. that it is W=Fd is the simplest case where F is constant and the displacement d is in a straight line.

Although I did go on to clarify that d had been defined already in your question.