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Elastic Cord- Youngs Modulus!

  1. May 26, 2010 #1
    1. Two part question.

    An elastic cord with cross sectional area 4.00mm^2 needs a force of 3.6N to increase its length by 12%

    Part One- Find the Youngs Modulus of Elasticity

    Part Two- The unstretched cord is 0.80m long. Find the energy stored in this strain.

    2. Relevant equations:
    Y= Stress/ Strain
    Stress= Force/ cross sectional area
    Strain= change in length/ original length


    Part One Attempt-
    Stress= 3.6N/ 4* 10^-2
    Stress= 90

    Strain= 9.6/ 80
    Strain= 0.12

    Y= 90/ 0.12
    Y= 750

    Now I dont know what to do! What are the Units? Is this correct?

    Part Two Attempt-

    I believe this has something to do with Potential Energy...is this correct?

    Any help would be much appreciated!!! Thanks so much for your time
     
  2. jcsd
  3. May 26, 2010 #2
    your first part is wrong. You HAVE to change to si units if you want to do the rest of the problem... also what is the deal with "3.6N/ 4* 10^-2" what that is effectively saying is that stress is 3.6 multiplied by 400!!!!!!!!!! do you understand that the the ^2 given in the question is part of the unit and that you DONT actually square the number!!!!!!! You need to work on your exponents and what they mean, there is nothing wrong with the actual physics you've done. (sort of)
     
  4. May 26, 2010 #3
    you also need to post the entire question you need help with. where did the lengths you have come from??
     
  5. May 26, 2010 #4
    Thanks for your help so far!

    I understand from your help on my last question that you dont square your numbers, but I havent. I thought I had to change my units to metres, so I changed 4 o (4*10^-2)? Maybe I should have just written 0.004 to save confusion.

    Am I right in even converting this to metres?

    Ive just attempted again:

    Stress= 3.6N/ 0.004
    Stress= 900

    Strain= 900/ 80
    Strain= 11.25

    Y= 90/ 11.25
    Y= 8

    Is this more like an answer I should be looking for?
     
  6. May 26, 2010 #5
    sorry, also forgot to mention that for some reason we are never given the lengths!! I assume because we are using percentages I could just input the easiest figure and the result will always be the same??
     
  7. May 26, 2010 #6
    kk go to google type in (4mm^2) to m^2 its 4*10^-6 not 0.004 also what i was saying before.. you had x/x^-2 what hapens when you divide by a number with a negative index?
     
  8. May 26, 2010 #7
    Ooooh OK I see what you are saying.

    Stress= 3.6N/ (4* 10^-6)
    Stress= 900000

    Strain= 900000/ .80
    Strain= 1125000

    Y= 90/ 1125000
    Y= 8^-5

    :( Now I am confused...and hopeless!
     
  9. May 26, 2010 #8
    no DO NOT PUT the - index in and your good.
     
  10. May 26, 2010 #9
    ok you were actually correct for part a sorry........thought you were making the same mistake as before....
     
  11. May 26, 2010 #10
    and yes for deleta L on L it will be 0.12... were did you get 0.8??
     
  12. May 26, 2010 #11
    OK, sorry for this, but now I am totally confused.

    Is the answer I had originally correct? 750? Or is my new answer correct? haha!?
     
  13. May 26, 2010 #12
    new your 1st one was way off
     
  14. May 26, 2010 #13
    your 1st stress, your youngs modulus is still wrong check you change in length!!!!!!!
     
  15. May 26, 2010 #14
    I got .8 because it was .8 of a metre? previously i had 80cm written in but i guessed because we are using metres, .8 would have been the correct input?
     
  16. May 26, 2010 #15
    Stress= 3.6N/ (4* 10^-6)
    Stress= 900000

    Strain= .096/ .80
    Strain= 0.12

    Y= 900000/ 0.12
    Y= 75* 10^5 ?????????????????
     
  17. May 26, 2010 #16
    ok but delta L would be .8*0.12
     
  18. May 26, 2010 #17
    Thanks for your help so far:

    Can anyone help with part two?

    So far I have equations:

    W= 1/2kx^2
    F=kx (so k= f/w)??

    So:

    k= 3.6/ 0.096= 37.5

    W= (1/2)(37.5)(0.096^2)
    W= 0.1728J ----does anyone know if this appears correct?
     
  19. May 26, 2010 #18
    looks good to me
     
  20. May 26, 2010 #19
    pat666, you are a champion :) Thankyou.
     
  21. May 26, 2010 #20
    i just had a proper look at it then and its actually not correct sorry. k doesn't equal f/w since w doesnt = x
    your actual procedure and answer is correct but this " k= f/w)" isnt. your answer is correct just that one error. (which you didnt use in your calculations)
    3.6=k*.096
    k=37.5Nm
    w=.5*37.5*.096^2
    w=0.1728J
    where are you getting these questions that dont have answers?
     
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