1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Energy stored in the wire

  1. Jan 8, 2015 #1
    1. The problem statement, all variables and given/known data
    Under tension T the wire has lenghth of m, its length becomes n when the tension is increase to T'. What is the extra energy stored in the wire as a result of this process?

    2. Relevant equations
    E=1/2 Fe

    3. The attempt at a solution
    Extra energy= E(n)-E(m) = 1/2 x (T'n-Tm)

    There is no such answer in the multiple choices. Am I wrong when I subtracted the two energy?
  2. jcsd
  3. Jan 8, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I might be wrong but is that the right equation for the energy stored in a "spring"?

  4. Jan 8, 2015 #3
    It is applicable to any specimens when they are extended or compressed within their limits.
  5. Jan 8, 2015 #4


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    E=1/2 Fe looks like some average force times extension when starting at zero force. $$\int_n^m T\; ds$$ would be a lot better. See what that gives. (What are the multiple choice options to choose from ?)
  6. Jan 8, 2015 #5
    I don't think they require the exact energy. The right answer is 1/2(T'+T)(n-m) but I have no idea why.
  7. Jan 8, 2015 #6


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    Well, that IS average force times extension
  8. Jan 8, 2015 #7
    But I just don't understand why i was wrong. Could you please explain how they get the result physically?
  9. Jan 8, 2015 #8
    Anybody explain the result for me please ?
  10. Jan 8, 2015 #9
    If I'm not mistaken ,, I think this is related a work-energy theorem
    the energy is equal to the external work

    $$E_f-E_i = 0.5 (T'_n-T_m)(n-m)$$

    the left side is the energy difference , the right side is the average work done by the tension force [average force times the distance]
    this is what i can say ,,
  11. Jan 8, 2015 #10
    I think that is not the right answer ,,

    the left side is an energy , while the right side is a force ,,,

    Check the units of each side ,,,

    Are they equal ??
  12. Jan 8, 2015 #11


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    I thought the same thought at first, until I realized it (the n and the m) was a multiplication, not a subscript.

    The formula stems from inserting T = k x and ds = dx in $$\int_0^n T\; ds = \int_0^n kx\; dx = \left [{1\over 2} k x^2 \right ]^n_0 = {1\over 2} kx\; x = {1\over 2} Tx$$

    (I strongly prefer and recommend ## {1\over 2} kx^2 ## !!!)

    Numerically there isn't much difference between the 'absent' and the 'right' multiple choice

    [edit] the integral bounds look a bit stupid. lower bound is equilibrium position (T=0)
    Last edited: Jan 8, 2015
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted