1. Not finding help here? Sign up for a free 30min 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!

Young's modulus problem - need a hint

  1. Sep 25, 2004 #1
    Young's modulus problem -- need a hint

    There are two wires, one brass the other copper, both 50 cm long and 1.0 mm diameter. They are somehow connected to form a 1m length. A force is applied to both ends, resulting in a total length change of 0.5 mm. Given the respective young's moduluses of 1.3 x 10^11 and 1.0 x 10^11, I'm supposed to find the amount of length change in each section.

    Apparently a variation of Hooke's law should be used here, such as F/A=Y(change in length/original length)

    I'm stuck on how can I solve this with 2 unknowns (force and change in length)?
    Regards
     
  2. jcsd
  3. Sep 25, 2004 #2

    Clausius2

    User Avatar
    Science Advisor
    Gold Member

    Hello redshift! I'm going to rewritte your problem in terms of stress [tex]\sigma[/tex] (Pa) and unitary deformation [tex]\epsilon=\frac{L-L_o}{L_o}[/tex] where Lo is the original lenght. So that, the stress exerted is the same in each section of the wire:

    Hooke's law: [tex] \sigma=E_t \epsilon_t=E_1 \epsilon_1=E_2 \epsilon_2[/tex] where "Et" (N/m^2) is the apparent Young modulus of the complete wire.

    Compatibility of deformations: [tex]\bigtriangleup L=\bigtriangleup L_1 + \bigtriangleup L_2[/tex]


    Then, you have three equations for three unknowns: Et, epsilon1 and epsilon2.

    Hope this help you a bit.




    You've got two unknowns for
     
  4. Sep 26, 2004 #3
    Many thanks

    I think I get it. Based on your equations, the ratio of the young's moduluses should equal the ratio of the individual increases, that is, 13/10 = L1/L2
    Therefore, 10L1 = 13L2
    Since, L1 = L2 = 0.5, then L1 = 0.5 - L2. Plugging this into the above gives 10(0.5 - L2) = 13L2, so that the increase of L2 (brass wire) is 0.21 mm.

    Many thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Young's modulus problem - need a hint
  1. Young modulus problem. (Replies: 16)

Loading...