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Homework Help: Youngs modulus

  1. Mar 29, 2003 #1
    youngs modulus....

    there are two rods rod1 , made of brass - length L1=2m
    area of cross section A1 2x10^-4 m^2 and young's modulus y1= 10^11
    rod 2 , made of steel , lenght L2 , cross sectional area A2=10^-4 m^2 and youngs modulus y2 = 2x10^11 .

    the question is if the two rods are fixed end to end , and two equal and opposite forces are applied at each end (the ends not fixed to each other-free ends )pulling the combination of both the rods outward,
    and the value of the forces applied are 5x10^4 on both sides.
    then find the length of rod 2 such that both have equal increase in length dl (read delta L ) as a result of the forces.

    here's what i did ,
    i assumed that because both the rods are fixed at one end , any extension that takes place will occur in the direction of the force

    i.e F = (y1.A1.dl)/L1
    i know F,A1,y1,L1 theredore i can find dl
    now i substituted this dl in the corresponding equation for rod 2 and then found L2 ( F=( y2.A2.dl)/L2 )
    and i got it to be equal to 2m but the answer in the solutions given out was 1.8m

    i want to know what is wrong with my assumption because i am sure something is wrong with it...

    or if take the lenght of the total rod to be L1+L2 i.e L2+2and take the midpt. of the rod as the origin for calculating ..
    oh well i'm very confused..
    please help me if u can!
    thanks
     
    Last edited by a moderator: Mar 29, 2003
  2. jcsd
  3. Mar 29, 2003 #2
    Well I can't see any flaw in your calculation. The steel rod has only half the cross section, but double strength, so the effect should be the same.

    The only correction I can think of, is: If a rod gets longer, it will also get thinner. So maybe you have to use different A's.

    On the other hand, if you plug in values, you find dl = 5mm. Or .25% of the original length. Not enough to explain the 10% difference. Plus, I doubt the rods can take such a strong force and still be in the elastic domain. Imagine you suspend a 5-ton truck by only a 2m x 9mm brass rod...
     
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