Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Frustrated by simple algebra problem

  1. Feb 22, 2014 #1
    1. The problem statement, all variables and given/known data
    For small changes in temperature, the formula for the expansion of a metal rod under a change of temperature is:
    L-Lo = aLo(t - to)
    L= length at temp. t
    Lo= initial length at temp. to
    a= constant that depends on metal
    A) express L as a linear function of t. Find the slope and y intercept(hint: treat the other quantities as constants.)

    2. Relevant equations

    3. The attempt at a solution
    Solution 1?: the slope is aLo as stated by the equation, and the y intercept is Lo...
    L= aLot-aLoto+Lo
    Doesnt work, still has variable to, lo, etc.

    Solution 2?: assume a=1
    Slope= Lo? Y intercept also lo?

    Solution 3: Lo, a and to=0
    L=0... doesnt work

    Or, pretend all constants=1
    Seems too specific.

    I don't really know from which other angle to tackle this problem, I would appreciate some ideas, although I can imagine the answer should be obvious to me. I don't know how to turn this fully into y=mx+b. Thanks in advance.
  2. jcsd
  3. Feb 22, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Are to, lo variables? Or are they constants which look like variables?
  4. Feb 22, 2014 #3
    They are constants i suppose, because they are the initial condition which doesnt change. But i dont understand what "treat them as constants" means... does it mean i could just ignore them?

    Tried another way..
    From L=aLot-aLoto+lo
    Y intercept= aLoto+lo
    Last edited: Feb 22, 2014
  5. Feb 22, 2014 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    That y intercept is -aL0t0 + L0 .

    Either way might be correct.

    The initial result is correct if the y-axis is at t = t0 .

    The result is the post quoted here is correct if the y-axis is at t = 0 .

    The slope is the same in both cases.

    The result you have in your Original Post makes more sense to me.
  6. Feb 22, 2014 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Your final answer here is not quite correct. If we use 'intercept' to have its normal meaning, then you need Intercept = L_0 - a L_0 t_0 (not L_0 + a L_0 t_0 as you wrote).

    "Treating them as constants" means that they are not the variables in this problem, but certainly you cannot ignore them. The only "variables" here are L and t. In a specific problem the parameters L_0 and t_0 would be given some numerical values, but that would still allow L and t to vary.
    Last edited: Feb 22, 2014
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?