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!

Expansion of ruler and rod help

  1. Feb 11, 2004 #1
    The length of a metal rod is measured to be 20.08 cm using a steel ruler when both the rod and the ruler are at 22oC. Both the rod and the ruler are raised to a temperature of 253oC. When the rod is measured at this higher temperature, its length is found to be 20.32 cm.

    ****
    a) What is the coefficient of expansion of the metal?
    b) You now make a rod of the same material but with twice the length. What will it coefficient of expansion be?
    c) You now make a rod of the same material but with twice the diameter. What will it coefficient of expansion be?
    //////

    So far I am stuck on part a. If I can get this part, then I should be able to get the rest.

    Now I know that the equation is delta L=L*(coefficient of expansion)*(delta T)

    Now it appears that I have all the informatin given in the problem, so I plug it into the equation, but it doesnt work. Then I realize that the ruler is stretching also, which means the number scale on the ruler also changes. Now I have to somehow relate that number scale to the coefficient of expansion, but I'm not sure how.

    I know from the book at the coefficient of expansion for steel is 11*10^-6 /degree C.
     
  2. jcsd
  3. Feb 12, 2004 #2

    Doc Al

    User Avatar

    Staff: Mentor

    First find the actual length of the expanded rod. You know the length of the expanded rod as measured by the expanded steel ruler. So, knowing the expansion of the steel, find the actual length of each "1 cm" marking on the ruler. Then you can convert to real units.

    Hint: Write down the final expression (for the coefficient of expansion of the rod) and simplify it before you start doing any arithmetic.
     
  4. Feb 6, 2012 #3
    Thread necromancy!

    I've got slightly different numbers: The length of a metal rod is measured to be 20.08 cm using a steel (α = 1.1e-005 (oC)-1) ruler when both the rod and the ruler are at 22oC. Both the rod and the ruler are raised to a temperature of 253oC. When the rod is measured at this higher temperature, its length is found to be 20.32 cm.

    When heated, the rod expands. However, the ruler also expands. So the rod doesn't actually expand from 20.08 to 20.32. I know the rod expands more than the ruler, because after heating, the rod is measured to be longer. If they expanded the same the length wouldn't change and if the rod expanded less the final length would be less than the original length.


    I used 1 cm because I need to find the actual length of each '1 cm marking' after heating.
    ΔLs = L [itex]\alpha[/itex] Δt
    ΔLs = (1 cm) (1.1e-5 °C^-1) (253°C - 20°C)
    ΔLs = .002563
    1 hcm (heated cm) = 1.002563 cm (real cm)

    If the rod now measures 20.32 hcm, so I convert my units:

    20.32 hcm * (1.002563 cm/1 hcm) = 20.37208 cm

    So now I have an actual length and can calculate the [itex]\alpha[/itex].

    [itex]\alpha[/itex] = ΔL/(L*Δt)
    [itex]\alpha[/itex] = .00435

    And it tells me NO!
     
  5. Feb 6, 2012 #4
    Doh!

    If I actually use a ΔL instead of L it works out.

    /alpha = 6.243e-5

    Thanks for being here so I can think this through! :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Expansion of ruler and rod help
Loading...