Linear Expansion: Accurately Measuring with Tape Measures/Rulers

[DJ-Smiles]

Ok So I was told to think about what would happen if you tried measure something with a metal ruler or tape measure in an environment that would cause negative linear expansion; so the ruler gets smaller. How would the accuracy be affected if the tape measure/ ruler was calibrated at a greater temperature?

So i was thinking that because of the linear expansion equation: ΔL=αLiΔT, it would be affected by the lengths, temperature differences and coefficients of linear expansion for the two materials (ruler/tape measure & the thing that is being measured).

Ultimately this leads me to the questions: will the ruler be ever be accurate?
what are some mathematical methods of finding this out?
and in different situations how would this affect the measurement?

some different situations would be:
same lengths for the two materials
different lengths
same coefficient
different coefficient
same Δtemp
different Δtemp

I would like to be able to write a complete paragraph on this topic with the use of both qualitative and quantitative data: theory and very basic maths. what equations could be used to find this and how could i know if the ruler will be accurate.

Thanks in advance for any help.

Gary.

 

[jbsteele]

In a situation where a metal ruler or tape measure is being used to measure something in an environment that causes negative linear expansion, the accuracy of the measurement can be affected if the tape measure/ ruler was calibrated at a greater temperature. This is due to the linear expansion equation: ΔL=αLiΔT, which is affected by the lengths, temperature differences and coefficients of linear expansion for the two materials (ruler/tape measure & the thing that is being measured). To calculate the accuracy of the ruler, one can use a formula such as ΔL=αLiΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the difference in temperature. This formula can be used to determine the accuracy of the ruler in various situations such as having the same or different lengths, coefficients of linear expansion, and temperature differences between the two materials. Depending on the values of these parameters, the accuracy of the ruler may vary.