# Urgent- having great difficulty with linear expansion of a tape measure

1. Jun 9, 2012

### 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.