Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0°C. (a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0°C?

Video transcript

Welcome back, everybody. We are looking at a suspension bridge that is constructed with these types of steel bars right here. Now, we are told, sorry, let me change color here. We are told that the length of these bars is 8 m and it's constructed during the winter time when the temperature is only two degrees Celsius. Now, the temperature when it hits summer will reach all the way up to 40 degrees Celsius. And we're looking at a steel metal bar here. So it's gonna, it's gonna expand and its expansive constant is 1.2 times 10 to the negative five degrees Celsius to the negative one. And we are tasked with finding how much space is needed. A delta L between the bars so that just the bars touch and are not compressed when the summertime does roll around. Luckily, we do have a formula for this. This is just simply going to be the expansive constant times the initial length of the individual bars times the change in temperature. So let's go ahead and plug in in our values. We have 1.2 times 10 to the negative five times our initial length of 8 m per bar times the change in temperature. Well, it's 42 degrees minus two degrees. So that's just 40 degree difference. Which when you plug into your calculator, you get 3.84 millimeters, which corresponds to our answer choice of a. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.