Newton's Laws Setting:
I was looking for a problem based in real engineering that would ask you to pay attention to all three of Newton's Laws and in particular would require care with Newton's 3rd Law. Roman arches (more generally called voussoir arches) seemed to fit the bill and I expected that you would be able to find lots of useful resource material about the physics. Imagine my surprise to find mostly graduate level analyses of these arches and almost nothing useful at the level of our class. Unfortunately for you that means it is a perfect portfolio problem. This is largely because the form of the problem I want you to address is a free standing arch (see image below) which is different than a classic archtectural arch.. Below you will find some useful links to help you understand these delightful and beautiful examples of engineering statics.
Your actual challenge is to use your skills with Newtonian Mechanics to determine the maximum load on the keystone that will cause the unrestrained base block to slide out IF you know the two coeficients of static friction (between the blocks themselves and between the block and the ground) for a 3 stone voussoir arch. Students who have too much free time are encouraged to consider the more general problem of a 5 or 7 stone (why is it always an odd number?) regular voussoir arch. Careful attention to your free body diagram(s) is a critical starting point.
Useful Documents:
Masonry at MIT: John Oschendorf has clearly spent some time analyzing masonry arches and he has a number of lovely and complex analyses of roman arches which are well beyond our level of study. I just offer this link to his website for the sake of your curiousity - I didn't find any particularly useful documents here.
Reading Bridges: This is a nice little article which suggests how you will go about the solution for you voussoir arch but is more focused on generalities than specifics. I think you may find it helpful.
Here is the image of a free standing voussoir arch (by artist Andrew Goldsworthy) like those we are studying:
