Hello, and welcome to my Christmas Club offering of a story to add to the lovely Sian's collection of Christmas memories.
At Christmas, we try and get a little bit of the festive season into lessons at school. As a teacher, one of the branches of mathematics that I teach at A-level is mechanics. Mechanics is all about modelling physical situations using mathematics and calculating effects and outcomes. A couple of years ago, I wrote a problem about Father Christmas getting stuck dangling off the edge of a rooftop inclined at an angle, and asked them to calculate the force the reindeer needed to exert on the reins in order to yank Father Christmas to safety. It required them to resolve forces, to consider the coefficient of friction between the hooves of the reindeer and the snowy rooftop, and to calculate the good man's eventual acceleration. I have included the full problem as an appendix to this post for the interested reader to attempt in a moment of idleness. Answers on a postcard.
I now use this problem each year. And this year I knew I had to go one better. This year there would be props. And so I made a gingerbread house for my girls in the 6th form so that they could really get a solid visual of just how the situation might pan out. And motivation with food never hurts. Either they can solve the problem, rescue Father Christmas and eat the gingerbread house, or they could sit and go hungry.
They worked pretty solidly actually, and I think it was out of genuine enthusiasm for the noble pursuit of Mechanics.
It must be noted that I am not particularly artistic and my fancy decoration skills are non-existent. I took a punt on the idea that dumping a whole bunch of melted white chocolate over the top of the gingerbread might a) look a bit snowy and b) be a crowd-pleaser even if it looks stupid. And it did indeed please the crowds. Including my Mathematical colleagues who cheerfully demolished the remaining foundations.
It was a bit touch-and-go when I found myself up at 6:15am on a Monday morning cursing the yellow quality of light-bulb light that meant I couldn't get good photos, and wondering how on earth I was going to transport a frankly structurally unsound gingerbread house on the tube in half an hour.
However, everything turned out fine and the whole episode with the gingerbread house and Father Christmas' mishap made for a lovely festive last lesson of the term. At the end of the class we munched quietly and watched a compilation of John Lewis adverts from years past. Which was lovely in a sort of heart-rending way and made some of the pupils tear up. So I sent them off feeling a bit Christmassy, and yet sobbing quietly. Unusual, but I think they had fun.
To read other festive stories from Christmas club, head over to Sian's where she's High in the Sky, collecting memories for us all to share.
P.S. As promised, here is the problem:
eg1. Father Christmas attempts to land on a snowy rooftop, but misses. The reindeer cling to the roof which is inclined at an angle alpha to the horizontal such that tan (alpha) = 3/4. Father Christmas, his sleigh and all the presents dangle over the edge of the roof on the end of the reins which run down along the line of greatest slope. The reindeer have a collective mass of 100kg and Father Christmas and his sleigh have a mass of 150kg.
(i) By modelling the reindeer and the sleigh as particles, and given that the coefficient of friction between the snow-capped roofs and the reindeer hoofs is 0.5, find the tension in the reins and state the minimum force the reindeer must exert on the reins in order to hold Father Christmas in limiting equilibrium. Don't forget to do a diagram.
(ii) The reindeer are fed carrots by the children in the house and with their strength renewed, make a huge effort and exert a force of 3000N on the reins. Given that Father Christmas is dangling at rest 2m below the roof, find his acceleration and the time taken for him to reach the edge of the roof and relative safety, giving your answer in surd form.
Finally, remember that if you miscalculate, not only do you get no presents; none of the boys and girls in the world will get presents. Father Christmas didn't take A-level maths so he only has you to save him.