I'm grateful for my wonderful job this time of year. Everyone in school is cheerful, if slightly manic, we get inundated with chocolates in the department and no one feels like doing much work. I tend to carry on regardless. For instance:
Student: Can't we have fun lesson today, Miss?
Me: All my lessons are fun!
Student: But it's Christmas.
Me:...No it's not. It's 14th December. There are still eleven more sleeps to go.
Student: But it's our last lesson.
Me: No it's not, we've got some in January. And then February. And with a shocking inevitability, we've got lessons in March. There are others too, but I don't want to overload you.
Student: But it's our last lesson before Christmas.
Me: Actually, you've got lessons tomorrow and Friday as well.
Student: I mean our last mechanics lesson before Christmas.
Me: Yes it is.
Student: So can we watch a video?
Me: I've got something way better than a video. It's in 3D and it happens in real time. There's an interactive element and this will be a totally unique, one-time-only performance.
Me: Go on, you can get there.
Student:....It's just going to be you teaching us mechanics isn't it?
Me: Yes! Got it in one!
Student: Nothing Christmassy.
Me: I'll see what I can do...
[On the board]
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 Chirstmas, 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 [That totally rhymes, by the way] 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, [Impersonate dangling Father Christmas] 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.
Remember gents, 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. No pressure.
Student: But carrots don't give you energy.
Me: Yes they do.
Student: No, they don't have much protein or carbs in.
Me: They have vitamins though.
Student: You don't convert vitamins into energy. And how come the reindeer don't weigh more?
Me: They're magic reindeer. They convert vitamins into energy instantly and therefore their mass is constant.
Me: You will happily accept the reindeer can fly but the vitamin-energy conversion bothers you?
Student: Yes miss. 'Cause everyone knows that reindeer can fly, but you're just making stuff up and calling it magic.
Student: And just adding Santa into the example doesn't make it a Christmas lesson.
P.S. The answers we are looking for are:
(ii) a=5.5 ms^-2 and t=2Root2/3
P.P.S. How did you do? If you got them wrong, no presents for you. Sorry.
P.P.P.S. Stop by on Sunday for an exciting scrappy announcement!