## Rugby, and Newtonian Mechanics

Yesterday we went to Headingley Carnegie to watch a game of rugby union. The match was in the British and Irish cup between Leeds Carnegie and Bristol, Leeds won 24-19, if you’re interested in that sort of thing.

About ten minutes into the second half Leeds brought on a prop forward by the name of Sam Lockwood. Sam is affectionately know as “the human wrecking ball” amongst the Carnegie faithful. The nickname has nothing to do with Myley Cyrus, and everything to do with the way he hits the defensive line, which has a similar effect to a wrecking ball.

Anyway, the first time he got the ball he hit the line in his usual fashion and the impact carried him and three defenders a good ten yards. This prompted a conversation about how he would be the last person we would like to run at us. During the conversation we were discussing that it isn’t purely a size thing, Sam is a big bloke but there are others bigger who don’t hit the line anywhere near as hard. We noted that it was down to the combination of size and speed. He moves much faster than most players his size. It was while discussing a size speed trade off, wondering if a player had an optimal size to speed ratio (I think a negative correlation between someone’s mass and their top speed would be fair assumption), that I realised what I was actually discussing was momentum.

Momentum is the product of mass and velocity (algebraically speaking, p = mv). I taught momentum and impulse before Christmas and didn’t think to use rugby at all, which is strange because I watch a lot of it.

I then thought further about the sport, and it occurred to me that there are tons of opportunities to analyse the mechanics of a rugby match. There is the force a player runs at, their momentum, the impulse, the friction exerted be the studs. The clash mentioned above where Sam Lockwood took three defenders ten yards could form the basis for a whole lesson itself! On top of this there is a huge variety of projectile problems one could look at.

The question of forward passes is an interesting one, and the angle the ball leaves the hand, the velocity of the player, the velocity of the pass, if all these vectors were resolved we could get some interesting results.

I am extremely excited about teaching mechanics now, the next mechanics module I teach is M3, and I intend to find some interesting rugby based problems in the content!

## More maths in the playground

My daughter is now a little over two, and as such I spend quite a lot of time at children’s play parks and the amount of maths you can find there is incredible.

I’ve written along these lines before. From silly things, like the fact our local park was the only place I’ve seen with a simple abacus that’s set up for a base ten, rather than base 11, world. To the more intricate mechanics behind swings and roundabouts.

Today, however, it was this that got me thinking:

“A slide?” I hear you thinking. “Surely there’s nothing too mathematical about that? Gravity means you go down it.” Well in some respects you would be exactly right. However, we don’t live in a model world, and there is the question of friction.

Today the park was rather damp, it had been raining over night, so we took a towel to dry the slide. Once the slide was dry my daughter went down it, but at an incredibly slow speed and stopped about halfway down. I have always noted that the speed of the slide varies incredibly, and had assumed it was due to the coefficient of friction varying between different materials. Her cotton trousers provide a much faster slide than her jeans, for instance. But today she had denim on and it doesn’t normally stop halfway down. I then thought about another recent trip where the slide had seemed slow, and that day it had been particularly warm.

It got me thinking, does the temperature affect the coefficient of friction between two materials? Or perhaps it’s humidity that has an affect? A little bit of research leads me to believe that both can be contributing factors. Definitely more ammo for investigation in a mechanics school trip!

After the slide, she wanted a go on this:

As you can see, the local see saw is fairly basic and works best if two people of a similar mass are on each end (obviously we aren’t). It’s still easy enough to work, but it made me think about another local-ish park that has a much more complex see saw where there are 3 seating positions on each end. That gives more variability to the user’s and would mean two children of different mass could select positions,that give similar, but opposing, moments and hence work the see saw as well as if they had equal mass. What a fantastic idea, and a fantastic use of maths!

I love the amount of maths that is present at local playparks, and one day I do hope to take a mechanics trip (perhaps a cross curricular one with physics) to investigate all these things. It would be awesome to make a TV show around it. Perhaps I’ll make my own Numberphile – esque video on it one day!## Share this via:

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