## The maths of the playground

May 4, 2014 1 comment

Since becoming a parent I have seen maths in many places I wouldn’t necessarily have thought I would have. The playground (or park) is one source that just keeps giving.

A week or two ago we were at a new playground and I found this abacus, and of course the maths links to an abacus are obvious, but what else is there?

Last year I was pushing my daughter on a swing and I couldn’t help but see the swing as a pendulum and wonder whether we could take a physics and maths cross curricular trip to the playground and investigate the simple (or more likely damped) harmonic motion on display from the children’s swings. I think the mechanics involved would be interesting and different swings could be tested to see which ones are more efficient. Given that some swings are extremely noisy, I would assume that these are the least efficient and would love to test this hypothesis.

Today I had another thought about playground maths. My daughter was playing on the roundabout, and after a while she got off and decided to start picking up the bark chips that cover the floor and plonking them onto the roundabout. We told her to stop and to spin the roundabout as that should make the chips fall off. She did this but the chips didn’t move. This was due to the fact her spin didn’t have enough speed to generate a centripetal force big enough to cause a reaction (or whispers centrifugal force shhh) larger than the maximum frictional force acting in the bark. This made me wonder how large the coefficient of friction would be between the painted metal roundabout and the bark chips and what the minimum speed required would be to move them. Again, I figured a cross curricular trip would be great to investigate this too. I didn’t have my phone handy, so couldn’t photograph the chips on the roundabout, or film the sight of them flying off quickly when I gave the roundabout a spin!

There you have it, children’s playgrounds, the perfect school trip for A Level maths and physics!