We like to get into the swing of fall by enjoying some of our favorite flavors of doughnuts, apple cider and pumpkin spice, with a unique math twist! As much as we love eating those doughnuts as they are, we like to play a fun game with them that gets everyone in a silly mood: the dangling doughnut game!
This is a fun challenge because once it’s bumped, the dangling doughnut starts swinging and it’s hard to get it to stop. The swaying doughnut becomes a pendulum. A pendulum is any object hung from a fixed point so that it swings freely back and forth under the action of gravity. It’s hard to eat a moving target!
Before you get to eating, take a few minutes to observe your doughnuts in motion. Once your doughnut pendulum gets swaying, it will move in a regular pattern. See for yourself! Get out a timer or stopwatch and measure how long it takes to complete a period, that is, the amount of time it takes the doughnut to return to its original position. Did that take more or less time that you predicted?
Hang the doughnuts from something taller than the participants. Use a tree branch, a clothesline, or something similar to hang the doughnuts. If you don’t mind a few crumbs on your floor, use a door frame. In a pinch, you could hang them from a long rod and have an adult hold it above everyone’s head.
Each doughnut’s ribbon needs to be customized for the player’s height. To do this, tie the ribbon around the doughnut. Then measure out the length of ribbon you’ll need to hang the doughnut so that the player can reach the doughnut with his or her mouth.
Measure the player’s height standing flat-footed, and then have them stand on their tip-toes and measure them again. Determine the difference between the two heights and subtract the difference from the length of your ribbon. You could also try measuring players in squatting position for another challenge. Make them work for that doughnut!
Once you have all the doughnuts tied, have the players line up in front of their doughnut. As soon as everybody is lined up, yell “Go!” No cheating, now – you can only use your mouth! Hands must be kept clasped behind backs. The first person to eat the whole doughnut wins. Really, everyone who plays wins, too, because … doughnuts, of course!
While the group is digesting, try to think of other examples of pendulums. How about the swings on the playground, the pirate boat rides at amusement parks, a yo-yo, or a grandfather clock?
Galileo spent quite a bit of time studying pendulums, and was able to express the motion of a pendulum in a mathematical equation. It turns out that the only thing that affects the period of a pendulum (the time it takes for one pendulum to swing) is the length of the string. Try it with your doughnut and different lengths of ribbon. Which doughnut swings faster – one on a long string or one on a short string? In the name of mathematical experimentation, you might as well grab another dozen doughnuts and eat your way to the correct answer!
You might think the weight of the object would affect the period of pendulum. Shouldn’t heavier objects move slower than lighter objects? Test it out. Have the kids find something heavier than the doughnut as well as something lighter than the doughnut. They can estimate which objects are heavier or lighter just by feel of the hand. If you have a kitchen scale, weigh the objects as well and compare how their estimates hold up to real numbers.
You know who else depends on the math of pendulums? Trapeze artists! After you read about how they use math skills to fly, check out our latest, circus-themed free printable activity guide, Ringmaster-ed Math.
Image courtesy of Angie Six