An Easy Swing?

I have taught several classes on Amusement Park Physics, and I usually include several activities on the carnival type games. Those games often use science, making something look simple and easy, when it is actually difficult to do. This activity is based on a carnival game where you try to swing a weight on a string and knock over a bottle.

To try this, you will need:

  • two chairs
  • string
  • a broom handle or similar long rod
  • a metal washer or other small, heavy weight that can be tied to the string
  • a pen or pencil with one end flat enough that you can stand it on end

The first thing we need to do is to make a pendulum. To do this, place the two chairs about 3 feet apart, with their backs towards each other. Place the broom handle across the backs of the two chairs. Tie one end of the string to the heavy weight. I used a fishing sinker, but you could use a heavy key, several coins taped together, or some similar weight. Stand the pen on its flat end, directly under the center of the broom handle. Tie the other end of the string to the center of the broom handle, so that the weight is just low enough so that it will hit the end of the pen.

Now we are ready for the game. It seems very simple at first. The idea is to pull the weight and release it so that it will knock over the pen. Easy, right? But wait. There is one more thing. It must not knock the pen over as it swings away from you. Instead, you must swing the weight past the pen and have it knock the pen over as it swings back to you. It still sounds easy. Try it. Yes, it can be done. It takes practice.

Why is this so hard? Move the pen and swing the pendulum a few times. Just watch it swing. If you swing it forwards, then it reaches a point where it reverses direction and comes back to you, and it goes almost as high as it did at the other end of its swing. It does not go quite as high because it loses a little of its energy to friction. The same is true if you swing the weight to the right. It moves to the right and then reverses to swing back to the left. It will swing left almost as high as it did to the right. Can you swing the weight to the right so that as it swings back, it will stop when it reaches the bottom of the swing and not swing up to the left? No, as long as it does not hit anything, it will continue to swing. Inertia will keep the weight moving until gravity, friction of some other force slows it down. That is the clue for why the game is so hard.

If you swing the weight so that it passes on the right side of the pen, you have combined swinging the weight forward with swinging it to the right, to make it miss the pen as it swings by. If you swing it forward and to the right, then when it reaches the point where it stops and reverses its course you would expect it to swing back and to the left. That is exactly what happens. If it misses the pen on the right side on the first half of the swing, it will miss the pen on its left side as it swings back. As long as the pen is standing directly under the point where the weight is tied, this is a very difficult task.

There are ways to win this game. One is to just barely miss the pen on the outward swing. Most people try to swing the string far to the right, thinking that it will make a small circle and hit the pen on the way back. Really, the farther to the right you swing the weight, the bigger the circle and the farther it will miss to the left as it swings back. If you can just barely miss the pen on the outward swing, it will lose a little of its energy, due to friction, and will hit the pen on its way back.

Another way is to give the weight a spin as you release it. This spin alters the path of the swing and with practice you can learn just the right amount of spin to get the weight to hit the pen. The people that run this game at the carnival spend lots of time practicing so they can demonstrate and show "how easy it is." They are not cheating and the game is not rigged. They are just using science in a game that looks easy but is not.

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