A Moment of Science

How High Can You Stack Pennies Before They Fall Over?

We've all played the penny stack game. Is there anyway to prevent the pennies from falling over?

penny stack

Photo: David Steltz (Flickr)

How high can you stack pennies?

Here’s a question of burning scientific importance. How high can you stack pennies before they fall over?

The answer? It depends.

Stacking Pennies

In a perfect universe, with perfectly flat pennies that align exactly on top of each other, the stack could go as high as you wish. In the real universe, however, you’ll be lucky if you can get them above about one foot.

Why Do They Always Fall Over?

It’s because of the center of gravity. The center of gravity is the point where all the individual weights average out. The entire stack acts as if its weight were located only at the center of gravity!

Now, since the center of gravity is the average of all those pennies’ weights, it will always be in the middle of the stack. That means the higher you make the stack, the higher the center of gravity goes.

Center Of Gravity

This is a problem because a low center of gravity is more stable than a high one.

Think how much easier it is to tip over a long two-by-four board balanced on one end than a block of wood the same width but only six inches high.

Adding More Wobble

In order to stay standing, the center of gravity has to be over the bottom penny.

If it moves out far enough so that a vertical line going down from that point doesn’t hit the bottom penny, the whole stack falls.

And every penny you add gives more wobble, making it more likely the center of gravity will stray outside that zone, even for a moment. When it does: crash.

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