Nov. 18, 2011

Science Dad on the Center of Gravity

by Vince Harriman

Click to enlarge images

I've been looking for more hands on type experiments for Beckett, mostly because I think he (and I and probably most people) seem to learn better when actually doing and seeing the science happening in front of him. We still talk about the earthquake that happened here at the end of the summer, probably because it happened on the first day of school. One of the things we talk about is building safety and how things move in an earthquake. This of course leads to discussions of gravity and how it affects everything. I wanted him to see how gravity acts on an object, so we came up with a basic demonstration and a magic trick to illustrate this mysterious force.

Gravity is one of the fundamental forces of nature -- all bodies exert a force that attracts them to one another. Go outside at night and find the middle star in Orion's belt -- known to astronomers as M42 or Orion's Nebula. It is a large and diffuse nebula just over 1300 light years from earth, and yes, it is pulling us toward it just as we are pulling it toward us with gravity.

We started with the magic trick -- start with a full unopened can of soda and see if you can balance it any way other than on its bottom. You can't. Lean it over just a little and the center of mass (center of mass and center of gravity are for all intents and purposes equal on small objects on earth) will cause the can to topple. Empty the can and try again, and again the can won't balance. Now put a small amount of water in the can (say less than a third full) and balance the can on its lip, like this:

This is one of those counter-intuitive demonstrations that actually illustrates a concept well: in this case the water contributes more to the center of mass and effectively 'supports' the rest of the can. We found a picture of the Leaning Tower of Pisa as our next starting point. Why doesn't that tower fall over?

Image courtesy Alkarex Malin äger, CC 3.0 license

Like the can, the tower doesn't fall over because the bulk of its mass is centered and positioned in a way that most of the tower is pulling down into the earth and only a little is pulling down out of this center line. What happens when towers lean, and what happens when they lean with more mass?
We started with a single large LEGO block:

We added a little bit of tape to the edge of our incline to keep the blocks from sliding, but you can clearly see that the single block really does not want to tip over. We added a block at time, measuring the incline before the tower fell:

We added more and more blocks, and each block more or less made the tower fall faster:

By inclining the tower, you can see how the center of mass goes from exerting pull straight down through the block tower to exerting pull down through empty space, until enough of the mass is unsupported by the blocks below and eventually the tower tumbles. Finally, we did a fun experiment that again has a surprising result. The math is a bit complicated, but the concepts and results are well worth trying this. How far out from the edge of table can you stack books? I had some DVD cases handy, and it looks like this:

How far can you stack them?

What you find is that if you are careful (and use equal size books for best results, DVDs are a bit light to get a good stack) is that you can balance books farther than you would expect. A great way to see this is to measure how far you can balance a single book -- it will extend just under half the length of the book. By your third or fourth book you should be well past that point.

About Vince Harriman

Science Dad, AKA Vince Harriman, is a freelance writer living in Annapolis. His two sons, Beckett-6 and Rowan-2 1/2 ask him 'why' approximately 6,542 times a day.

The views expressed are those of the author and are not necessarily those of Science Friday.

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