Dear Science,

My 9-year-old son went on a field trip to the Space Needle. The kids' task was to find certain objects on a list, from the city below. When the pencil that my son and his friend were using broke, my son encouraged his partner to throw it over the edge to the ground below. (Surely doing a science experiment of his own.) When his second pencil broke, they did it again, and this time they got caught. What velocity can a pencil reach, and assuming the eraser end is the heaviest end, is it even possible for the pencil to land point-down? What are the chances it could harm someone standing on the sidewalk down below?

Embarrassed But Curious

Kudos to your kid for his experimental nature. But please encourage him to try less hazardous ones in the future. Still, don't worry about him killing anyone with a pencil flung off the Space Needle; at worst, someone just lost an eye.

Let's consider the pencil at the moment after it was flung from the Space Needle. It's going to start falling, thanks to the force of gravity tugging it down. Gravity accelerates everything, regardless of mass, at about 10 meters per second squared. The observation deck of the Space Needle is about 160 meters above the ground. Calculus was invented for this sort of problem. (Thanks, Newton!) A pencil dropped from 160 meters will hit a velocity of about 60 meters per second just before it hits the ground, assuming gravity is the only force acting on the pencil. But it isn't. We've forgotten about the air!

Two forces tug on the pencil in the vertical axis. Gravity is pulling down; the pencil must move the air out of the way as it falls, creating a drag force that pushes the pencil up. The faster the pencil is going, the stronger this force becomes. As the pencil accelerates, the upward drag force will increase until it perfectly balances the downward force of gravity. When these two opposing forces are in balance, the pencil has hit its terminal velocity. Running through a bit of math (and a few guesses), Science has figured the terminal velocity of a pencil dropped is about 15 meters per second, quite a bit less than when we weren't accounting for the air. The 160 meters is enough distance to fall for the pencil to achieve its terminal velocity.

How much punch does a pencil traveling at about 15 meters per second have? About 1 joule of energy. A paintball has about 12 joules of energy. It wouldn't be fun to be below your son's pencil, but you'd probably survive.

Free-Body Diagrammingly Yours,