MY LETTER TO ASK MARILYN
Ask Marilyn is a column in the Parade Sunday supplement to your local newspaper wherein Marilyn vos Savant (the world's smartest human, based upon IQ score) answers questions from her readers. No, I haven't made any of this up. She was in part the inspiration for Mr. Know-it-all. I peruse her column often but it suffers from the fact that by and large her intellect is too great for me while eating breakfast on a Sunday morning. I say this so you can understand why I reacted with such fervor when she touched on a topic I actually know something about -- although I have to admit I had to get out my bother's old physics text book and look up the order of Newton's Laws. Here was the situation: A reader asked if Wile E. Coyote could save himself from harm by jumping up and down on a falling rock. Marilyn answered you couldn't jump up and down on a falling rock "because there would be no resistance" and further they should install airbags on airplane ceilings so people wouldn't get hurt during severe turbulence. I told you, her intellect is too much for me.
Just to warn you, this letter is long, rambling, and about physics. Many people can't take the physics part.
Your answer to the Wile E. Coyote falling letter was so poor I must assume it was written by someone filling in while you were on vacation. To your assertion that you can't jump on a free falling rock because there is no resistance, don't tell that to the astronauts on Mir, as they will no longer be able to get around once they find that their free fall (AKA orbit) won't allow them to use Mir to push off from. And they'll be stranded there as rockets won't be able to reach them as you've repealed Newton's Third Law of opposite and equal reaction. Apparently, you've confused mass and weight, which is a product of mass and gravity. Remember, Newton's Second Law, that force is proportional to the change in momentum, which is the product of mass and velocity, which is often reduced to F=ma assuming that mass isn't changing. If the rock has mass, which it does, then momentum can be changed by applying force. As long as your foot is in contact with the rock and your calf is not fully contracted, you can apply a force to the rock. Therefore, you can jump on a rock when you are both in free fall. Whatever change in momentum you cause to the rock, you cause to yourself. A rock with a lot of mass will only have a small change in velocity, while a rock with little mass will have a big change in velocity. This will probably affect how much total force you can apply since the longer you are in contact with the rock (which is limited by the length of your foot), the longer you can apply force. Of course, you will have to be careful not to move much of you're body as the conservation of angular momentum will cause you to tumble -- there are at least two sports devoted to tumbling in free fall: freestyle or hot-dogging skiing, and a form of skydiving.
Still, by contracting your calf muscles you will be able to jump without flexing your legs, which would cause you to lose contact with the rock. In a vacuum, you would never return to the rock, as your velocity would always be less that of the rock, so you would in fact continue to move away from the rock. Sadly, this wouldn't help you avert tragedy as your downward velocity would continue to increase as soon as your feet left the rock. In atmosphere, if your wind resistance divided by your mass was less than the rock's ratio, your descent wouldn't be as retarded by the air and you would catch back up to the rock, other wise you would again continue to move away from the rock. Again, as far as jumping to save yourself, it won't work. Consider falling 100 feet in a vacuum from a massive (relative to your mass) rock. A jump a foot in the air (remember, you're using just your calf muscles) is a change in velocity of about 5.5 mph (that's how fast you would be moving neglecting gravity). If you did nothing, you would land at about 55 mph. If you were to jump just as soon as you started to fall from 100 feet, you would make your slightly fall worse, as you would now suffer a fall from 101 feet in the air. If you wait to the last second, you would decrease you're impact velocity by 5.5 mph, or to 49.5 mph. This might be of benefit in shorter drops, but wouldn't be much help in long ones. The idea that jumping at just the right moment would cause you to only suffer as if you had dropped a foot is wrong. Velocities are additive and this idea neglects the fact that you are plummeting at great velocity when you jump. From your viewpoint, you may feel like you've just jumped a foot, but don't forget from this viewpoint the ground is rushing up at you at a great and ever increasing velocity as well. Oh, on a final note I have jumped on several occasions in an express elevator (not that I was in any danger), and in a descending elevator the fall back to floor is slightly but perceptibly longer that than the ascent portion of the jump, while in an ascending elevator the fall back is perceptibly shorter than the ascent, and the entire jump is perceptibly shorter in an ascending elevator than a descending one. I don't recommend jumping in elevator with strangers on board as it tends to alarm most people and telling them you're just conducting a science experiment does nothing to calm their fears.
And as to the suggestion that air bags be installed on the roofs of planes for safety during sudden descents, one can only wonder if (1) you're safer installing multiple pyrotechnics in every aircraft to protect against a rare problem (about 1 death a year worldwide, at worst) (2) you're spending dollars to fix a rare problem when you could be spending dollars to fix common problems (over 40,000 die a year in the US alone in car accidents).
Somehow, I don't expect a reply, but I do feel better.
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This page last updated 24 January 1998
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