I find myself thinking about Galileo, for no apparent reason, and his famous Tower of Pisa experiment, which he may or may not have actually performed.  You know the one: dropping two balls of unequal mass simultaneously to show that acceleration due to gravity is independent of mass.  In short, the two unequal balls arrive at the earth at the same time.  In physics, this is an example of what is known as the Weak Equivalence Principle (WEP), which I point out only for the pleasure of using such a silly term.

Despite being undeniably true, this is, to me, counterintuitive.  Think of the implications.  Suppose you are in the vacuum of space, maybe took a wrong turn on the way to the coffee shop, or something.  About ten feet away is a softball.  According to the WEP, you and the softball will move towards each other at exactly the same rate as you and the earth, if it were ten feet away.  Lucky for you, though, the damage inflicted by the softball will be considerably less than that inflicted by the earth in a similar situation.  Okay, the softball is much smaller and has much less mass than the earth, so what’s my point?

Let’s substitute something else for the softball, say, the moon.  By the magic of imagination, retracing your steps to see how you missed the coffee shop, you find yourself ten feet from the moon.  Once again, you and the moon move together at that same rate, independent of mass.  This time, though, you will definitely feel something when you finally make contact, because the moon is much, much bigger than a softball.  (Never thought you’d see that phrase in print, did you?)

We’ve all seen that footage of Neil Armstrong bouncing about on the moon.  I love that little tune that he sings, by the way.  Anyhow, it’s apparent that jumping that high on earth would result in much more jarring to the body.  But the moon, though smaller than the earth, is easily sufficiently massive to stop you cold when you hit it.  Remember, starting at ten feet away, you will strike the surface of the moon at exactly the same speed as you would on earth, coming to a full and immediate stop in both cases, or as close to full and immediate as measurable.  So why is there more damage to your poor, unsuspecting body when you do it on earth?

I remember reading a variation on this question years ago, in some “Ask the Scientist” thingie: if two cars of identical mass collide, how is the force different from one of those cars hitting a stationary wall?  Mr. Scientist, no doubt sighing inwardly, patiently explained that it had to do with the momentum of both masses.  To get the same force with just the one car, it would have to be going twice as fast, and even the thickest of us can see the difference there.  But what if you substitute a mountain for the wall?  Or drop the car from a sufficient height so that it’s going the same speed at impact as in the collision with the wall?  Even double the speed, to take account of the second car?

Or jump off a ten foot platform on the moon?

Don’t mind me; I still can’t see why levers work; and don’t even bring up pulleys.