Dear Straight Dope:

i often hear scientists and science popularizers insist that if a hammer and a feather were dropped from a given height, say, one of the towers that consitute the world trade center, they would both hit the sidewalk below at the same time, allowing for the condition that you've evacuated all the air from NewYork for the duration of this experiment. yet these so-called scientists seem to forget that the hammer and the feather consist of mass themselves and are in fact attracting the earth while the earth is attacting them ... consequently, the hammer + the earth create a sum total of greater gravitational attraction than the sum gravitational attraction of the feather + the earth ... thus: the hammer would in fact hit before the feather! could you please set these so-called scientists straight?

Ian replies:

Um … yeah, I’ll set someone straight, B, I promise.

Historically, many of these so-called scientists made names for themselves by formulating mathematical explanations for physical processes, gravitation in particular. The ancient Greeks, specifically Plato and Aristotle, felt kind of the same way you do about it; bigger, heavier objects must fall faster than lighter ones. Common sense, right? Galileo, though, took great pains to measure the speeds of falling objects. Using inclined planes to slow things down, and water clocks and metronomes to measure time, Galileo found that objects released from the same height fall at the same speed, and reach the ground at the same time, regardless of their masses. He probably never did drop anything from the Leaning Tower of Pisa, though.

Now, mass is not irrelevant to discussions of gravitational pull. The FORCE of gravity is dependent on the masses of the two objects attracting each other. This is Newton’s Law of Universal Gravitation

G m1 m2

F = —————

gravity r ^2

… where m1 and m2 are the masses of the two objects, r is the distance between them, and G is the universal constant of gravitation, 6.67 x 10^-11 N m^2 / kg^2 . (Physicists, please accept my apology for leaving out the vector e; this is getting too complicated as it is.) The practical application of this on earth is the more massive something is, the more earth attracts it, and the more it attracts the earth, i.e., the more it weighs. This is the "sum total of gravitational attraction" that you mention. If you remember your physics, you will probably recall another of Newton’s equations, which relates force to acceleration, namely F = ma. Since what we’re really after is the acceleration, rearrange this equation, solving for a, and you get a = F/m. In this case, we are looking for the acceleration of the falling object, m2. If we take the force from the above equation and plug it into this one, you algebra lovers out there can see that we are eventually going to divide (m1 m2) by (m2), and the mass of the falling object effectively cancels out of the equation. (Realize this is a highly simplified situation; for more details, please check out a so-called physics book.) As a consequence, acceleration on a falling body is seen to be independent of the mass of the falling body itself. So, subtracting the effects of air resistance, the hammer and feather fall at the same speed, and hit the ground at the same time.

The falling hammer and feather experiment was actually performed by the crew of Apollo 15 on the surface of the moon, on August 2, 1971. You can check out http://www.lpi.usra.edu/expmoon/Apollo15/apo15g.avi for more information on this experiment, and even download an .AVI movie of the experiment itself.

Send questions to Cecil via cecil@straightdope.com.

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