DiscoveringGravity

DiscoveringGravity - index next Discovering Gravity Michael...

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index next Discovering Gravity Michael Fowler 1/22/07 Terrestrial Gravity: Galileo Analyzes a Cannonball Trajectory From the earliest times, gravity meant the tendency of most bodies to fall to earth. In contrast, things that leaped upwards, like flames of fire, were said to have “levity”. Aristotle was the first writer to attempt a quantitative description of falling motion: he wrote that an object fell at a constant speed, attained shortly after being released, and heavier things fell faster in proportion to their mass. Of course this is nonsense, but in his defense, falling motion is pretty fast—it’s hard to see the speed variation when you drop something to the ground. Aristotle most likely observed the slower motion of things falling through water, where buoyancy and fluid resistance dominate, and assumed that to be a slowed-down version of falling through air—which it isn’t. Galileo was the first to get it right. (True, others had improved on Aristotle, but Galileo was the first to get the big picture.) He realized that a falling body picked up speed at a constant rate in other words, it had constant acceleration (as he termed it, the word means “addition of speed” in Italian). He also made the crucial observation that, if air resistance and buoyancy can be neglected, all bodies fall with the same acceleration , bodies of different weights dropped together reach the ground at the same time. This was a revolutionary idea—as was his assertion that it should be checked by experiment rather than by the traditional method of trying to decipher what ancient authorities might have meant. Galileo also noted that if a ball rolls without interference on a smooth horizontal surface, and friction and air resistance can be neglected, it will move with constant speed in a fixed direction—in modern language, its velocity remains constant. He considered the motion of an object when not subject to interference as its “ natural ” motion. Using his terminology, then, natural horizontal motion is motion at constant velocity , and natural vertical motion is falling at constant acceleration . But he didn’t stop there—he took an important further step, which made him the first in history to derive useful quantitative results about motion, useful that is to his boss, a duke with military interests. The crucial step was the realization that for a cannonball in flight, the horizontal and vertical motions can be analyzed independently . Here’s his picture of the path of a horizontally fired cannonball:
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2 The vertical drop of the cannonball at the end of successive seconds, the lengths of the vertical lines ci , df , eh are the same vertical distances fallen by something dropped from rest. If you drop a cannonball over a cliff it will fall 5 meters in the first second, if you fire it exactly horizontally at 100 meters per second, it will still fall 5 meters below a horizontal line in the first second.
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This note was uploaded on 03/02/2012 for the course PHYS 109 taught by Professor Fowler during the Fall '08 term at UVA.

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DiscoveringGravity - index next Discovering Gravity Michael...

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