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At the onset of “modern science” as we now call it; Galileo also philosophically studied different objects falling through varying mediums. He extended his observations to predictions of how objects would fall in a vacuum – a concept so abstract for its time that it was thought to be insane by many, particularly as Aristotle’s work led people to believe that that vacuums were impossible.
Galileo’s belief at the time was that two objects, regardless of material or size, would fall and reach the ground at the exact same time. As noted in his biography, here is where Galileo conducted his famous velocity experiments by dropping objects from the Leaning Tower of Pisa to disprove Aristotle’s theory that heavier objects fall faster. Galileo used two objects of the same materials but differing masses dropped from the same height (what exactly the two objects were differ by source), discovering that both landed at the same time. He also observed that various objects (say, a feather or sheet of paper and a meal ball) with different shapes would not fall at the same speed leading him to suspect an upward air force accounting for such differences. Using his pendulum clock, Galileo was able to perform some tests on these situations.
The first experiment Galileo undertook was dropping objects in a tank of water. He dropped long objects both vertically and horizontally. He found that lighter; less streamlined objects took longer to reach the bottom, and heavier streamlined objects reach the bottom in about the same amount of time as in air. These findings supported his theory of additional forces acting upward on objects falling. While there was less of this resistance in air, it was evidently still present.
Galileo’s belief at the time was that two objects, regardless of material or size, would fall and reach the ground at the exact same time. As noted in his biography, here is where Galileo conducted his famous velocity experiments by dropping objects from the Leaning Tower of Pisa to disprove Aristotle’s theory that heavier objects fall faster. Galileo used two objects of the same materials but differing masses dropped from the same height (what exactly the two objects were differ by source), discovering that both landed at the same time. He also observed that various objects (say, a feather or sheet of paper and a meal ball) with different shapes would not fall at the same speed leading him to suspect an upward air force accounting for such differences. Using his pendulum clock, Galileo was able to perform some tests on these situations.
The first experiment Galileo undertook was dropping objects in a tank of water. He dropped long objects both vertically and horizontally. He found that lighter; less streamlined objects took longer to reach the bottom, and heavier streamlined objects reach the bottom in about the same amount of time as in air. These findings supported his theory of additional forces acting upward on objects falling. While there was less of this resistance in air, it was evidently still present.
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The next such way of testing his theory was with his inclined plane experiment of 1604. In these tests, Galileo tested how far balls rolled down ramps in specified times. By breaking the forces acting upon the ball into components, Galileo was able to isolate the vertical component to deduce how a free falling object would act. Timing was done without the aid of a modern clock (a water clock or pendulum clock was said to be used), so only small angles of incline were used to facilitate accuracy.
The experimentation had its challenges, none-the-less. Surface friction was difficult to account for and work with on the plane, and nothing could completely eliminate it. Despite this, Galileo was successful in determining that the distance fallen by a body is proportional to the square of elapsed time. As such, Galileo was able to plot his findings linearly, and the results followed a general equation of a line, proving constant acceleration:
The experimentation had its challenges, none-the-less. Surface friction was difficult to account for and work with on the plane, and nothing could completely eliminate it. Despite this, Galileo was successful in determining that the distance fallen by a body is proportional to the square of elapsed time. As such, Galileo was able to plot his findings linearly, and the results followed a general equation of a line, proving constant acceleration:
y = mx + b
Or graphically illustrated as:
Where y is the velocity, x is the time, and b is the initial velocity. The value of m would be velocity divided by time, or acceleration. In a format we are likely more familiar with:
v2 = v1 +at
More specifically, when the initial velocity was 0, the equation is:
v = at
Constant acceleration followed. Galileo defined the concept of constant acceleration as even increments of velocity in relation to time. In other words, velocity is proportional to time in uniformly accelerated motion. To express this mathematically, Galileo recognized the need for a constant that accounts for the interval of increases in velocity over time. As we now know. 9.8 m/s/s is the accepted gravitational acceleration constant applied to make the equation functional, but its prevision varies slightly by location on the earth (International Bureau of Weights and Measures). Following his experimentation, Galileo formulated the equation for falling bodies in uniform acceleration:
d=½ a t2
The basis for this equation was that if two objects are falling, and the first is falling twice as long (as the second), it will travel four times that of the second. This finding contradicted Aristotle’s previous belief that every object had a natural falling speed related to its weight.
It is certainly worth noting that Newton eventually adopted Galileo’s applications of theoretical situations, leading to what is now often called the “Galilean-Newtonian Paradigm” furthering the scientific revolution.