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The research about motion of falling bodies In the past, it is unbelievable that we use displacement、velocity、speed、acceleration to describe the motion of objects. For centuries, we just can use word based on the writing of the Greek philosopher Aristotle to describe the motion of objects.Aristotle asserted that any object, after it is released, quickly reaches some final speed, which it maintains to the end of its path. When we pick up a stone and release it, the stone strives to return to its natural place and quickly gets a speed that it maintains during its entire fall. According to the common observation that a heavy stone fall faster than a feather, Aristotle reasoned that weight is a factor that governs the speed of the fall. Consequently, the heavier the object, the greater would be its potential to return to the earth. This description of motion is in accordance with common observation of falling leaves, raindrops and stones. In all cases, the body encounters resistance to its fall from the air. But what if there were no air to offer resistance and impede the fall? How would objects fall through a vacuum? Aristotle argued that all bodies, in a vacuum, being unresisted, would fall with the same infinite speed. But he, like most other ancient Greeks, considered infinity as an incoherent concept. Aristotle dismissed motion through a void because he concluded that the vacuum could not exist.Above all we have examined present a qualitative description of motion. But physics in general consisted mainly of qualitative explanations until Galileo grasped the usefulness of mathematics in describing the world.In 1638, Galileo publish his work Dialogues Concerning Tow New Sciences, in which he did a great step toward the understanding of motion. His insight was to imagine a body falling without any resistance. He realized that in a vacuum all bodies, heavy or light, would fall at the same rate. This was a wise insight because Galileo could not produce a vacuum. However, he could imagine one. We can see that Aristotle believed that a vacuum or a void was impossible. Galileo thought that the question of the existence or nonexistence of the void was unimportant. What was important was that to understand falling bodies, the effects of air resistance should be ignored. He did a assument: Consider a heavy rock linked to a light one by a cope. According to Aristotle, when they are released, the heavy one pulls the lighter one down and tries to make it fall faster than it would if unattached. Meanwhile, the lighter one tends to slow down the heavier one. It should therefore fall faster than the heavy one. If we ignore air resistance, the Aristotlian view leads to a contradiction. Thus, Galileo concluded instead that all bodies would fall at the same rate in a vacuum.Both Aristotle and Gelileo are focused on how the speed of a falling body changes. But Leonardo da Vinci, in the fifteenth, formulated a different kind of law.Leonardo da Vinci expressed his law in terms of quantities that are easy to measure: intervals of distance and time. He proposed that the distances fallen in successive equal intervals of time are proportional to the consecutive integers. This statement needs to be explained: Suppose that, starting from rest, a body falls one unit of distance in the first time interval. After the second time interval, the body will have fallen an additional two units of distance; after the third time interval, it will have fallen three more units of distance, and so on according to the consecutive integers. Leonardos law also makes a statement about the average speed of the object as it falls. We can discover this relation if we recall the definition of average speed and apply his law, for equal successive time intervals, the distance traveled is proportional to the consecutive integers. The average speed for each successive time interval, therefore, will be the distance interval, which as he said goes as the consecutive integers, divided by the time interval. Since all the time intervals are equal, the average speed over speed over consecutive time intervals is also proportional to the consecuti
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