Summary of La Ley de la caida de los Cuerpos (Universo Mecánico 02)

00:00:00 - 00:25:00

In this video, scientists discuss the law of gravity and how it affects objects falling in a mechanical universe. They explain how this law was discovered and refined over time, and how it is still being studied today. They also show how the law of gravity can be used to calculate the speed of objects falling in a uniform manner.

• 00:00:00 The law of gravity, discovered by Galileo, was refined by Isaac Newton and provided a theory of cosmic mechanics. It was one of the major mysteries of physics, and its interpretation is still difficult without the use of mathematical formulas known as derivatives. We will now understand what this means and finally, despite its apparent complexity, this law is violating our most basic intuition due to the fact that it occurs in the vacuum. It is probably for all of us our first encounter with nature's laws.
• 00:05:00 According to Galileo, the theory that heavy bodies fall faster than lighter ones was correct nearly 400 years ago. He noticed that in a vacuum, all bodies fall at the same rate, and he realized that the only logical opinion was that all bodies fall at the same speed when resistance to air is eliminated. If all bodies fall at the same speed, the next question is: at what speed does a body fall? Our own experience tells us that the speed of a body as it falls increases with each passing moment, which means it falls faster and faster with each descent. Galileo arrived at the conclusion that distances are related to the negative integers, that is, one unit of distance is traversed in the first interval, two units in the second, and so on. His theory of accelerated movement is that a body falls greater distances in successive intervals as it falls. This theory can be seen in action at an amusement park in California, where people pay to ride a roller coaster that drops them through space under the influence of gravity. Gandhi is much better and this part of the walk is free, so really the visitors are paying for measures that allow them to survive any speed, but what about Galileo?
• 00:10:00 In this video, Galileo Galilei is discussed. He was correct in his predictions of the distances bodies would fall according to the rule of least squares. In successive intervals of time, the distances traveled Falling according to the odd numbers continued. Something more than Galileo saw in the distance traveled in an instant after the first interval of time. After the second interval, four units of distance traveled. After the third interval, nine units of distance traveled. After the fourth interval, sixteen units of distance traveled. In other words, at the end of each interval, the distance traveled was equal to the square of the time elapsed. This equation can be written in a simple equation using distance and time as variables: distance traveled = distance traveled / (time elapsed x time elapsed). This constant, numerically, is equal to the distance traveled falling during the first two seconds, or 16 feet. In any point during the fall, the distance traveled is equal to the square of the time. For example, after two seconds, the distance traveled would be 32 feet per second, or 9 meters per second. However, what this woman really wants to know is the instantaneous velocity at any given instant. To do this, the equation must be divided by the variation in distance over time. However,
• 00:15:00 In this video, we solve the problem of calculating the average speed of objects falling in a mechanical universe. We begin at any time, and for any interval, and can calculate a second, medium, or zero second speed. Now we can reduce the interval and make it smaller and smaller, until we reach the limit. In that instant, we have calculated a derivative, which we call vv. vv is equal to 2 c. If we keep using the value 16 for f, we could say to that young woman, "Don't worry, señora. The distance you've traveled is only 16 times t squared feet, or 5 meters, and your average speed in each instant was 32 times t feet per second, nearly 10 meters per second." Obviously, she is impressed. Calculating a derivative can be a question asked by the viewer, so we finish by introducing the differential calculus. This is the mathematics of using derivatives to calculate a particular value. We call it the differential equation, and it can be used to calculate the rate of change of anything, including the speed of objects falling in a mechanical universe.
• 00:20:00 In this video, scientists show that velocity also increases with time, but they have recently found that acceleration does not depend on time at all. This is simply a constant, independent of the value of t, always equal to 2.12. They also found that gravity is responsible for the falling bodies' constant acceleration. They had three questions about the fall of bodies: how fast do they fall, with what velocity, and how quickly their velocity changes with time. They solved these problems using algebra and then used the derivative to explain the movement of bodies falling in a uniform manner. This type of motion is called an accelerated uniform motion and is difficult to understand, but not impossible to describe. Galileo, 300 years ago, used nearly the same mathematical methods to analyze the same problem. Finally, they showed that the constant acceleration of bodies causes them to fall at a constant speed in a straight line. This was one of the major achievements of classical physics, and it was Galileo who first formulated it in a simple and elegant way. Today, we want to know why this happens and what is the nature of gravity that leads to such an unusual behavior. This is one of the deepest questions in physics and we are making progress in understanding it.
• 00:25:00 The law of gravity states that objects fall with a constant acceleration. This is represented by the equation: obj=ac*t, where obj is the object, ac is the acceleration, and t is the time. Newton and Bone Line discovered the differential equation that describes how this acceleration changes with time. This equation is known as the calculus of variations. They sacrificed their discovery in a bitter argument over who first discovered it. The three propositions are the legs of a history that we are trying to develop. There is no contestation according to the law of gravity, an object falls with a constant acceleration and covers a distance proportional to the square of the time.