Gravitational Force Between The Earth And Objects example essay topic

email: triax @aol, com Galileo GaliliGalileo Galilei was born in Pisa Italy on February 15, 1564. Later in the 1570's his father, Vincenzo Galileo moved his family to the near by city of Florence. He was the oldest of four children, and as a child he was the most likely inclined to be the smarter of the family. It was here that Galileo's formal education began at a school in a near by monastery. This school was taught by monks, and for a while it was belied that Galileo would grow up to become a member of the religious orders. At the school he studied Greek, Latin and logic. since his father was a musician, he received an introduction and a musical background.

Then finally in 1581 he was accepted and entered the University of Pisa, where he was studying medicine. Then after some time passed he grew bored of medicine. He found a deep interest in the field of mathematics. It seemed that all of his time was spent studying mathematics. When he turned twenty-one he was forced to leave the university because of a lack of interest, ending his formal education. After he left all his time was spent he continued his research of mathematics.

While he was studying he became an acquaintance Marchese de Monte. After Marchese de monte saw Galileo's work he grew interested in him. Shortly afterward he was taken in by Marchese to assist him in his research. It was as if Galileo was his apprentice. They both worked together to formulate the Treatise on the Centers of Gravity. It was this paper that they wrote which first made Galileo's presence felt in the world of science.

Marchese helped him to obtain a position as a professor at the University of Pisa. There he spent the next two years teaching. He was forced to leave because other professors and students themselves considered his teachings to be radical and extreme. After he was forced to leave he headed back home to spend time with his family.

A short while after he arrive to Florence his father passed away. He was forced to stay and maintain the family. Then in 1952 he managed to he was offered a job at the University of Padua. There he worked for many years with other scientist teaching and studying as well. In 1604 Galileo heard that the rulers of Florence and Venice were becoming interested in a new creation. It was an optical instrument used to observe distant objects.

This was an early version of our modern day telescope. Galileo had set out to build one of his own telescope. Then four days later he presented his telescope to the Venice senate, and was given a double in raise and he secured a permanent job. Galileo used pendulums extensively in his experiments. Early in his career, he researched the characteristics of their motion.

After investigating their behavior, he was able to use them as time measurement devices in later experiments. Pendulums are mentioned in both Galileo's Dialogue Concerning the Two Chief World Systems and his Dialogues Concerning Two New Sciences. In these two works, Galileo discusses some of the major points he discovered about pendulums. Pendulums nearly return to their release heights. All pendulums eventually come to rest with the lighter ones coming to rest faster. The period is independent of the bob weight.

He said the square of the period varies directly with the length. So the time the it takes for the pendulum to swing from one side to the other squared varies according to the length of the swing. Galileo observed that the bobs of pendulums nearly return to their release height. In his experiment the pendulums were released from different heights. The height the pendulum returned to was noted and compared to the release height. Every time he released the pendulum it returned to the almost the same release height.

Galileo noted that each time he swung pendulums the lighter one came to rest faster. As a test of this observation, he dropped two pendulums of the same size but different weight at the same time and height. A bob of lead was the same as bob of cork. He released the two at the same time after he pulled them both back about five degrees. Then he saw that after the cork pendulum stopped the lead pendulum kept going. He that the average number of swings for the cork bob was less than the average number of swing for the lead bob.

Galileo claimed that the pendulum period was different from the height at which they are released in Two New Sciences. To get to his conclusion he suspended two pendulums with identical lead bobs. He released them at the same time from different angles. One was pulled back about 5 degrees while the other was released from about 45 degrees.

The pendulum pulled back five degrees was allowed to travel through thirty cycles, and the numbers of complete swings of the other pendulum during this time were counted. The pendulum which traveled through the larger angle had a longer period. He saw that pendulums with different release heights do not have the same period. It appeared that pendulums with larger release heights have longer periods. The difference was small.

After studying at the University of Pisa, he was appointed to the chair of mathematics. It was at Pisa, the famous leaning tower gave way to Galileo's most famous experiment. First of all the theory which almost everybody had accepted at the time was the traditional theory of Aristotle, who believed that heavier objects fall more quickly than lighter ones. Imagine Aristotle at the top of the leaning tower of Pisa, dropping off two cannonballs, one twice as heavy as the other.

According to Aristotle, it should fall twice as fast. If it were four times heavier, it should fall four times faster. But in fact, what the leaning tower of Pisa type of experiment demonstrated, when actually performed, was that Aristotle was wrong. No matter what the difference in weight, two heavy objects will fall simultaneously at virtually the same speed. It was for there reasons that Galileo was in lack of better terms fired from his teaching position at Pisa. Galileo's interest in disproving Aristotle's Theory about falling objects, came about he had first thought about this during a hailstorm.

It was then when he saw that both large and small hailstones hit the ground at the same time. When Galileo thought about it, it didn't make sense to him. What was the chance that if hail was to fall the larger stones dropped from a higher point in the clouds or that the lighter ones started falling earlier than the heavier ones. Neither of the two seemed very probable to Galileo. When Galileo showed his class that his way of disproving Aristotle ideas he climbed the tower and through two boulders of different weights off. He had predicted that the two would fall simultaneously through his ideas of the hailstorm.

When he did it he found his results to be true. At his time, what he did by disproving Aristotle was going against society. For awhile he was considered an outcast because of his research. Galileo next set out to work with inclined planes and how gravity affected acceleration. His main interest in gravity was to see if there was a way for him to slow down or cancel gravity effect, so he could observe the rate of acceleration. He believed that if he could get gravity off the object in motion, then as soon as it reached id full speed it wouldn't stop unless it was acted upon.

Here is a demonstration of his idea. Suppose that we were to stand on top of a hill and at the bottom there is a flat surface extending for miles. Then if we were to roll a ball down the hill it would pick up speed because gravity would pull it down faster, picking up momentum. The increase of momentum is referred to as acceleration. Now as soon as the ball reached the flat part of the hill it should continue rolling until it is acted upon. But we know that it would stop because friction would be the force acting on it.

At this point Galileo reasoned that gravity is no longer pulling on the ball to increase its accelerating its motion, but rather gravity becomes constant and the ball should ideally travel in a straight line. This idea is the basic idea through which inertia is based on. Inertia is the property of matter that causes it to resist any change of its motion in either direction or speed. This property is accurately described by the first law of motion of the English scientist Sir Isaac Newton: An object at rest tends to remain at rest, and an object in motion tends to continue in motion in a straight line unless acted upon by an outside force. For example, passengers in an accelerating automobile feel the force of the seat against their backs overcoming their inertia so as to increase their velocity. As the car decelerates, the passengers tend to continue in motion and lurch forward.

If the car turns a corner, then a package on the car seat will slide across the seat as the inertia of the package causes it to continue moving in a straight line. Any body spinning on its axis, such as a flywheel, exhibits rotational inertia, a resistance to change of its rotational speed. To change the rate of rotation of an object by a certain amount, a relatively large force is required for an object with a large rotational inertia, and a relatively small force is required for an object with a small rotational inertia. Flywheels, which are attached to the crankshaft in automobile engines, have a large rotational inertia.

The engine delivers power in surges; the large rotational inertia of the flywheel absorbs these surges and keeps the engine delivering power smoothly. An object's inertia is determined by its mass. Newton's second law states that a force acting on an object is equal to the mass of the object multiplied by the acceleration the object undergoes. Thus, if a force causes an object to accelerate at a certain rate, then a stronger force must be applied to make a more massive object accelerate at the same rate; the more massive object has a larger amount of inertia that must be overcome.

For example, if a bowling ball and a baseball are accelerated so that they end up rolling at the same speed, then a larger force must have been applied to the bowling ball, since it has more inertia. Gravitation is property of mutual attraction possessed by all bodies of matter. The term is sometimes used synonymously, but properly refers only to the gravitational force between the earth and objects on or near it. The law of gravitation, first formulated by the English physicist Sir Isaac Newton in 1684, states that the gravitational attraction between two bodies is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them.

In algebraic form the law is stated = G m 1 m 2 2d where F is the gravitational force, m 1 and m 2 the masses of the two bodies, d the distance between the bodies, and G the gravitational constant. The value of this constant was first measured by the British physicist Henry Cavendish in 1798 by means of the torsion balance. The best modern value for this constant is 0.0000000000667 newton meter squared per kilogram squared (6.67 + 1011 N m 2 kg-2). The force of gravitation between two spherical bodies each having a mass of 1 kilogram and having a distance of 1 meter between their centers is 0.0000000000667 newtons. This is a very small force; it is equal to the weight of an object on earth with a mass of about 1/150,000,000,000 kilograms.

Acceleration is also known as linear acceleration or the rate at which the velocity of an object changes per unit of time. Acceleration is a vector that is, it has both magnitude and direction. Acceleration is uniform if the rate of change of an object's velocity is the same over successive and equal time intervals. For example, an object that is released and allowed to fall freely towards the ground is accelerated uniformly. An object tied to a string and swung at a constant speed in a circle above a person's head is also accelerated uniformly; in this case, the acceleration vector points along the string toward the person's hand. Angular acceleration is the rate at which the rate of rotation of a spinning object changes per unit of time.

In the winter of 1609 he set out his telescope up and began to investigate the stars and the skies. He recorded his findings in Side rous Nunc uis, which later made him famous all through out Europe. In his paper he stated his findings. He found that the moons surface was similar to that of the Earth, in that it was mountainous. He discovered that the Milky Way was made up of key stars. Later he found that the planet Jupiter had what appeared to be rings.

Than when he built a Microscope of greater magnitude he saw and identified four rings. When looking into the sky one day he noticed that Venus was much larger than previous previously believed. He noticed that the planet Venus had several stages just like the Earth's moon. From there he would later build and help the world today understand the mystery of our solar system. The telescope is a man made instrument that is used to magnify objects at a distance. The development of the telescope is credited to three people: Hand Lippershey- the inventor, Galileo- credited for the use in scientific investigation, and Johannes Kepler was the first to apply the convex lens to a telescope, for a greater magnification and field of vision.

The telescope which Galileo used is referred to a refracting telescope. It is made up of a hallow tube and two lenses, on one side the eyepiece and on the other side the glass lens referred to as the objective lens. The objective lens gathers the light gathers the light from the object being viewed. When the light hits the objective being viewed. When the light hits the objective lens the rays are bent until they come to a point. An image of the object being viewed is found at the focal point.

When the light reached the eyepiece the image of the focal point is enlarged, and the object being viewed is enlarged and appears to be much larger. Since the image was bent as it passed the objective lens, the image viewed appears to be upside down... By adding another piece of glass the image can be bent right side up once again. After his writing of Physics and the telescope he began to gain recognition. The recognition caught the attention of Cosimo de Medici.

Cosimo de Medici was one of the for fathers of modern day Cosmology. When he got in contact with Galileo he invited him to return to Florence as a mathematics advisor to the Duke. He was quick to accept and spent much of his time there holding conferences to demonstrate and reveal his ideas of the skies and gravity. Then later his job took him to Rome. For four months in 1611 he spent his time teaching, Discussed and demonstrating his ideas and discoveries. After returning to Florence in 1613, he wrote a letter in which he attempted to demonstrate that the Copernican Theory agreed with both the Catholic Doctrines and Biblical interpretations.

The people and groups against Galileo's ideas sent a copy of the letter to the philosophers of Rome. Then in 1616, he was summoned to Rome for an official evaluation of his faith, and the role his faith played on his scientific thinking. He was allowed to leave with no charges of heresy. He was cleared of charges, but was told that he couldn't publically write of or comment on the Caper nical Theory.

The Copernican theory is based on the idea that the planets revolve around the sun. As the planets revolve around the sun, they also spin one a day. This spin was te cause for the forming of night into day and day into night. This idea was formulated by a man with the name of Nichol ous Copernicus of Poland. All of his thoughts were revealed in his book entitled "On the Revolution of the Heavenly Spheres. He had no way of proving himself other that he mathematical equations.

Then in 1634 going against his ban on discussing the Copernican theory. He released his book entitled Dialogue Concerning the Two Chief World Systems. In his book he compared the Copernican theory to the Ptolemaic theory. He stated and proved his ideas that the Copernican theory of the planets was more logical. because he went against his orders he was called back to Rome one more time. This time he was not able to escape the accusations of heresy. He was ordered take back his statements in his book and was then sentenced to life in prison.

Since he grew old and his health deteriorated, the church allowed him to spend the remainder of his days in a small village outside of Rome. There he wrote his final book on entitled Discourse on Two New Sciences, in 1638. In that book he indicated his mathematical equations to prove his ideas of Physics, inertia and falling bodies. Shortly after the release of his book he lost his sight.

Then in 1642 he died in Florence, ending his life sentence for heresy against the church. Galileo is considered the founder of mere dn day physics. His contributions are still the basis of what we study today. He was a man far beyond his time.