Newton. Inderpreet Singh

Transcription

1 Newton Inderpreet Singh May 9, 2015

2 In the past few eras, there have been many philosophers who introduced many new things and changed our view of thinking.. In the fields of physics, chemistry and mathematics, philosophers came up with new philosophies in order to have a better understanding of concepts. Newtons works of mathematics are related to other areas like modern physics. He is also known as the father of calculus [2] because he invented the main concepts of calculus. He compiled all his concepts in a book called Philosophiae Naturalis Principia Mathematica. Isaac Newton was born in the Hamlet of Woolsthrope, Lincolnshire, England on January 4, When Newton was born he was very weak and his mother, Hannah Ayscough would always say that he could have fit inside a quart mug. [3] His father, also named Isaac Newton, was a local farmer who died three months before Newton was born. When Newton was three, his mother remarried and went to live with her new husband, leaving Newton to his caring and loving grandmother. In his juvenile years, Newton went to The Kings School, Grantham and learned Latin but no mathematics. Later on, in June 1661, he was admitted to Trinity College, Cambridge, with the proposal of his uncle, Rev William Ayscough. In 1665, Newton invented the binomial theorem and began to develop a mathematical theory; today we call this mathematical theory calculus. He saw the development of his theories on calculus, optics and the law of gravitation.. Even though, Newton worked with many things, his major works are developing the law of universal gravitational, fluxions in calculus and the three laws of motion. First, the law of universal gravitation states that any two bodies in the universe 1

3 attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. [1] F = G(m 1 m 2 )/d 2. F is the force, G is the gravitational constant (6.610 ( 11)m 3 /(Kgs 2 )),m1 and m2 are the masses of the objects, and d is the distance between the masses.it has been said that there is a story behind how Newton discovered the universal law of gravitation. Newton was sitting under a tree, and an apple fell on his head. Then, he suddenly thought about the universal law of gravitation. Even though, the story is not completely in details, it has the basic plot of what actually happened. After observing the fallen apple, Newton thought that if the gravitational force can reach an apple on the tree, then it can reach much further. Also, orbiting of any object in the space could be a consequence of the gravitational force because the velocity of an object can be changed by the acceleration due to gravity in such a way that it follows an orbit around earth. A good example of this would be the moon. Finally, Newton came to the conclusion that every object in the universe exerts gravitational force on others. [4] Moreover, Newton published the law of universal of gravitation in Philosophiae Naturalis Principia Mathematica. It was an enormous achievement for Newton because it unifies the laws that govern the motion of heavenly bodies in the universe. Second, Newtons other major work is fluxions, which lead to the development of calculus. Basically, fluxions, also called derivatives, are the rates of change for an object; it is the action of flowing or changing. Also, we can find derivative by finding 2

4 the slope of the tangent line on a specific point. Fluxions allow us to find the velocity, acceleration etc. for an object. The velocity is the first derivative of the position and acceleration is the second derivative of the position. For example, lets say that position of an object is defined by some function f(x). Then the velocity, which is the first derivative, can be found by using the following equation: f (x) = lim(xa)(f(x) f(a))/(x a)orf (x) = lim(h0)(f(a + h) f(a))/h Both of these equations allow us to find the slope of the tangent line which is the derivative of a function. Furthermore, Newton used the term fluxion because in Latin, it literally translates to flow. Newton imagined a quantity flowing from one magnitude to another. [2] His methods of fluxions are also stated in his book of Philosophiae Naturalis Principia Mathematica. From 1665 to 1667, due to the great plague of London, Cambridge was closed so Newton developed the method at Woolsthrope manor. He did not want his findings known; therefore, they were hidden from the world for many years. [3] Also, Newton developed the three laws of motion, which are mainly used in physics. These three laws have mathematical and physical inferences which help us to understand the motion of objects in the universe. Newtons first law of motion states that, Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. [1] This law is also called the law of inertia. Basically, it means that an object will remain in the same course, unless an outside force is applied to it. An outside force will change the motion of an object. A simple example would be that a book is kept on the table. It will not move or remain at the 3

5 same position, unless someone applies an external force to it. Next, Newtons second law of motion states that Force is equal to the change in momentum (mass times velocity) per change in time. For a constant mass force equals mass times acceleration. [4] It means that force can be determined by how heavy an object is and how fast its accelerating. Therefore, it shows us an exact relationship between force, mass and acceleration. If force is put on an object it will change its acceleration, thus changing the velocity in the direction of the force. Moreover, the acceleration is directly proportional to the force; as acceleration goes up force goes up as well or vice versa. Second law is expresses by an equation: F = ma F is the force, m is the mass, and a is acceleration. The units that describe force are called newtons, and mass is in kilograms and acceleration is meters/second 2 Newtons third law states that, For every action, there is an equal and opposite reaction. [2] It means that when objects interact, there are forces that act on interacting objects. The size of the force on one object is same as the size of force of another objects. Whenever an object pushes another object, it gets pushed back in the opposite direction with the same force. A real life example of this law could be how swimmers start off their race. When swimmers start off they push the walls or blocks with their feet; the faster they push the faster they start off. This is because wall exerts the same force on swimmer as he applies it to the wall, but in opposite direction. So, if the swimmer applies a big force to the wall, then the wall will exert the same force, in the opposite direction, on the swimmer. Similarly, track runners use the same technique. They 4

6 push on their blocks as hard as they can to start off fast, and block exert the same force on the runner, but in opposite direction. This way runners get pushed and starts off faster. Lastly, everything that Newton has contributed plays an important part in mathematics and science. Newton compiled all his work in the book called Philosophiae Naturalis Principia Mathematica, which was published in Especially, Newtons law of universal gravitation and three laws of motion helped us to understand the universe better. Also, his development of fluxions led to calculus, which we know use to find rates of objects or the action of flowing. Newton not only contributed in mathematics, but also contributed a whole lot in physics. 5

7 Bibliography [1] Burton D, Isaac Newton , The history of mathematics, an introduction, McGraw-Hill New York, [2] Chris Pinaire,Newton s Law of Motion,National Aeronautics And Space Administration, [3] Andrew Motte, Sir Isaac Newton s Mathematical Principles of Natural Philosophy and his system of the world, [4] Cohen B, Sir Isaac Newton: The Universal Law of Gravitation, Astronomy 161 The Solar System. 6