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MECHANICS UNIT 5
Gravitation and Central Force Motion
Author of this note Mr. K. Prasad BSc from University of Calicut, MSc from university of Delhi, and M.B.A from IGNOU Delhi, These notes were prepared during my teaching session for under graduate students (11 Th and 12 Th class) of my school physics department. This note is helpful for under graduate students and junior level graduates. I declare that these notes are my original works based on my knowledge in physics and the books mentioned below are the reference books I used for preparing these notes.
Table of contents (1)Newton’s law of Gravitation (2) The formula of Newton's Law of Gravity (3) Qualities of Gravitational Force (4) Weight (5) Gravitational potential energy (6) Gravitational potential energy example (7) Inertial and gravitational mass (8) Gravitational mass (9) Gravitational potential and field due to spherical shell and solid sphere (10) Formula for Gravitational Potential Energy Reference Books: An Introduction to Mechanics, Daniel Kleppner& Robert Kolenkow, 2007, TataMcGrawHill Mechanics, DS Mathur, PS Hemne, 2012, S. Chand University Physics, FW Sears, MW Zemansky& HD Young 13/e, 1986, AddisonWesley Mechanics Berkeley Physics course, v.1: Charles Kittel, et.al. 2007, TataMcGrawHill Physics – Resnick, Halliday & Walker 9/e, 2010, Wiley Engineering Mechanics, Basudeb Bhattacharya, 2nd edn., 2015, Oxford UniversityPress University Physics, Ronald Lane Reese, 2003, Thomson Brooks/Cole
The law of gravity is a significant revelation in the field of material science. It gives knowledge into the connection among mass and power. The law of attractive energy expresses that-each item in the universe draws in each and every other article with the end goal that the power applied will be relative to the result of the majority and conversely corresponding to the square of the distance between them. The formula of Newton's Law of Gravity Newton's Law of Gravitation is figured out as: FG=G (m1m2) /r In the above condition, the qualities are characterized as: Fg is the power of gravity that is ordinarily in newtons. G is the gravitational steady that adds the appropriate degree of proportionality to the situation. The value of the gravitational constant is 6.67259∗10−11N∗m2/kg2 the value will change assuming that different units are being utilized. (m1 and m2) are the majority of the two particles that are commonly in kilograms. r is the straight-line distance between the two particles that are commonly in meters. As indicated by Newton's Law of Gravitation The greatness of the power acting between two point masses is straightforwardly corresponding to the result of their masses. The size of the power acting between two point masses diminishes quickly as distance increments. Numerically we compose, Consider two articles having masses m1 and m2 isolated by a distance r, as displayed in the figure. As indicated by the Statement of the Law of Gravitation, The greatness of the power following up on the body is straightforwardly relative to the result of the majority of collaborating bodies, then, at that point, we get: ⇒Fαm1m2..... (1) The worth of the proportionality consistent is found to be G=6.673×10−11Nm2/kg Condition (4) is known as the numerical type of Newton's law of attractive energy or the law of gravitational power. From condition (4) we find that the power
following up on one another will be straightforwardly relative to the result of point masses and contrarily corresponding square Newton's Law of Gravitation is figured out as: FG=G (m1m2) /r In the above condition, the qualities are characterized as: Fg is the power of gravity that is ordinarily in newtons. G is the gravitational steady that adds the appropriate degree of proportionality to the situation. The value of the gravitational constant is 6.67259∗10−11N∗m2/kg2 the value will change assuming that different units are being utilized. (m1 and m2) are the majority of the two particles that are commonly in kilograms. r is the straight-line distance between the two particles that are commonly in meters. As indicated by Newton's Law of Gravitation The greatness of the power acting between two point masses is straightforwardly corresponding to the result of their masses. The size of the power acting between two point masses diminishes quickly as distance increments. Numerically we compose, Consider two articles having masses m1 and m2 isolated by a distance r, as displayed in the figure. As indicated by the Statement of the Law of Gravitation, The greatness of the power following up on the body is straightforwardly relative to the result of the majority of collaborating bodies, then, at that point, we get: ⇒Fαm1m2..... (1) The worth of the proportionality consistent is found to be G=6.673×10−11Nm2/kg Condition (4) is known as the numerical type of Newton's law of attractive energy or the law of gravitational power. From condition (4) we find that the power following up on one another will be straightforwardly relative to the result of point masses and contrarily corresponding square Of the distance between them it is otherwise called the reverse square regulation. In certain articles, it is additionally alluded to as the primary law of gravity. The gravitational power acting between two articles is simply because of their masses. The gravitational power is one of the four fundamental powers of material science. Some of the time it is likewise alluded to as Newton gravity or
deliberate speed increase because of gravity at the Earth's surface is found to be about 9.8m/s2 or 980cm/s The proportion of how much matter is in an item is known as mass, while weight is the proportion of the gravitational power applied on the material in a given gravitational field; subsequently, mass and weight are corresponding to one another. W ∝ m Where, m - The mass of the object W = mg Where, g - Acceleration due to gravity. It is seen that the mass of the given article will be consistent, yet the weight relies upon the place of the article. Question For what reason doesn’t the Moon Crash into the Earth? What is the Value of Gravity on the Moon in Newtons? Ans: Moon is the regular satellite of the earth. The powers of speed and gravity keep the moon in a consistent circle around the earth. The Moon appears to spin around the earth, unaffected by gravity. In any case, the explanation the Moon stays in circle is exact in light of gravity. Presently the worth of gravity on the moon can be determined by utilizing Newton's law of attraction. This is about Newton's Laws of Gravitational powers made sense of with tackled models. Center around how the terms are utilized to decide the recipe and the worth of the gravitational steady. Gravitational potential energy Gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field. In simple terms, it can be said that gravitational potential energy is an energy that is related to gravitational force or to gravity.
Gravitational potential energy example A book on a high bookshelf has higher potential energy than a book on the bottom shelf because it has farther to fall. Inertial and gravitational mass Inertial mass is a mass parameter giving the inertial resistance to acceleration of the body when responding to all types of force. Gravitational mass Gravitational mass is determined by the strength of the gravitational force experienced by the body when in the gravitational field g. Gravitational potential and field due to spherical shell and solid sphere Gravitational potential energy is the energy procured by an object because of a change of its position when it is available in a gravitational field. In basic terms, one might say that gravitational potential energy is an energy that is connected with gravitational power or to gravity. At the point when a collection of mass ( m ) is moved from infinity to a point inside the gravitational impact of a source mass ( M ) without speeding up it, how much work done in displacing it into the source field is put away as expected energy. This is known as gravitational likely energy. It is addressed with the symbol Ug. Formula for Gravitational Potential Energy The formula for gravitational potential energy is as described below
U =mgh
Where u is the gravitational potential energy m is the mass of the object g is the gravitational field h is the height.
