PHY101 General Physics I (2 Units) PDF

PHY101- GENERAL PHYSICS I (2 UNITS) Module 1 Gravitation: Newton’s Law of Gravitation Newton’s Law of Gravitation Newton's law of gravitation states that everybody in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inve...

PHY101- GENERAL PHYSICS I (2 UNITS) Module 1 Gravitation: Newton’s Law of Gravitation Newton’s Law of Gravitation Newton's law of gravitation states that everybody in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The direction of the force is along the line joining the particles. Mathematical derivation: The direction of force is along the line joining the centers of two objects. Let two objects A and B of masses M and m lie at a distance d from each other as shown in figure. Let the force of attraction between two objects be F. According to the universal law of gravitation, the force between two objects is directly proportional to the product of their masses. That is, And the force between two objects is inversely proportional to the square of the distance between them, that is, Combining equation (i) and (ii) Where G is the constant of proportionality and is called universal gravitation constant. 1 The SI unit of G can be obtained by substituting the unit of force, distance and mass in equation (iii). Some importance facts of Universal Law o HYPERLINK "https://www.pw.live/question- answer/state-the-universal-law-of-gravitation-45292"f Gravitation The universal law of gravitation successfully explained several phenomena which were believed to be unconnected: the force that binds us to the earth; the motion of the moon around the earth; the motion of planets around the Sun; and the tides due to the moon and the Sun. Gravitational force between light objects and heavy objects: The formula applied for calculating gravitational force between light objects and heavy objects is the same, i.e. Let us take three cases: 1. When two bodies of mass 1 kg each are 1 metre apart. 2 This is extremely small. Hence, we conclude that though every pair of two objects exerts gravitational pull on each other, yet they cannot move towards each other because this gravitational pull is too weak. 2. When a body of mass 1 kg is held on the surface of Earth. Gravitational force of attraction between the body and Earth, It means that the Earth exerts a gravitational force of 9.8 N on a body of mass 1 kg. This force is much larger as compared to the force when both the bodies are lighter. That is why when a body is dropped from a height, it falls to the Earth. 3. When both the bodies are heavy. Let us calculate gravitational force of attraction between Earth and the Moon. The gravitational force between Earth and Moon, This is really large. It is this large gravitational force exerted by Earth on Moon, which makes the Moon revolve around the Earth. Question 1. Two persons having mass 100kg each are standing such that the centre of gravity is 1m apart. Calculate the force of gravitation and also calculate the force of gravity on each. 3 Force of gravity, Force of gravity, F’ is much greater than F so the persons will not move towards each other but each of them moves towards the earth. GRAVITATIONAL FORCE BETWEEN DIFFERENT OBJECTS: Gravitational Force between Sun and Earth: Gravitation force between the sun and the earth, 4 The gravitational force between the sun and the earth is very large (i.e. 3.6 × 1022 N). This force keeps the earth bound to the sun. Gravitational Force between Moon and Earth: Gravitational force between the earth and the moon, This large gravitational force keeps the moon to move around the earth. This large gravitational force is also responsible for the ocean tides Question 2 Two bodies A and B having mass 4m and 8m respectively are kept at a distance d apart. Where a small particle should be placed so that the net gravitational force on it due to the bodies A and B is zero? Solution: it is clear that the particle must be placed on the line AB, suppose it is at a distance x from A. Let its mass is m’. 5 The force on m’ due to A, Figure 1 6 Gravitational Potential Energy Gravitational potential energy is the energy an object has due to its position above Earth, energy due to its height. We know this energy exists because it takes effort to lift an object up to a height and also because when we release an object, it falls, gaining kinetic energy. The gravitational potential 𝐺𝐺𝐺𝐺 𝑈𝑈 = 𝑟𝑟 Or the gravitational potential energy is given as 𝐺𝐺𝐺𝐺𝐺𝐺 𝑈𝑈 = 𝑟𝑟 M is the source mass placed along the x-axis. m is the test mass at infinity. r is the distance from the source mass at which the gravitational potential energy is determined. Escape Speed If you fire a projectile upward, usually it will slow, stop momentarily, and return to Earth. There is, however, a certain minimum initial speed that will cause it to move upward forever. This minimum initial speed is called the (Earth) escape speed. Consider a projectile of mass m, leaving the surface of a planet (or some other astronomical body or system) with escape speed v. The projectile has a kinetic energy K given by and a potential energy U given by the eqn. 1 𝐺𝐺𝐺𝐺 𝐾𝐾. 𝑒𝑒 = 𝑚𝑚𝑣𝑣 2 = 2 𝑟𝑟 Where The gravitational potential 2𝐺𝐺𝐺𝐺 𝑉𝑉 = is called the escape velocity. 𝑟𝑟 𝐺𝐺𝐺𝐺 Note that we have 𝑔𝑔 = where we have 𝑉𝑉 = 2𝑔𝑔𝑔𝑔 𝑟𝑟 2 If the average radius of the Earth is , then 𝑉𝑉 = √2 × 9.8 × 6 × 103 = 11.2 𝐾𝐾𝑠𝑠 −1 Any particle with velocity greater than this will escape from the atmosphere of the Earth 7