Gravity and Motion 2014 PDF

2014 ---- Structured summary ================== Snapshot -------- Gravitational forces, potential energy, and motion of objects under gravity are discussed, including the law of universal gravitation, gravitational potential, and motion of planets and satellites. Key findings ------------ - T...

2014 ---- Structured summary ================== Snapshot -------- Gravitational forces, potential energy, and motion of objects under gravity are discussed, including the law of universal gravitation, gravitational potential, and motion of planets and satellites. Key findings ------------ - The chapter does not discuss the limitations of the laws of gravity or their applications. It is a general introduction to the concept of gravity and its laws. - The limitations of the text are that it assumes a basic understanding of physics and mathematics, and that it does not provide experimental data or practical applications of the concepts discussed. - The chapter does not suggest future work or areas of research. It is a foundational introduction to the concept of gravity and its laws. - The future work suggested by the text is to apply the concepts of gravity and gravitational potential to more complex systems, such as multiple-body problems and relativistic gravity. - The chapter does not discuss specific practical applications of the laws of gravity. However, it provides a foundation for further study of gravity and its laws, which have numerous practical applications in fields such as astronomy, engineering, and physics. - The practical applications of the text include the design of satellite orbits, the calculation of gravitational forces in engineering and astronomy, and the understanding of planetary motion and the behavior of celestial bodies. ### Gravity And The Universe We know that everything falls towards the ground, and it\'s harder to go uphill than downhill. A long time ago, a scientist named Galileo figured out that everything falls towards the ground at the same speed, no matter how heavy or light it is. He even did experiments to prove it! People have also been looking at the stars and planets in the sky for a long time. They noticed that some stars stay in the same place, while others seem to move around. A long time ago, people thought that the Earth was the center of the universe, and everything else moved around it. But then a scientist named Copernicus said that the Sun was the center, and the planets moved around it. Later, a scientist named Kepler looked at the planets and figured out three important laws about how they move. The first law says that planets move in oval shapes around the Sun. The second law says that planets move faster when they\'re close to the Sun and slower when they\'re far away. The third law says that the time it takes a planet to go around the Sun is related to how far away it is. A scientist named Newton used Kepler\'s laws to figure out a big secret about the universe. He said that everything in the universe pulls on everything else, and that\'s what makes things fall towards the ground. He also said that the force of gravity gets weaker as things get farther apart. This is called the Universal Law of Gravitation. ### Gravity And Masses When two objects have mass, they pull on each other. This is called gravity. The bigger the objects, the stronger they pull on each other. If we have three equal masses in a triangle, the force on a mass in the middle of the triangle is zero because the forces from the other masses cancel each other out. If we have a big hollow ball and a small mass inside it, the force on the small mass is zero because the forces from all parts of the big ball cancel each other out. If the small mass is outside the big ball, the force on it is as if all the mass of the big ball is at its center. A long time ago, a scientist named Newton discovered the law of gravity. He said that every object in the universe pulls on every other object. The force of gravity depends on the mass of the objects and how far apart they are. Later, another scientist named Cavendish measured the strength of gravity between two objects. He used a special tool to measure how much two balls attracted each other. This helped us understand how gravity works. The Earth is like a big ball, and it pulls on everything near it. The force of gravity on the surface of the Earth is what keeps us on the ground. If we go up high or down deep into a mine, the force of gravity is a little weaker. But it\'s strongest on the surface of the Earth. ### Gravity And Energy Gravity is a force that pulls objects towards each other. The force of gravity between two objects depends on their mass and the distance between them. When an object moves against gravity, its potential energy changes. The change in potential energy is equal to the work done on the object by the force of gravity. The force of gravity on an object near the surface of the Earth is constant and directed towards the center of the Earth. The potential energy of an object at a height h above the surface of the Earth is proportional to its mass and the height. The gravitational potential energy of an object can be calculated using the formula W(h) = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the surface of the Earth. The concept of potential energy can be applied to other situations, such as the energy of an object in a gravitational field. The total energy of an object is the sum of its kinetic energy and potential energy. The escape speed from the Earth\'s surface is the minimum speed an object must have to escape the Earth\'s gravity. It is calculated using the formula v = √(2GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the Earth. Earth satellites are objects that orbit the Earth. Their motion is similar to the motion of planets around the Sun, and Kepler\'s laws of planetary motion apply to them. The speed of a satellite in a circular orbit around the Earth decreases as the distance from the Earth increases. The time period of a satellite in a circular orbit around the Earth is given by the formula T = 2π√(r\^3/GM), where r is the radius of the orbit and M is the mass of the Earth. ### Satellites And Gravity Satellites are objects that orbit around the Earth. They can be in circular or elliptical orbits. The time it takes for a satellite to complete one orbit is called its period. The period of a satellite depends on its distance from the Earth. There are different types of satellites, such as geostationary satellites and polar satellites. Geostationary satellites are special because they seem to be standing still in the sky, even though they are moving very fast. They are used for communication and can send signals to a wide area on Earth. Polar satellites, on the other hand, move in a north-south direction and can view the entire Earth in strips. Gravity is the force that pulls objects towards each other. The Earth\'s gravity pulls satellites towards it, keeping them in their orbits. The force of gravity also keeps us on the ground and gives us our weight. But if we were in a satellite, we would feel weightless because the satellite is falling towards the Earth at the same rate as we are. This is called weightlessness. Satellites are used for many things, such as taking pictures of the Earth, predicting the weather, and sending signals for communication. They are very important for our daily lives. ### Gravity And Motion Gravity is a force that pulls objects towards each other. The Earth\'s gravity pulls us towards its center. Objects in space, like satellites, orbit around the Earth because of gravity. The Earth\'s gravity also keeps us on the ground. When an object moves in a circle, like a satellite orbiting the Earth, its angular momentum is conserved. This means that the object\'s speed and direction of motion stay the same. The total energy of an object is the sum of its kinetic energy (the energy of motion) and potential energy (the energy of position). The gravitational potential energy of an object is negative because it is attracted to the Earth. Gravity is a central force, which means it pulls objects towards the center of the Earth. The force of gravity between two objects depends on their mass and the distance between them. Astronauts in space experience weightlessness because they are in \"free fall\" towards the Earth, just like the satellite they are in. The gravitational force is still acting on them, but they don\'t feel it because they are falling with the satellite. The constant in the formula can be chosen to be zero, which means the potential energy is zero at infinity. The gravitational force between two objects is not necessarily along the line joining their centers of mass. However, for a spherically symmetric body like the Earth, the force on a particle outside the body is as if the mass is concentrated at the center. Gravity cannot be shielded, unlike electrical forces. This means that a hollow sphere or any other means cannot block the gravitational force of nearby matter. An astronaut inside a space ship orbiting the Earth cannot detect gravity because they are in \"free fall\" with the ship. If the space station is large, the astronaut may be able to detect gravity, but it would be very small. The tidal effect of the moon\'s pull on the Earth is greater than the sun\'s pull because the moon is closer to the Earth. Analysis ======== Study subjects -------------- **4 mass pairs** Answer Consider four masses each of mass m at the corners of a square of side l ; See Fig. 8.9. **We have four mass pairs at distance l and two diagonal pairs at distance 2 l Hence, W (r ) = − 4 G m 2 − 2 G m 2 l**. Abstract ======== Points to ponder Exercises Additional exercises8.1 INTRODUCTIONEarly in our lives, we become aware of the tendency of all material objects to be attracted towards the earth. Anything thrown up falls down towards the earth, going uphill is lot more tiring than going downhill, raindrops from the clouds above fall towards the earth and there are many other such phenomena. Historically it was the Italian Physicist Galileo (1564-1642) who recognised the fact that all bodies, irrespective of their masses, are accelerated towards the earth with a constant acceleration. It is said that he made a public demonstration of this fact. To find the truth, he certainly did experiments with bodies rolling down inclined planes and arrived at a value of the acceleration due to gravity which is close to the more accurate value obtained later. Bibliography ============ 1. (2014). Introduction Kepler's laws Universal law of gravitation The gravitational constant Acceleration due to gravity of the earth Acceleration due to gravity below and above the surface of earth Gravitational potential energy Escape speed Earth satellites Energy of an orbiting satellite Geostationary and polar satellites Weightlessness.