Section 2 Newton’s law of universal gravitational Chapter 7 Section 2 Newton’s law of universal gravitational

Objectives Explain how Newton’s law of universal gravitation accounts for various phenomena, including satellite and planetary orbits, falling objects, and the tides. Apply Newton’s law of universal gravitation to solve problems.

Law of universal gravitational Apples had a significant contribution to the discovery of gravitation. The English physicist Isaac Newton (1642-1727) introduced the term "gravity" after he saw an apple falling onto the ground in his garden. "Gravity" is the force of attraction exerted by the earth on an object. The moon orbits around the earth because of gravity too. Newton later proposed that gravity was just a particular case of gravitation. Every mass in the universe attracts every other mass. This is the main idea of Newton's Law of Universal Gravitation.

Law of universal gravitational Isaac Newton compared the acceleration of the moon to the acceleration of objects on earth. Believing that gravitational forces were responsible for each, Newton was able to draw an important conclusion about the dependence of gravity upon distance. This comparison led him to conclude that the force of gravitational attraction between the Earth and other objects is inversely proportional to the distance separating the earth's center from the object's center. But distance is not the only variable affecting the magnitude of a gravitational force. Consider Newton's famous equation Fnet = m • a

Law of universal gravity Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple. And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law), that force must also depend upon the mass of the earth. So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object. But Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. Newton's place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather due to his discovery that gravitation is universal. ALL objects attract each other with a force of gravitational attraction. Gravity is universal. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers.

Centripetal force The centripetal force that holds the planets in orbit is the same force that pulls an apple toward the ground—gravitational force. Gravitational force is the mutual force of attraction between particles of matter. Gravitational force depends on the masses and on the distance between them.

Newton developed the following equation to describe quantitatively the magnitude of the gravitational force if distance r separates masses m1 and m2: The constant G, called the constant of universal gravitation, equals 6.673  10–11 N•m2/kg.

The solution is as follows: Example # 1 Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 106 m from earth's center. The solution of the problem involves substituting known values of G (6.673 x 10-11 N m2/kg2), m1 (5.98 x 1024 kg), m2 (70 kg) and d (6.38 x 106 m) into the universal gravitation equation and solving for Fgrav. The solution is as follows:

The solution is as follows: Example # 2 Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center. The solution of the problem involves substituting known values of G (6.673 x 10-11 N m2/kg2), m1 (5.98 x 1024 kg), m2 (70 kg) and d (6.39 x 106 m) into the universal gravitation equation and solving for Fgrav. The solution is as follows:  

Example #3 Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects? solution If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). But this affect is offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 (22); the result is that there is no net affect on force. F = (16 units) • 4 / 4 = 16 units

Student guided practice Find the Force of Gravity(N) Mass object 1 Mass object 2 distance Force of gravity Football player 100 kg Earth 5.98 x10^24 kg 6.38x10^6( on surface) Ballerina 40 kg

Gravitational force The gravitational forces that two masses exert on each other are always equal in magnitude and opposite in direction. This is an example of Newton’s third law of motion. One example is the Earth-moon system, shown on the next slide. As a result of these forces, the moon and Earth each orbit the center of mass of the Earth-moon system. Because Earth has a much greater mass than the moon, this center of mass lies within Earth.

Gravitational force Newton’s law of gravitation accounts for ocean tides. High and low tides are partly due to the gravitational force exerted on Earth by its moon. The tides result from the difference between the gravitational force at Earth’s surface and at Earth’s center.

Gravitational force Cavendish applied Newton’s law of universal gravitation to find the value of G and Earth’s mass. When two masses, the distance between them, and the gravitational force are known, Newton’s law of universal gravitation can be used to find G. Once the value of G is known, the law can be used again to find Earth’s mass.

Field force Gravity is a field force. Gravitational field strength, g, equals Fg/m. The gravitational field, g, is a vector with magnitude g that points in the direction of Fg. Gravitational field strength equals free-fall acceleration.

Gravitational force weight = mass  gravitational field strength Because it depends on gravitational field strength, weight changes with location: On the surface of any planet, the value of g, as well as your weight, will depend on the planet’s mass and radius.

video Let’s watch a video on universal law