![]() Sample Problem #1ĭetermine the force of gravitational attraction between the earth (m = 5.98 x 10 24 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 10 6 m from earth's center. As a first example, consider the following problem. Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance. Using Newton's Gravitation Equation to Solve Problems m 2 units and divided by d 2 units, the result will be Newtons - the unit of force.When the units on G are substituted into the equation above and multiplied by m 1 The units on G may seem rather odd nonetheless they are sensible. (This experiment will be discussed later in Lesson 3.) The value of G is found to be G = 6.673 x 10 -11 N m 2/kg 2 The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. The constant of proportionality (G) in the above equation is known as the universal gravitation constant. Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation.Īnother means of representing the proportionalities is to express the relationships in the form of an equation using a constant of proportionality. The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration. Thinking Proportionally About Newton's Equation If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power). If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power). So as two objects are separated from each other, the force of gravitational attraction between them also decreases. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled and so on. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of one of the objects is doubled, then the force of gravity between them is doubled. So as the mass of either object increases, the force of gravitational attraction between them also increases. Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. Newton's conclusion about the magnitude of gravitational forces is summarized symbolically as 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. ALL objects attract each other with a force of gravitational attraction. 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. Newton's law of universal gravitation is about the universality of gravity. 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.īut Newton's law of universal gravitation extends gravity beyond earth. 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. Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple. Consider Newton's famous equation F net = m But distance is not the only variable affecting the magnitude of a gravitational force. 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. Believing that gravitational forces were responsible for each, Newton was able to draw an important conclusion about the dependence of gravity upon distance. As discussed earlier in Lesson 3, Isaac Newton compared the acceleration of the moon to the acceleration of objects on earth.
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