Gravitational Force:. As we all know that the fall of an apple made Newton to think on the subject of the motion of the planters. He recognized that the apple falls on the surface of earth only because of the earth attraction towards the apple . He was in doubt whether this force of attraction could extend beyond the tree to cloud, to moon and even beyond the moon. He thought that the force on the apple must be directly proportional to its mass. In addition ,according to his own third law of motion, the apple would also attract towards Earth. Similarly ,the force of attraction is also proportional to the mass of earth and the mass of the object. Another factor involved is the distance between the apple and the earth. He concluded that this force of attraction is inverse of the distance between them. This attractive force between objects and the earth is called the Gravitational force. Newton was so confident about his governing laws of motion on Earth,that he suggested that this force would work anywhere in the universe. He assumed that the same force of attraction would act between two masses ma and mb. The law of Gravitation states. The gravitation between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. He proposed his law of gravitation ,which is represented by the following equation. Law of universal Gravitation:
In the above equation ,d= distance between the centers of the two objects. G= Universal Constant. ma ,mb = Masses of two objects
Different objects exerts the force according to their masses. How large is the constant G? As you know that the force of gravitational attraction between two objects on earth is small. You can,t feel the slightest attraction even between two huge objects. It took about 100 years after the Newton,s law of motion.
Henry Cavendish Experiment:. In 1797 AD, a scientist from British, Henry Cavendish had first Performed experiment to measure the gravitational force between two masses in the laboratory .He was the first to give accurate values results about the gravitational constant. He used the equipment given below in the figure 4.17. The apparatus consisted of a torsion balance made of a six- foot (1.8m) wooden rod suspended from a wire, with a 2- inch (51 mm) diameter 1.61 - pound (0.73kg) lead sphere attached to each end. Two 12- inch (300mm) 348- pound (158kg) lead balls were located near the smaller balls, about 9 inches (230mm) away, and held in place with a separate suspension system.The experiment measured the giant gravitational attraction between the small balls and the large ones. The two large balls were positioned on alternate sides of the horizontal wooden arm of the balance. Their mutual attraction to the small balls caused the arm to rotate, twisting the wire supporting the arm.
The arm was stopped rotating when it arrived at an angle where the rotating force of the wire balanced the combined gravitational force of attraction between the large and small lead spheres. By measuring ,the angle of the rod,and with the known value of twisting force ( torque) of the wire, Cavendish determined the force of attraction between the pairs of masses. Since the gravitational force of the Earth on the small could be measured directly by weighing it, the ratio of the forces allowed the density of the earth to be calculated ,using Newton,s law of gravitation.
weight and weightlessness; the acceleration of objects due to earth,s gravitation can be found by using Newton ,s law of universl gravitation and second law for a free falling object. Let's the force between the earth and an object paced on earth is given by. G me,m/F= D2..........1 we know F= ma ...........2 Combining equation 1 and equation 2. a= G me / D2. On the earth surface the distance between will be d = Re ,so the above equation will become g= G me/ Re2. As the distance is increasing then the value of the g will be reducing according to the inverse square relationship. You have seen the photos of the astronauts that feel the condition of weightlessness of space shuttle. This situation is called " zero- g" .The shuttle distance from the surface of earth in only 400 km. At that distance the value of "g" is 8.6 m/S2 ,thus the gravitational force is certainly not zero in the shuttle.
Example problem 2 : There are two 5.0 kg masses ,which are 2.5 meter apart from their centers. Determine the force of attraction between them?
Known: M1= 5.0kg M2= 5.0kg d= 2.5 meter G= 6.67× 10-11 Nm2 / kg2
Unknown: Force of attraction=? Formula;. F= Gma mg / D2.
Calculation: F= 6.67× 10-11 Nm2/ kg2× 5.0kg× 5.0kg/ F= 26.68× 10-11 N Two 1.0 kg masses have their centers 1.0 meter apart .
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