![]() ![]() This lab will demonstrate how to measure the acceleration g, given in Equation 3. Again, because the Earth is so much more massive than a person, the gravitational force a person, or even many people, exert on the Earth essentially goes unnoticed. The people exert an equal and opposite force on the Earth. Similarly, for people standing on the ground, the Earth is exerting an even larger force on them than on the apple. Thus, the apple falls toward the Earth, not the Earth toward the apple. For larger objects, a larger force is required to make them accelerate. The reason that the Earth is essentially unaffected by the force of the apple on the Earth is that the mass of the Earth is so much larger than that of the apple. In the famous example of the apple falling from a tree, the Earth is exerting a force on the apple to make it fall, and the apple is exerting an equal and opposite force on the earth, given by Equation 1. For people standing on the ground, this direction is simply referred to as "down." Canceling the mass m on both sides of the equation substituting g for a and noting that the distance between the objects' centers of mass is just the radius of the Earth, r E, the magnitude of the downward force can be rewritten as: In this context, the acceleration vector is typically denoted as a scalar g, with an implied direction pointing radially inward, toward the center of the Earth. ![]() Where G is a universal constant of proportionality that has been measured experimentally and m E is the mass of the Earth. Using Newton's second law, F = m a, the force on the mass m due to the Earth's gravity can be written as: The following description will investigate the gravitational force between the Earth and an object of mass m on its surface. Where r ^ denotes that the direction of the force is pointed radially inward. The gravitational force F between two masses m 1and m 2, with their centers of mass separated by a distance r, can be written as: Accurately knowing this value is extremely important, as it describes the magnitude of the gravitational force on an object at the surface of the Earth. Gravitational acceleration g, which is the acceleration an object on the surface of the Earth experiences due to the Earth's gravitational force, will be measured in this lab. This force acts along the line joining the two particles. The law states that every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. He observed the motion of the moon and the orbits of the planets and eventually formulated the universal law of gravitation. He then surmised that if gravity can act at the top of the tree, it can also act at even larger distances. He noticed the acceleration of the apple and deduced that there must have been a force acting upon the apple. Legend states that Isaac Newton saw an apple fall from a tree. Source: Ketron Mitchell-Wynne, PhD, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA ![]()
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