Ch0112 - Chapter 12 Gravitational Force Near the Surface of...

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Chapter 12 Gravitational Force Near the Surface of the Earth, First Brush with Newton’s 2nd Law 69 12 Gravitational Force Near the Surface of the Earth, First Brush with Newton’s 2 nd Law Some folks think that every object near the surface of the earth has an acceleration of 9 . 8 m/s 2 downward relative to the surface of the earth. That just isn’t so. In fact, as I look around the room in which I write this sentence, all the objects I see have zero acceleration relative to the surface of the earth. Only when it is in freefall, that is, only when nothing is touching or pushing or pulling on the object except for the gravitational field of the earth, will an object experience an acceleration of 9 . 8 m/s 2 downward relative to the surface of the earth. Gravitational Force near the Surface of the Earth We all live in the invisible gravitational field of the earth. Mass is always accompanied by a surrounding gravitational field. Any object that has mass, including the earth, is surrounded by a gravitational field. The greater the mass of the object, the stronger the field is. The earth has a huge mass; hence, it creates a strong gravitational field in the region of space around it. The gravitational field is a force-per-mass at each and every point in the region around the object, always ready and able to exert a force on any particle that finds itself in the gravitational field. The earth’s gravitational field exists everywhere around the earth, not only everywhere in the air, but out beyond the atmosphere in outer space, and inside the earth as well. The effect of the gravitational field is to exert a force on any particle, any “victim,” that finds itself in the field. The force on the victim depends on both a property of the victim itself, namely its mass, and on a property of the point in space at which the particle finds itself, the force-per-mass of the gravitational field at that point. The force exerted on the victim by the gravitational field is just the mass of the victim times the force-per-mass value of the gravitational field at the location of the victim. Hold a rock in the palm of your hand. You can feel that something is pulling the rock downward. It causes the rock to make a temporary indentation in the palm of your hand and you can tell that you have to press upward on the bottom of the rock to hold it up against that downward pull. The “something” is the field that we have been talking about. It is called the gravitational field of the earth . It has both magnitude and direction so we use a vector variable, the symbol g h to represent it. In general, the magnitude and the direction of a gravitational field both vary from point to point in the region of space where the gravitational field exists. The gravitational field of the earth, near the surface of the earth is however, to a very good approximation, much simpler than that. To a very good approximation, the gravitational field of the earth has the same value at all points near the surface of the earth, and it always points
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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Ch0112 - Chapter 12 Gravitational Force Near the Surface of...

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