G1 - 1 The Acceleration Due to Gravity Introduction:...

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1 The Acceleration Due to Gravity Introduction: Acceleration is defined as the rate at which the velocity of a moving object changes with time. Accelerations are always caused by forces. In this laboratory we will investigate the acceleration due to the force of gravity. Theory: In its simplest form, Newton's law of force relates the amount of force on an object to its mass and acceleration . F = m a (1) or force = mass times acceleration. Therefore, to impart an acceleration to an object, one must impart a force. One of the most obvious (and the weakest) of all forces in nature is the gravitational force . Newton's Universal Law of Gravitation describes the gravitational force (F g ) as follows: F g = Gmm' r 2 (2) This equation states that the force between the two masses m and m' is equal to the product of their masses ( mm' ) multiplied by a constant ( G ) and divided by the distance between them squared ( r 2 ). The constant ( G ) is called the gravitational constant . To compute the gravitational force between the Earth and an any object, we substitute the mass of the Earth ( M E ) and the distance from the object to the center of the Earth ( r ). When the objects are on or near the Earth's surface, this distance can be approximated by the value for the radius of the Earth * ( R E ) so that Equation (2) becomes: * We can approximate this because in the scale of the size of the Earth (many hundreds of kilometers) the value for r at the top of our lab table is virtually equal to the value of r at the floor. Algebraically this is shown by: R E 2245 R E + D R
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2 F g = GmM E R E 2 (3) in which we see that the force only depends on the mass of the object, because G , M E , and R E are all constants . This force (measured at the Earth's surface) is called the weight of the object. Now looking at Equation (1) and equating F to the gravitational force (F g ) , we see that: ma = GmM E R E 2 = mg , (4) where g = GM E R E 2 . In this last equation, we see that
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This note was uploaded on 10/14/2010 for the course APHY 140 taught by Professor Ham during the Spring '09 term at Adams State University.

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G1 - 1 The Acceleration Due to Gravity Introduction:...

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