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Unformatted text preview: Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision pulley, ramps, weights, metal track. 3 Theory According to Newton any two objects will attract one another if they both have mass. This attraction, F , is given by the formula F = GM 1 M 2 r 2 (1) where M 1 and M 2 are the masses of the two objects and r is the distance between the centers of mass of the two. G is a constant of proportionality, 6 . 67 10- 11 Nm 2 /kg 2 . If one of these objects is the Earth ( M E ) and the other is a relatively small object near the surface of the Earth ( M o ), the distance between the two is essentially the radius of the Earth, R E . Then equation 1 becomes F = GM E M o R 2 E (2) where M E is the mass of the Earth (5 . 983 10 24 kg ), R E is its radius (6 . 371 10 6 m ) and M o is the mass of the object. If the object is in free fall, this is the only force acting on it and F = M o a = M o g (3) where g is the acceleration due to the gravity of the Earth. Combining the last two equations gives M o g = GM E M o R 2 E (4) g = GM E R 2 E (5) or g = 9 . 807 m/s 2 (6) In situations where the object is not in free fall it will still interact with the Earth and this will cause the object to have a weight, W , which is given by M o g . The weight of an object as well as the acceleration due to gravity are variables, but if one stays near the surface of the Earth both may be considered to be constant. In this experiment g will be determined by a number of methods. 1 3.1 Atwoods Machine A common device used to calculate accelerations is Atwoods apparatus. In this case, it consists of two masses, m 1 and m 2 , attached by a string (assumed massless) which in turn is on a pulley....
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