Conclusions In this experiment, the acceleration due to gravity was measured by timing a freely falling metal ball. Time of falling and vertical displacement the ball felt were Time of falling and vertical displacement the ball felt were.
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We will get through this together.Sincerely,Elizabeth DouglasCEO, wikiHow. A lab report describes an entire experiment from start to finish, outlining the procedures, reporting results, and analyzing data. The report is used to demonstrate what has been learned, and it will provide a way for other people to see your process for the experiment and understand how you arrived at your conclusions. The conclusion is an integral part of the report; this is the section that reiterates the experiment’s main findings and gives the reader an overview of the lab trial. Writing a solid conclusion to your lab report will demonstrate that you’ve effectively learned the objectives of your assignment.
Experimental study of gravitationThe essence of Newton’s theory of gravitation is that the between two bodies is proportional to the product of their masses and the inverse square of their separation and that the force depends on nothing else. With a small modification, the same is true in general relativity. Newton himself tested his assumptions by experiment and observation. He made experiments to confirm the principle of equivalence and checked the inverse square law as applied to the periods and diameters of the orbits of the satellites of Jupiter and Saturn.During the latter part of the 19th century, many experiments showed the force of gravity to be independent of, electromagnetic fields, shielding by other matter, orientation of crystal axes, and other factors. The revival of such experiments during the 1970s was the result of theoretical attempts to relate gravitation to other forces of nature by showing that general relativity was an incomplete description of gravity. New experiments on the were performed, and experimental tests of the inverse square law were made both in the laboratory and in the field.There also has been a continuing interest in the determination of the constant of gravitation, although it must be pointed out that G occupies a rather anomalous position among the other constants of.
In the first place, the mass M of any celestial object cannot be determined independently of the gravitational attraction that it exerts. Thus, the combination G M, not the separate value of M, is the only meaningful property of a,. Second, according to general relativity and the principle of equivalence, G does not depend on material properties but is in a sense a geometric factor. Hence, the determination of the constant of gravitation does not seem as essential as the measurement of quantities like the electronic. It is also much less well determined experimentally than any of the other constants of physics. Experiments on gravitation are in fact very difficult, as a comparison of experiments on the inverse square law of electrostatics with those on gravitation will show.
The electrostatic law has been established to within one part in 10 16 by using the fact that the field inside a closed conductor is zero when the inverse square law holds. Experiments with very sensitive electronic devices have failed to detect any residual fields in such a closed cavity. Gravitational forces have to be detected by mechanical means, most often the, and, although the sensitivities of mechanical devices have been greatly improved, they are still far below those of electronic detectors. Mechanical arrangements also preclude the use of a complete gravitational enclosure. Last, extraneous disturbances are relatively large because gravitational forces are very small (something that Newton first pointed out).
Thus, the inverse square law is established over laboratory distances to no better than one part in 10 4. TheRecent interest in the inverse square law arose from two suggestions.
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First, the gravitational field itself might have a mass, in which case the constant of gravitation would change in an exponential manner from one value for small distances to a different one for large distances over a characteristic distance related to the mass of the field. Second, the observed field might be the superposition of two or more fields of different origin and different strengths, one of which might depend on chemical or nuclear constitution. Deviations from the inverse square law have been sought in three ways. There have been careful comparisons of the value of the attraction of as measured on the surface and as experienced by artificial satellites.Early in the 1970s an experiment by the American physicist Daniel R. Long seemed to show a deviation from the inverse square law at a range of about 0.1 metre. Long compared the maximum attractions of two rings upon a test mass hung from the arm of a torsion balance. The maximum attraction of a ring occurs at a particular point on the axis and is determined by the mass and dimensions of the ring.
If the ring is moved until the force on the test mass is greatest, the distance between the test mass and the ring is not needed. Two later experiments over the same range showed no deviation from the inverse square law. In one, conducted by the American physicist Riley Newman and his colleagues, a test mass hung on a torsion balance was moved around in a long hollow cylinder. The cylinder approximates a complete gravitational enclosure and, allowing for a small correction because it is open at the ends, the force on the test mass should not depend on its location within the cylinder.
No deviation from the inverse square law was found. In the other experiment, performed in Cambridge, Eng., by Y.T. Chen and associates, the attractions of two cylinders of different mass were balanced against a third cylinder so that only the separations of the cylinders had to be known; it was not necessary to know the distances of any from a test mass. Again no deviation of more than one part in 10 4 from the inverse square law was found. Other, somewhat less-sensitive experiments at ranges up to one metre or so also have failed to establish any greater deviation.The geophysical tests go back to a method for the determination of the constant of gravitation that had been used in the 19th century, especially by the British astronomer. Suppose the value of gravity g is measured at the top and bottom of a horizontal slab of of thickness t and density d. The values for the top and bottom will be different for two reasons.
First, the top of the slab is t farther from the centre of Earth, and so the measured value of gravity will be less by 2( t/ R) g, where R is the radius of Earth. Second, the slab itself attracts objects above and below it toward its centre; the difference between the downward and upward attractions of the slab is 4π G t d. Thus, a value of G may be estimated. Stacey and his colleagues in Australia made such measurements at the top and bottom of deep mine shafts and claimed that there may be a real difference between their value of G and the best value from laboratory experiments. The difficulties lie in obtaining reliable samples of the density and in taking account of varying densities at greater depths. Similar uncertainties appear to have afflicted measurements in a deep bore hole in the Greenland ice sheet.New measurements have failed to detect any deviation from the inverse square law. The most thorough investigation was carried out from a high tower in Colorado.
Measurements were made with a at different heights and coupled with an extensive survey of gravity around the base of the tower. Any variations of gravity over the surface that would give rise to variations up the height of the tower were estimated with great care. Allowance was also made for deflections of the tower and for the accelerations of its motions.
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The final result was that no deviation from the inverse square law could be found.A further test of the inverse square law depends on the theorem that the divergence of the gravity vector should vanish in a that is free of additional gravitational sources. An experiment to test this was performed by M.V. Moody and H.J. Paik in California with a three-axis superconducting gravity gradiometer that measured the gradients of gravity in three perpendicular directions. The sum of the three gradients was zero within the accuracy of the measurements, about one part in 10 4.The absolute measurements of gravity described earlier, together with the gravity surveys made over the surface of Earth, allow the mean value of gravity over Earth to be estimated to about one part in 10 6. The techniques of space research also have given the mean value of the radius of Earth and the distances of artificial satellites to the same precision.
Thus, it has been possible to compare the value of gravity on Earth with that acting on an artificial satellite. Agreement to about one part in 10 6 shows that, over distances from the surface of Earth to close satellite orbits, the inverse square law is followed.Thus far, all of the most reliable experiments and observations reveal no deviation from the inverse square law. The principle of.
The direct measurement of the force between two masses in the laboratoryThe first approach was suggested by Newton; the earliest observations were made in 1774 by the British astronomer on the mountain of Schiehallion in Scotland. The subsequent work of Airy and more-recent developments are noted above. The laboratory balance method was developed in large part by the British physicist during the late 1800s, but all the most recent work has involved the use of the torsion balance in some form or other for the direct laboratory measurement of the force between two bodies. The torsion balance was devised by Michell, who died before he could use it to measure G. Cavendish adapted Michell’s design to make the first reliable measurement of G in 1798; only in comparatively recent times have clearly better results been obtained.
Cavendish measured the change in deflection of the balance when attracting masses were moved from one side to the other of the torsion beam. The method of deflection was analyzed most thoroughly in the late 1800s by, an English physicist, who carried it to its highest development, using a delicate suspension fibre of fused silica for the pendulum. In a variant of that method, the deflection of the balance is maintained constant by a servo control.The second scheme involves the changes in the period of oscillation of a torsion balance when attracting masses are placed close to it such that the period is shortened in one position and lengthened in another. Measurements of period can be made much more precisely than those of deflection, and the method, introduced by Carl Braun of Austria in 1897, has been used in many subsequent determinations.
In a third scheme the of the suspended masses is measured as they are moved relative to the large attracting masses.In another arrangement a balance with heavy attracting masses is set up near a free test balance and adjusted so that it oscillates with the same period as the test balance. The latter is then driven into resonant oscillations with an amplitude that is a measure of the constant of gravitation. The technique was first employed by J. Zahradnicek of Czechoslovakia during the 1930s and was effectively used again by C. Pontikis of France some 40 years later.Suspensions for two-arm balances for the comparison of masses and for torsion balances have been studied intensively by T.J.
Quinn and his colleagues at the, near Paris, and they have found that suspensions with thin ribbons of metal rather than wires provide the most stable systems. They have used balances with such suspensions to look for deviations from the predictions of general relativity and have most recently used a torsion balance with ribbon suspension in two new determinations of the constant of gravitation.Many new determinations of G were made in the five years from 1996 to 2001 and are summarized in the table. However, despite the great attention given to systematic errors in those experiments, it is clear from the range of the results that serious discrepancies, much greater than the apparent random errors, still afflict determinations of G. In 2001 the best estimate of G was taken to be 6.67553 × 10 −11 m 3 s −2 kg −1. Results before 1982 indicate a lower value, perhaps 6.670, but those from 1996 onward suggest a higher value.
Values of the constant of gravitationauthoryearmethodG (in units of 10 –11m 3s –2kg –1)H. Cavendish1798torsion balance (deflection)6.754J.H. Poynting1891common balance6.698C.V. Boys1895torsion balance (deflection)6.658C. Braun1897torsion balance (deflection)6.658C. Braun1897torsion balance (period)6.658P.R.
Heyl1930torsion balance (period)6.669J. Zahradnicek1932torsion balance (resonance)6.659P.R. Chrzanowski1942torsion balance (period)6.672C. Pontikis1972torsion balance (resonance)6.6714G.G. Luther and W.R. Towler1982torsion balance (period)6.6726H. De Boer1987mercury flotation (deflection)6.667W.
Michaelis et al.1996flotation (null deflection)6.7164C.H. Bagley and G.G. Luther1997torsion balance (period)6.6740O.V. Karagioz et al.1998torsion balance (period)6.6729J. Luo et al.1999torsion balance (period)6.6699M.P.
Fitzgerald, T.R. Armstrong1999torsion balance (null deflection)6.6742F. Nolting et al.1999common balance6.6754U. Kleinvoss et al.1999pendulum deflection6.6735J.H. Gundlach, S.M. Merkowitz2000torsion balance (acceleration)6.67422T.J. Quinn et al.2001torsion balance (servo)6.67553T.J.
Quinn et al.2001torsion balance (deflection)6.67565The variation of the constant of gravitation with timeThe 20th-century English physicist, among others, suggested that the value of the constant of gravitation might be proportional to the age of the universe; other rates of change over time also have been proposed. The rates of change would be extremely small, one part in 10 11 per year if the age of the is taken to be 10 11 years; such a rate is entirely beyond experimental capabilities at present. There is, however, the possibility of looking for the effects of any variation upon the of a celestial body, in particular the Moon. It has been claimed from time to time that such effects may have been detected. As yet, there is no certainty. Fundamental character of GThe constant of gravitation is plainly a fundamental quantity, since it appears to determine the large-scale structure of the entire universe. Gravity is a fundamental quantity whether it is an essentially geometric, as in general relativity, or the strength of a, as in one aspect of a more-general field of unified forces.
The fact that, so far as is known, gravitation depends on no other physical factors makes it likely that the value of G reflects a basic restriction on the possibilities of physical measurement, just as is a consequence of the fact that, beyond the shortest distances, it is impossible to make separate measurements of length and time.
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