'Equilibrium Experiments\r'

'Aim:\r\nTo investigate the theory of proportionality via the completion of cardinal experiments which rely on the subroutine of equations TPL ro principal(prenominal)e? +TPMcos?, which can be rewritten as (Mass Ag) cos?+(Mass Bg) cos?. For the second part of the investigation I ordain try to prove the equation (W*x)/d + encumbranceing of a ruler.\r\nIntroduction\r\nIn this investigation I pass on carry out two experiments, which in each case will prove a different aspect of the theory of equilibrium. There ar two theories I wish to prove. The first is ” tautness (Tpl) in the string Pl is equate to the weight of A and tension in the string pm (Tpm) is capable to the weight of B. For equilibrium the sum of the vertical components of these two tensions must be equal to the weight of c. Which intend that: Tpl cos? + Tpmcos? = MassCg which can be written as (MassAg) cos ? +(MassBg) cos ? = MassCg (equ 1)\r\nAlso: the moment of a force nearly a bear witness is equal to the magnitude of the force x its perpendicular surmount from the pivot. For equilibrium, the moment of the weight about the pivot will be equal to the moment in the adversary direction due to the weight of the ruler. Therefore (W*x)= weight of the ruler times distance d\r\n tilt of ruler = (W*x)/d. (equ 2)\r\nDiagram\r\n order for experiment a\r\n1. Set up the arrangement shown in recruit 1, check that the point p is in equilibrium.\r\n2. preeminence the evaluate of smokestackes A, B, and C and measure the be givens LPO ? and MPO ?.\r\n3. keep crowd together A and B constant and contrast the fresh think of of angles ? and ? for\r\ndifferent values of bundle C\r\n4. Record results in tabular from.\r\nMethod for experiment b\r\n1. Set up weapon as in fig 2.\r\n2. Find point of equilibrium.\r\n3. Note value for the plenty used and the distances x and d.\r\n4. Repeat last two stages for several cross outs of masses and record results in tabular form\r\n deliberation\r\nTh ese where done on paper by consecrate for ease of presentation\r\nError Analysis\r\nI bedevil generated my errors on the fact that I judgement that I could further read the I fill the error of. The way in which I got the last answer out was to run through the weighing twice, once with the answer I got †the error and thence again this time with the answer I got + the error. I think that in the first experiment I was a little over the top with the error. I said that I could read the angle to about 5. But when I did the calculation again with the new values. I found that the gap was quite massive. And that I was quite close to the true value and that although the value did ruination in the gap, the gap could have been a lot smaller. This say to me that the error need non have been so orotund, and that I read the angle quite well.\r\nFor exp B\r\nConclusion\r\nIn proof I have found out that equ 1 stand true. In the aim I set out to see if I could prove it I have put in all the results. The answers I get out are generally good. They are the same as the mass or in the cases were they are not they are close and fall well in the range of the errors. Problems with this experiment: the main problem I had with this experiment is the way I was told to find the angle. This way was not that accurate. It left a large margin for error. This is some of the anomalies may have crept in.\r\nFor the second of the two experiments I found that the mass of the ruler was 0.128g. This was obtained by weighting the ruler on a set of scales. After putting the come through the formula for weight of ruler, and then dividing the issue by g, which was 10, I managed to get a value for the mass of the ruler. On average this value was 0.119g, which is only about 7% away form the authentic mass of 0.128g.on farther analysis and after calculating the upper and lower bounds by changing the results by adding or subtracting the errors I found that the end point from adding the errors to the results and the outcome from subtracting the errors was the same, 0.119g.\r\nThis meant that the error was not a large enough value to affect the results a crucial way. Therefore finally I found that the mass on the ruler to 0.119g this is 7% out for the value, which I recorded as the mass for the ruler. The reason for this is unknown. I can only guess to the reason. One hatchway is the mass I recorded for the ruler was out. And as my results are so consistent this is a large possibility.\r\n'