Calculating Free Fall Acceleration

Calculating Free Fall AccelerationIntroductionA research by Heckert (2010) shows in 1600s, the famous physicist Galileo . Galilei assemble the swinging motion of a large chandelier in the Pisa cathedral. He began to seriously analyse the chandelier, and recorded the time the light took to swing. In the 16th century, at that place was no stopwatch so that Galileo timed the swing by pulse. In addition, he was the first European to really study this phenomenon and he discovered that their method could be used for calculate the local gloominess.For Galileo his pendulum was the light but generally speaking a pendulum lowlife be delimit as a consistence suspended from a fixed point which swing disengagely by the motion of gravity and momentum. It is used to regulate the movements of clockwork and other machinery.In its simplest form and avoiding the maths there are three parts to the basic laws of a pendulum. First the time for each vibration is depending on the aloofness of the sop ups. In addition, mass of the tail does not affect the motion at all. Second, a pendulums horizontal speed is the same as the vertical speed would be, if the bob had fallen from its highest point. Thirdly, the unbowed of head of the bob is inversely proportional to disembarrass fall acceleration and the square of period of the body is proportional to length of the pendulumThe background definition and the laws of a pendulum target be used to calculate the free fall acceleration. Using a simple gravity pendulum like Galileos Pendulum System, I would like to show how to find the surmount ways in order to quiz free fall acceleration.Methods1. Experiment equipmentProtractorSteel BobStopwatchVernier CaliperIron Support meetMeter RulerInelastic String2. Apparatus setup Figure1-1Figure1-1 shows that iron support stand was put beside edge of test desk in case the summit meeting of stand was shorter than the length of test string. Next, the make clunk was hung by an inelasti c string and the iron support stand was used to support the weight of steel ball. Last, the clip was clamped to the string in order to keep a constant length. At the same time, the bob swing in a vertical break through which parallels the stand.3. ProceduresFirst of all, the simple pendulum was made up by hanging a bob from the top of stand and the bob was released in a constant height, because protractor was used to control the degree betwixt 5 and 15 to normal line. Secondly, pendulum would begin to oscillate in vertical surface in a level(p) action, and then the stop watch was used to record the time of each swing. Finally the most authorised data which describes this oscillation is period and we did antithetic types of test by different length of string, like 30cm, 45 cm, 60 cm, 75 cm, 90cm, 105 cm, and 120 cm.ResultsTable of resultExperiment timesLength of string(cm)Trials 1Trials 2Total Average periodOscillationtimesAverage period of each swingT2(second square)Time diss ipaten for one finish up Oscillation(seconds)130cm56.60s56.50s56.55s50 times1.13s1.28s2245 cm68.60s68.50s68.55s50 times1.37s1.88 s2360 cm79.00s78.90s79.00s50 times1.58s2.50 s2475 cm87.60s87.90s87.75s50 times1.76s3.08 s2590 cm96.05s96.00s96.05s50 times1.92s3.69 s26105 cm104.00s104.00s104.00s50 times2.08s4.33 s27120 cm110.50s111.00s110.75s50 times2.22s4.91 s2Table-1.1Table-1.1 shows the data of 7 experiments using different length of string and how the data changed, as the length of string was increased the period of each oscillation was increase as well.L is the distance from the frame of the stand to the center of the mass the length includes the radius of ball. The period of oscillation is the time required for the pendulum to complete one swing. For one complete swing, the steel ball must move from the left to the right and back to the left. T2 can be understood as the square of the period of oscillation, the equation below shows how T2 was reason.Square both sidesT2= 4 2 (L/g ) T2 = L (4 2 g)Multiply both sides by gg T2 = 4 2 LDivide both sides by T2Discussion and AnalysisThe results of experiment show the relation between T2 and length of string. To turn to discuss the results it is important to understand some key ideas, there are controlled variable, experimental variable, error and uncertainty.Firstly, according to Science Buddies(2009) said that a controlled variable can be defined as the factor which is unchanged or kept constant to prevent its effects or error on the outcome. It was verified the behavior of the relationship between independent and dependent variables. The factors which can be regarded as controlled variable were steel ball, oscillation times the angle of each swing and the height when the steel ball was released. An answer from wiki (2009) the definition of experimental variables is the variable whose values are independent of changes in the values of other variables. Experimental variable in this experiment is the length of string.According to dictionary the error can be defined as a deviation from accuracy or correctness. And the uncertainty means that the lack of certainty, a state of having limited knowledge so that it is impossible to exactly describe existing phenomenon or future outcome confidently.Errors were caused by any individual who could be affected by many factors. Such as before we measure the length of string, we need to measure the radius of ball by vernier caliper in case the string is shorter than actual length. Secondly, we need to take care of how much oscillation times we did. Thirdly, we need to keep the pendulum swing in a same surface in case the extra energy was wasted. At last, taking more time measurements of experimental variable which is length of string may be more accurate average for each trial.Find two point from the graph A(x1, y1) B(x2, y2), use the formula(y2-y1)/(x2-x1) the result of gradient is 4.03.The table shows the results of free fall accelerationGradient(T 2/L)4.03Calculate data in using formulaG9.79ms-2Confines of Error0.22%Table2-1To summarize the weakness that is error and uncertainty and calculating the acceleration of gravity to within 5%, and table 2-1 shows that the experiment obeys the allowable confines. Confines of Error were calculated by the difference between actual gravity and what I got, and the values were divided by the actual values.ConclusionTo sum up, the calculation of Galileo that free fall acceleration from the formula, this can infer the result of free fall acceleration. I need to compare the calculation of Galileo which free fall acceleration should be 9.81ms-2. In fact, a gravity pendulum is a complex machine, depending on a number of variables for which we are ready to adjust.In addition, firstly we try to understand the method that Galileo did in 1600s, and making a plan to have a complete the system. Then form the data I found some different values some gravity, and the factor to influence the values. Th e main factor is that the different length of string influence the period instead free fall acceleration, the period square and length have a constant ratio to calculated the acceleration.Turning to Dohrman, P (2009) it can be argued that the factors which influence the fact are length of the string, period of each cycle by using those two factors we can get the local gravity. All above those factors can influence the values of free fall acceleration, and we got the less number than actual values. I need to take care of them and have an improvement. For instance, first difficulty is that measuring the length is deciding where the centre of the bob is. The uncertainty in determining this measurement is probably about 1 mm. Secondly, the stopwatch measures to 50 of oscillation although the overall accuracy of the time measurements may be not certain. According toDohrman (2009) the human reaction time to lead off and stop the watch has a maximum range of 0.13 seconds and the average i s0.7. Finally, 9.79ms-2 was calculated by the gradient and the formula in part of result.