Experiment of Hookes Law

Experiment of Hookes LawInvestigating Hookes LawAimThis experiment is aimed to investigate the relationship amidst the cud that is world slotted at the cobblers last of outflow and the eon interpreted for the spring to make a 20 comp permite oscillations.HypothesisAs the chaw of the end of the spring increases, the time period for the spring to complete 20 oscillation forget also increase. This is because in newtons second law which is F = ma, if the acceleration is being derived with the presence of time in its formula, it will be F = m(v-u)/t. Which proves that, mass is instantly proportional to time. As the mass increases, the time will also increase.VariablesIndependent variable Mass that is being slotted at the end of the spring (kg)Dependent variable Time period taken by the spring to make 20 complete oscillations (s)Controlled variable i) Spring constantii) Gravitational accelerationiii) Length of springiv) Amount of spring oscillationsv) Air resistancevi) amplitud e of oscillationsControlling the variablesMass that is being slotted at the end of the springThe mass that is being slotted at the end of the spring is manipulated from 0.1kg, 0.2kg, 0.3kg, 0.4kg and 0.5kg.Time period taken by the spring to make 20 complete oscillationsWith the aid of digital stop watch, the time period is taken when the spring had completed in making 20 oscillations. This operation is repeated 3 times and an average reading is taken.Spring constantThe spring constant is kept constant so that the results are relative to severally other. It will be controlled by using the same spring throughout the whole experiment.Gravitational accelerationThe gravitational acceleration is kept constant by conducting the experiment in the same place until the end.Amount of spring oscillationsThe amount of oscillations is controlled to 20 so that the results are more accurate. The exact results will be dual-lane by 20 afterwards.Air resistanceDue to the place that the experiment i s being conducted in a room, the fan and the air conditi angiotensin converting enzymer are switched off to veer the air resistance. The experiment is conducted in the same place until the end to fix the air resistance.Amplitude of oscillationsThe amplitude will be controlled each time the mass is increased by using the same length in extending the spring to make is bulk large. For each trial, the spring is extended 5cm consumewards. This procedure will be support by a meter ruler.Materials listRetort standClamp and standMeter rulerMass holderSlotted massDigital stopwatchSpringDiagramMethodSet up the apparatus as shown in the diagram, with one end of the spring attached to the horizontal support on the clamp stand.Attach the slotted mass of 0.1kg at the end of the spring.Put the meter ruler next to spring and mea genuine the extension.Pull the slotted mass holder down to 5cm and then release it.Let it oscillates for 20 times. Take the time taken for the spring to oscillate compl etely for 20 times using digital stopwatch. double up step 4 to 6 ii more times.Record the information each time and take an average reading.Repeat step 2 to 7 by using different slotted mass, from 0.2kg, 0.3kg, 0.4kg, and 0.5kg.ResultsData presentationA graph to show the relationship between the mass that is being slotted at the end of the spring, M, and the time taken for one oscillation, T.Data analysisThe relationship between mass that is being slotted at the end of the spring and the time taken for spring to oscillate one cycle appears to be non-linear. The data therefore will be processed in order to find a relationship between this two variables either it is directly proportional or not. The graph is parabolic. Hence the T potful be manipulated to become T2 so that the graph smoke be plot with a variable of mass against T2.Data processingTable 2 Mass that is being slotted at the end of spring, M, and square up of time taken for one oscillation, T2Presentation and analys is of the processed dataA graph shows the relationship between the mass that is being slotted at the end of the spring, M, and the form of time taken for one oscillation,T2.Analysis of the graphGradient of best fit line = 0.50/0.32 = 1.56 kgs-2Gradient of steepest line = 0.50/0.30 = 1.67 kgs-2Gradient of shallowest line = 0.42/0.34 = 1.24 kgs-2For the second graph, it was proved that mass that is being slotted at the end of spring is direclty proportional to the squared of time period.Mathematically, m T2After the investigation and the experiment that had been done, it was found that the formula relating the mass that is being slotted at the end of spring and time period of an oscillating spring is We know that T = 2/Where = k(constant) in this investigation.Therefore,T = 2T2 = Which is of the form,y = mx + c (equation of true(a) line)From the investigation, y is m, m is 42/k and x is T2.The gradient of the line is therefore equal to 42/k , we can now find the spring constantTh erefore, k on the best fit line 1.56 = 1/ = 1/1.56 k = 61.59 Nm-1The range of uncertainty in this value can be calculated using both the maximum and the minimum lines on the graph.Maximum gradient 1.67 = 1/ = 1/1.67 k = 65.93 Nm-1 token(prenominal) gradient 1.24 = 1/ = 1/1.24 k = 48.96 Nm-1Therefore the spring constant, k is in the range of 48.96 Nm-1 to 65.59 Nm-1.ConclusionThe aim of this experiment is to investigate the relationship between the mass that is being slotted at the end of spring and time period of oscillation. As the hypothesis being made earlier that mass would be directly proportional to time period of oscillation, it is clearly was wrong as the graph of mass against time period is obviously non-linear. The second graph of mass against squared of time period is however turned out to be linear and therefore it can be concluded that mass is directly proportional to the squared of time period.After the investigation, this conclusion is supported as the equation for ti me period of an oscillating spring isT = 2T2 = So, T2 mThe gradient of straight line was then used to calculate the spring constant, k, for the spring used in this experiment. This is because the gradient is equal to 1/The value can be compared to the supposed value by using Hookes so as to verify the result whether it is plausible or not. When the spring is acted a force of 1N, the extension was seen to be 1.6cm. The spring constant can be determine by using the formula of Hookes lawF = kxk = 1/0.016k = 62.5 Nm-1 compute percentage deviation x 100% = 1.5%The real value and the theoretical value is not that far and only 1.5% in the percentage deviation. In conclusion, it can be said that this experiment is successful and the results are accurate.EvaluationThe method and apparatus used worked well throughout the whole experiment. The results obtained are differ from the actual results. This is because they are maybe some mistakes were made during winning the reading or making th e experiment works. There are some improvements that were made when collecting the data that were not stated in the original plan.Parallax error occurs when reading the ruler which the recorders eye level is not perfectly perpendicular to the ruler.The slotted mass were considered to be the same. Just one of the slotted mass was weighted and for one slotted mass the mass is 0.1kg. Without hesitation, the other slotted mass were all considered to be 0.1kg in mass too. This may have produced a systematic error, depending on how accurate the masses were and consistency of their inaccuracy.When lighter slotted mass were used, the oscillations was so fast. Random errors can occur. Suggested that, the spring should be let to oscillation more so that the results will be more precise.Suggested improvementsThe investigation could has been more accurate and precise if the following modifications were to be takenMake sure that the eye is perpendicular to the ruler when taking the reading when doing the extension of spring. This will avoid parallax error.Use another ruler to point at the ruler when taking the reading. This will aid to read the meter ruler easier and more precise. This will avoid parallax error.To make the time taken more accurate, use ultra-sonic motion sensor that is placed below the oscillating spring. The ultra-sonic motion detector will collect data more precisely because it does not involve the human interaction which is moved(p) by human reaction.Take more reading and take the average as the lesser the reading are taken, it will create more haphazard errors.