Elasticity Experiment: Application of Hookes Law

Elasticity Experiment Application of Hookes LawNguyen Manh TriInvestigation of snapshot ledger entryGeneral statementAny string that able to stretch and come back its original length can be considered as a alternate. from to each unrivalled one spring has constant of resilient bandity (stiffness) that depends on its material. A simple spring generally is made from metal.BackgroundElastic pull step ups of the springs appear at the ends of the springs and material solvent on the affect or association with it as it is deformed (Elert, 1998). The direction of elastic personnel department counters the direction of the external force causing deformation. Specifically, when stretched, the elastic force of the spring towards the axis of the spring on the inside even when compressed, the elastic force of the spring axis oriented outwards.The most popular law of catch is Hookes law. When a force is applied to an elastic object, the object will be stretched. A win over in length l is formed. In the elastic limit, the magnitude of the elastic force of the spring is proportional to the deformation of the spring. Hookes law can be expressed as = k ()where k is a constant nourish which fates the stiffness of the object (Belenki, Salaev and Sulemanov, 1988). The k value has unit of newton per meter.A spring of length l1 is hung up by a support as shown in figure 1. If a mass is applied to the other end the spring, the spring will be stretched, resilient until all the energy is bypast and form a new length l2. Then the system is balanced, the applied force, the weight of the mass, must equal the substituteoring forceMg = k(l2 l1) = kl prefigure 1Mathematically, Mg = k can be written asl = 1.0Equation 1.0 also can be performed as a analog equation (Treloar and Dunn, 1974)y = mxwhere y is l and x is M.Then if we hang more and more weights for the spring and measure the length l for each, the slope of the graph is (Bbc.co.uk, 2014). Consequently, we can find t he constant value k by calculating the gradient.For rubber or steel wire rope elastic force only when external forces are stretched. In this case the elastic force is called tension. Tension set point and direction like elastic force of the spring. For the contact surface is deformed when pressed against each other, with the elastic force perpendicular to the contact surface.AimsTo determine the constant of elasticity of several contrasting springsTo find out the elastic limit.HypothesisThere are number of factors which affect the springs constant. One of these factors is the types of material, which makes the stiffness of springs different. Hookes law is accurate with simple objects such(prenominal) as springs. With material such as rubber or plastics, the dependence between the elastic forces in the deformation could more complicate (Belenki, Salaev and Sulemanov, 1988).In essence, the elastic interaction forces between molecules or atoms, i.e. the electromagnetic force between e lectrons and protons inside the elastic material.When the large deformation to a certain value, the elastic force does not appear again, and this value is called the elastic limit, if you exceed the time limit elastic deformation material will not be able to return original shape after contact not deform more. cipher 2 Elastic limitMethod and MaterialsFigure 3 Experimental set-upMethodThe experiment was set up as shown in figure 3.The retort stand was placed firmly on the table.A spring was attached to the retort stand.The length of the spring (l1) in rest state was measurable (using ruler) and recorded.The mass hanger (10 grams) was hung up the other end of the spring.New length of the spring (after applied the mass hanger) was measured (using ruler) and recorded. The change of length of the spring was calculated and recorded. One set of data was obtained afterwards.A weight was placed on the mass hanger.New length of the spring (after applied the weight) was measured (using rule r) and recorded. The change of length of the spring was calculated and recorded. Another set of data was obtained afterwards.Another weight was placed (20 grams total) and step 8 was then tell.Step 9 was repeated until no weight left. 8 other sets of data were obtained afterwards.Steps 3 to 10 were repeated for the new springs (the remaining 2 springs). Finally, 30 sets of data were obtained (10 sets each spring).ResultsTable 1 First spring resultsl1 for the jump spring = 13 mmM (g)l2 (mm)l = l2 l1 (mm)10141201633018540207502186024117025128025129028151003118Table 2 Second spring resultsl1 for the first spring = 20 mmM (g)l2 (mm)l = l2 l1 (mm)10200202003022240244502886032127035158039199042221004626Table 3 Third spring resultsl1 for the first spring = 20 mmM (g)l2 (mm)l = l2 l1 (mm)1020020200302004022250244602777032128034149038181004020Figure 4 Change of length against mass for the first springFigure 5 Change of length against mass for the second springFigure 6 Change of length against mass for the third springAs shown in figure 4, 5, and 6 three straight lines are formed and show a bm that the weight increases with increasing l.DiscussionCalculation Results from part 1 experimentFrom figure 4,y = 0.1834x 1therefore,gradient (m1) = 0.1834 mm/gFrom figure 5,y = 0.3062x 6therefore,gradient (m2) = 0.3062 mm/gFrom figure 6,y = 0.2774x 8therefore,gradient (m3) = 0.2774 mm/gSince the spring constants are measured bygradient (m) = therefore,k = We also have g = 9.81 (ms-2),k1 = = = 53.50 mmgs-2k2 = = = 32.04 mmgs-2k3 = = = 35.36 mmgs-2Results analysisBecause of above factors, some points such as (10 0) from figure 5 and (10 0), (20 0) from figure 6 are not involved in the trend line. The bantamest share of the ruler is 1mm so it is unable to distinguish the l between 0 gram and 10, 20 grams. Parallax break also is a cause of these irrelevant points. Because of the very first l are too small, scathe cant overs between eyes and ruler may cause the errors of these points.Y-intercepts for 3 springs are -1, -6 and -8 respectively. The y-intercept -1 is a very small value and is able to show the accuracy of the experiment. The others two are much bigger because of different constant k values of springs (53.50, 32.04 and 35.36 respectively). For the first spring, which has k value are 53.50, it is much easier to distinguish different l values for the first weights. Consequently, there is no strange point is recorded for this spring, all the points involves in the trend line. For the last two springs, k values are almost half of the first one and it hard to distinguish l values for the first weights. This is the reason why strange points are recorded and do not involve in the trend lines. Consequently, the trend lines of these springs tend to go far away the origins when pass the y-axis.Errors analysis and other factors affecting the experimentParallax errorParallax error is the most popular error in physics (Aphysicsteacher.blogspot.co. uk, 2009). Because this experiment contain many small values (smaller than mm), so parallax error may cause many wrong data and strange points. The concept of parallax error is related to the term parallax. For instance, in figure 7, different positions of eyes result in 3 values for the measurement (two of them are wrong values).Soparallax is the change in the apparent position of an object when the position of the observer changes.Figure 7 Example for parallax errorConsequently, the accuracy of the measurement depends on the angle between eyes and ruler. Because of this error, l values are slightly greater or smaller and results in slightly change of k values. To minimize this error, a pointer can be apply to help read the scale on the ruler and the scale had to be viewed at eye level (Cyberphysics.co.uk, 2014).TemperatureMaterials caloric expansion coefficient and stiffness are connected. This connection is mathematically formulated as = where the G is a constant value (0.4 G is a constant value so if temperature is increased, density increases and stiffness increases if temperature decreased, density decreases and stiffness decreases.Accuracy of rulerThe smallest share of plastic ruler is 1mm. As mentioned above, there are many small values so it is necessary to consider the error percentage caused by accuracy of ruler.ImprovementTo minimize parallax error, a pointer can be used to help read the scale on the ruler and the scale had to be viewed at eye level (Cyberphysics.co.uk, 2014).To minimize temperature error, the air temperature should be held on specimen (room temperature 298K).To minimize accuracy of ruler error, an instrument which has small length accurately should be used (Mohindroo, 2006). The accuracy of the result can be greatly improved. endThe constant of elasticity of 3 springs are 53.50, 32.04 and 35.36 respectively by calculating as mentioned above. Summarizing the three points, this experiment has met the objectives stated in the introduction. Knowledge about elasticity and constant of elasticity has learnt through this study.It is unable to find out the elastic limits because if keep adding weights until the springs can stretch more, the springs will be damaged and will not be able to come back its original shapes (Sadd, 2005).There are some factors are mentioned above, which are affect the results of this experiment. These factors do not change the results significantly (strange points were recorded only for the very first weights).ReferenceBbc.co.uk, (2014). BBC GCSE Bitesize Hookes Law. online Available at http//www.bbc.co.uk/schools/gcsebitesize/science/add_aqa/forces/forceselasticityrev2.shtml Accessed 26 Mar. 2015.Belenki, G., Salaev, . and Sulemanov, R. (1988). Deformation effects in layer crystals. Sov. Phys. Usp., 31(5), pp.434-455.Cyberphysics.co.uk, (2014). Hookes Law. online Available at http//www.cyberphysics.co.uk/topics/forces/hooke.htm Accessed 26 Mar. 2015.Elert, G. (1998). Elasticity T he Physics Hypertextbook. online Physics.info. Available at http//physics.info/elasticity/ Accessed 29 Mar. 2015.Mohindroo, K.K. (2006). +2 Practical Physics Vol. II Fifth Revised Edition. New Delhi Pitambar Publishing.Sadd, M. (2005). Elasticity. capital of The Netherlands Elsevier Butterworth Heinemann.Treloar, L. and Dunn, A. (1974). Rubber and rubber elasticity. New York Wiley.