Elasticity Experiment: Application of Hookes Law

E finalicity Experiment Application of Hookes LawNguyen Manh TriInvestigation of childs playIntroductionGeneral statementAny string that competent to continue and come back its original space brook be aimed as a leakage. Each edge has eonian of malleableity ( abrasiveness) that depends on its material. A simple spring gener aloney is made from metal.BackgroundElastic push backs of the springs egress at the ends of the springs and material effect on the skin senses or railroad tie with it as it is tryed (Elert, 1998). The direction of resilient force counters the direction of the foreign force causing deformation. Specifically, when stretched, the elastic force of the spring towards the axis of the spring on the privileged even when compressed, the elastic force of the spring axis oriented outwards.The most popular fair play of snap fastener is Hookes law. When a force is utilise to an elastic object, the object depart be stretched. A change in length l is forme d. In the elastic sterilise, the order of magnitude of the elastic force of the spring is proportional to the deformation of the spring. Hookes law stack be expressed as = k ()where k is a uniform value which tapers the stiffness of the object (Belenki, Salaev and Sulemanov, 1988). The k value has social unit of newton per meter.A spring of length l1 is hung up by a bracket as appearancen in exercise 1. If a mass is utilise to the separate end the spring, the spring will be stretched, resilient until all the energy is gone and form a new length l2. in that locationfore the system is balanced, the applied force, the charge of the mass, must equal the succouroring forceMg = k(l2 l1) = klFigure 1Mathematically, Mg = k rotter be written asl = 1.0Equation 1.0 also can be performed as a linear equation (Treloar and Dunn, 1974)y = mxwhere y is l and x is M.Then if we hang more(prenominal) and more weights for the spring and measure the length l for each, the gradient of the graph is (Bbc.co.uk, 2014). Consequently, we can distinguish the constant value k by calculating the gradient.For no-account or steel wire rope elastic force only when external forces are stretched. In this case the elastic force is called tension. tightness ascertain point and direction like elastic force of the spring. For the contact surface is deformed when pressed against each other, with the elastic force rectangular to the contact surface.AimsTo determine the constant of elasticity of several different springsTo find out the elastic limit.Hypothesis at that place are number of factors which presume 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 as springs. With material such as rubber or plastics, the dependence in the midst of the elastic forces in the deformation could more complicate (Belenki, Salaev and Sulemanov, 1988).In essence, the elastic inte raction forces mingled with molecules or atoms, i.e. the electromagnetic force between electrons and protons inside the elastic material.When the large deformation to a certain value, the elastic force does non 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 impact not deform more.Figure 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 measured (using ruler) and recorded.The mass hanger (10 grams) was hung up the other end of the spring. sore 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 ma ss hanger. parvenu length of the spring (after applied the weight) was measured (using ruler) 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 past repeated.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 remain 2 springs). Finally, 30 sets of data were obtained (10 sets each spring).ResultsTable 1 starting signal spring resultsl1 for the origin spring = 13 mmM (g)l2 (mm)l = l2 l1 (mm)1014120163301854020750218602411702512802512902815 deoxycytidine monophosphate3118Table 2 Second spring resultsl1 for the original 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 C hange 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 trend that the weight increases with increasing l.DiscussionCalculation Results from dispel 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 grow g = 9.81 (ms-2),k1 = = = 53.50 mmgs-2k2 = = = 32.04 mmgs-2k3 = = = 35.36 mmgs-2Results analysisBe casing of above factors, some points such as (10 0) from figure 5 and (10 0), (20 0) from figure 6 are not entaild in the trend line. The smallest share of the ruler is 1mm so it is unable to distinguish the l between 0 gram and 10, 20 grams. Parallax illusion also is a cause of these strange points. Because of the very first l are too small, wrong angles 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 the true of the experiment. The others two are very 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 priming why strange points are recorded and do not involve in the trend lines. Consequently, the trend lines of these springs tend to go far outside the origins when pass the y-axis.Errors a nalysis and other factors affecting the experimentParallax errorParallax error is the most popular error in physics (Aphysicsteacher.blogspot.co.uk, 2009). Because this experiment pick out many small values (smaller than mm), so parallax error may cause many wrong data and strange points. The concept of parallax error is link 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 utilize to help read the outmatch on the ruler and the surmount had to be viewed at eye take aim (Cyberphysics.co.uk, 2014).TemperatureM aterials thermal expansion coefficient and stiffness are connected. This connection is mathematically hypothesise 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 direct (Cyberphysics.co.uk, 2014).To minimize temperature error, the air temperature should be held on standard (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.ConclusionThe 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). summonBbc.co.uk, (2014). BBC GCSE Bitesize Hookes Law. online purchasable 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 The 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. Amsterdam Elsevier Butterworth Heinemann.Treloar, L. and Dunn, A. (1974). Rubber and rubber elasticity. New York Wiley.