Preparation of Aspirin: Hookes Law of Elasticity - Essay Example

? Preparation of Aspirin By Presented to June 2, Investigation of Elasti The property of a material to bend, stretch or compress and return to its original shape is the elasticity of the material. If a material restores back to its original shape and size, it is described as being more elastic. An example of this is a rubber band which is easily stretched and easily returns back to its initial position when it is released (Pickover, 2008). Another example of an elastic material is a spring. When the material is stretched, the material develops a resistance force that tends to pull back the material to its original shape and size. The resistance force is directly proportional to the amount of stretch of the material being stretched. This relationship is described by Hooke’s law of Elasticity which states that, ‘when an object such as a spring or a metal is stretched by a distance say x, the restoring force, F which is exerted by the object is directly proportional to the stretch until the material reaches the elasticity limit’ (Pickover, 2008). Elastic limit is the point at which beyond it, the material is not restored to its original shape. This relationship is indicated in equation below in which F stands for restoration force, x is the stretch length and k is the constant of proportionality. From Newton’s second, force is directly proportional to mass, i.e. , Replacing F with mg in Hooke’s law equation, the equation becomes This can be re – arranged to give Plotting a graph of extension versus mass gives a straight line whose gradient is the ratio of since g is known, which is the elasticity constant can be calculated by dividing gravitational field strength by the slope. Also, the Hooke’s law can be interpreted by the equation Whereby F is the force, K is the elastic constant and x is the extension / stretch. Plotting a graph of force against the stretch distance results in a line passing through the origin of the graph and its gradient is k, which the elasticity constant of the material. The elasticity constant of a material varies with the type of the material. In this experiment, the elasticity of various materials will be investigated by studying the extent to which they obey hook’s law (Raymond & Chris, 2011). Also, the periodic motion of a spring will be studied. Apparatus The following apparatus were used in this experiment, Metre stick mass hanger Steel spring 10 g and 100 g masses Retort stand Rubber cord Methodology One end of the rubber cord was fixed firmly onto the retort stand while the other end attached to the mass. This is as indicated in the diagram below. The relaxed length, of the rubber cord was measured with no mass attached and then determination of suitable mass ranges to be utilized in measuring the rubber cord extension was done. The masses were then successfully applied onto the rubber cord and the extension length recorded. Several masses were added successfully and the length extension measured making sure the cord is not overloaded to prevent permanent deformation. This procedure was repeated using two different springs and the resulting data were recorded in form of a table as below. Results and discussion Results for spring 1 Extension, x (m) Mass 0.0093 2 0.0225 4 0.0415 6 0.0588 8 0.0710 10 From the graph, a graph of force against extension was plotted as below. The equation of the resulting graph is . This implies that the slope of the line is 0.6538, thus the constant of elasticity, k is 9.81/0.6538=14.9088. Spring 2 results Mass Extension(m) 0 0 2 0.002644 4 0.005288 6 0.010575 8 0.013219 10 0.015863 The equation of the resulting graph is. This implies that the slope of the line is 0.0017, thus the constant of elasticity, k is 9.81/0.0017=57.7. Spring 3 Results Mass Extension 0 0.00 2 2.64 4 5.29 6 10.58 8 13.22 10 15.86 The equation of the resulting graph is This implies that the slope of the line is 1.66 and therefore It’s expected that the graph passes through the origin, but in this case, it’s not through the origin due to several errors during the process of the practical (Raymond & Chris, 2011). There are several sources of error in this experiment. Most of the errors can be detected and corrected while a small percentage are undetectable and hence it is impossible to correct such errors. The detectable errors are errors due to a spring that had been overloaded hence it lost its elasticity and hence does not obey Hooke’s law, wrong reading of the measurement i.e. reading the extension of the spring and not zeroing the scale before starting to take measurements. The undetectable errors are errors resulting from the vibrations of the building and change in temperature which affects the scales of the measuring instruments. Conclusion Comparing the spring constants of the three springs, i.e. spring 1, spring 2, and spring 3 with spring constants of 14.9088, 57. 7, 5. 90 respectively, it can be deduced that spring 2 is more elastic as compared to spring 1 and spring 3, and spring 1 is more elastic as compared to spring 3. This implies that spring 3 can support a large amount of load before exceeding the plastic limit. Spring 1 and spring 2 have a tendency of exceeding the plastic limiting and hence deforming on addition of extra masses beyond the given 10 grams. Moreover, from the resulting calculated spring constant, it can be concluded that different springs have different spring constants hence this dictates the amount of load the spring can support. From the analysis of the results and the graph, it can be concluded that the springs obey Hooke’s law and thus, the elasticity characteristics of the spring were determined. Works Cited AP Central - Hooke's Law Lab. 2013. AP Central - Hooke's Law Lab. [ONLINE] Available at:http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/39138.html. [Accessed 12 April 2013]. Dynamics - Hooke's Law Experiment. 2013. Dynamics - Hooke's Law Experiment. [ONLINE] Available at:http://batesvilleinschools.com/physics/phynet/mechanics/newton3/Labs/SpringScale.html. [Accessed 12 April 2013]. Hooke's law. 2013. Hooke's law. [ONLINE] Available at:http://webphysics.davidson.edu/applets/animator4/demo_hook.html. [Accessed 12 April 2013]. Masses & Springs - Mass, Springs, Force - PhET. 2013. Masses & Springs - Mass, Springs, Force - PhET. [ONLINE] Available at:http://phet.colorado.edu/en/simulation/mass-spring-lab. [Accessed 12 April 2013]. Pickover, C., 2008. Elasticity. In Archimedes to Hawking:Laws of Science and the Great Minds Behind Them. Nairobi: Oxford Univeesity Press. pp.4 - 14. PhysicsLAB: Springs: Hooke's Law . 2013. PhysicsLAB: Springs: Hooke's Law . [ONLINE] Available at: http://dev.physicslab.org/Document.aspx?doctype=3&filename=Dynamics_HookesLawSprings.xml. [Accessed 12 April 2013]. Physics revision | GCSE and A Level Physics Revision | Cyberphysics, the revision website. 2013. Physics revision | GCSE and A Level Physics Revision | Cyberphysics, the revision website. [ONLINE] Available at:http://www.cyberphysics.co.uk/topics/forces/hooke.htm. [Accessed 12 April 2013]. Raymond, S. & Chris, V., 2011. College Physics. 1st ed. Cengage Learning. Read More