Hooke's Law

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,
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