# Spring Constant Lab

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Physics 221 ------------------------------------------------- Spring Constant Lab ------------------------------------------------- Group #6 November 12, 2013 Han Obi Tim Zach Nicholas I. Purpose The purpose of this lab was to study the relationship between the force acting on the spring scale and the change in the length, the displacement, of the of the spring scale due to the increasing weights upon said spring. Through careful analysis of data and graphs, which depicted the force vs. position of hanging masses, allowed for the slope of the spring constant to be calculated. II. Description and Theories A. Principles and Theories Used to Obtain our Result An conventional spring, when subjected the weight (w=mg) of an object at one of its terminations, will displace a certain distance, x, with an equal and opposite force, F, being created in the spring of which opposes the pull of the weight. This conventional spring will become significantly distorted if it is subjected to a large enough weight and the force, F, will only be able to return the spring to its original configuration once the burden is removed. The force that will restore the spring to its original configuration is directly proportional to the displacement that occurred. The following equation represents this relationship where k denotes the spring constant or stiffness of the spring, F=-kx Since x symbolizes the displacement or change in the length of the spring the above equation can now be surmised in the following manner, F=mg=-k∆l This new form makes it evident that a linear proportion exists between the plot of F as function of changing in length, ∆, thus confirming the spring does in fact obey Hooke’s Law. This enabled the group to determine the spring constant k. B. Derivation of Equations Definitions To gain a better understanding of the terms used here