HOOKE'S LAW AND TREES

Abstract

Are the mathematical relationships that occur for springs, determined by Hooke (Bellis 2006) applicable to tree branches? Springs store and release energy with every extension and release. In a similar fashion, energy is stored and released in tree branches each time weights are added and removed, or when a tree branch is set into oscillation. This paper proves that the well known physics equations used to describe springs can be applied to tree branches as well. Their stiffness, "k", can be determined using a "Hookian- method. Likewise the stiffness of the branch,"k", can also be determined using an oscillation method, which is often used for springs as well, to determine "k". The value "k- was determined using two different methods on each tree branch. Fifty Pinus strobus branches were tested. The statistical results showed a powerful alignment with the concept that mathematical equations used to describe the stiffness of springs can be applied to tree branches as well. It was also evident that the quality of the results depends on a relationship between the range of the weight set used with the weight of the branches tested. In other words, any one set of weights must be matched with a set of branches that will demonstrate a result which can be quantified, but yet does not go beyond the elastic limits of the branch. By the same token, the results must be measurable. The data collected in this research can be expanded upon by testing to see if the physics equations used for tree branches can be then applied to tree trunks, which in turn would allow scientists to examine deflections in trees during wind storms. As a result determinations about the stiffness of trees based on the oscillation method could be determined in a nondestructive way.