Theory of elasticity is a topic that keeps improving by using on many fields such as geometry, physics, chemistry and engineering. Energy density is given as some functions of curvature and torsion. If the curve of the N will be an external for the variation problem that minimizes the value of energy density; then this curve is called as relaxed elastic line. The relaxed elastic line on an oriented surface is considered as a model of DNA molecule. In this study, we worked on the second type relaxed elastic lines on the semi-dual spaces which has an important point on kinematic and Einstein's relativity theory. We also obtained boundary conditions for this type of curves. Moreover, the minimization problem of the energy which occurs with an applied force on an elastic line was discussed. Then, we researched the formed potential energy due to the applied force. Also, during the calculation of the potential energy on the elastic line, the amount of the potential energy for unit length of the elastic line was used. Afterwards, by integrating that amount, total potential energy calculated. So, we study to make a contribute both Einstein's relativity theory and kinematic.