Elastic Potential Energy
Section: Deformation of Solids | Syllabus: Cambridge AS Level Physics 9702
6.5 Elastic Potential Energy (E_P) Work is done to stretch/compress a material. This work is stored as elastic potential energy. Work Done = Area under Force-Extension Graph Figure 6.17: Work Done as Area (Force-Extension graph showing the area under the line (triangle for elastic) represents Work Done.) Within Limit of Proportionality E_P = fractionFx = fractionkx^2 Worked Example: Archer's Bow Question: Force 60.0 N, Extension 0.119 m.
Calculate Energy. Answer k = 60/0.119 = 504 ext N m^-1. E_P = fractionkx^2 = 0.5 × 504 × (0.119)^2 = 3.57 J. Plastic Deformation & Energy If the material deforms plastically, the work done is still the area under the graph, but it's not just a simple triangle.
Figure 6.19: Plastic Work Done (Graph showing loading curve going non-linear. Area under the whole curve is total work done.) Assignment 6.1: Rubber Band Hysteresis Rubber does not obey Hooke's Law. The loading and unloading curves are different.
Figure 6.24: Hysteresis Loop (Extension-Force graph showing loop. Area between curves = Thermal energy dissipated (heat).)
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