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.)

E_P = (1/2)Fx = (1/2)kx^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 = (1/2)kx^2 = 0.5 × 504 × (0.119)^2 = 3.57 J.

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.)

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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