A uniform rod of length / is acted upon by a force F in a gravity-free region, as shown in the figure. If the area of cross-section of the rod is A and it's Young's modulus is Y, then the elastic potential energy stored in the rod due to elongation is
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The acceleration of the rod is
So, the tension in the rod at a distance x from the free end is
The longitudinal stress developed inside the rod at a distance x from the free end is
The strain energy density (energy per unit volume) is
where dV= Adx is the volume of a small part of the rod
So the energy stored in the rod is
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