Wednesday, 26 October 2016

newtonian mechanics - Where is the energy lost in a spring?



Thinking about springs, and their extensions, I recently came to a confusion which I hope this wonderful community can help me solve.


the figures The question is this. When the block is initially attached to the spring, the spring has some extension x0. Now the spring gets extended to some extension x=mgk by an external force maintaining equilibrium at all the points such that KE=0 at the bottom.


As my reference is the line shown in the figure, the initial potential energy U is 0 due to both gravity and spring potential energy(x=0).


Now as the block comes down, the spring potential energy is: U(spring)=12kx2. Final extension is mgk. So spring potential energy is m2g22k But the decrease in gravitational potential energy is mgx which equals m2g2k.


This means that potential energy has decreased. Intitially, Unet=0 but finally Unet=m2g22k.


Where if any, did this energy get compensated(to ensure COE is still true)?




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