Conservation of Energy Equation

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In an AP Physics C course for mechanics, what other variables are usually added to this equation? :


[tex] U_g+U_{sp}+K+W_{nc} = U_g+K [/tex]


Also, why is a spring's potential energy only on the left hand side? Would it ever go on the right hand side? (final).
 
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It entirely depends on what you want to model and what the unexplained terms mean. There is no universal equation of conservation of energy, only the principle of conservation and a manifestation of it as an equation specific to a particular situation.
 
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In an AP Physics C course for mechanics, what other variables are usually added to this equation? :


[tex] U_g+U_{sp}+K+W_{nc} = U_g+K [/tex]


Also, why is a spring's potential energy only on the left hand side? Would it ever go on the right hand side? (final).
That equation seems to be for a specific problem. It's not true in general.

If you drop a mass onto a vertical spring, then at the moment right before it hits the spring, its total energy at that moment, [itex]E_0[/itex] will be:

[itex]E_0 = U_{g,0} + K_0[/itex]

where [itex]U_{g,0}[/itex] is its gravitational potential energy, and [itex]K_0[/itex] is its kinetic energy, at that moment.

The spring will compress under the impact of the mass, and some of that energy will go into the potential energy of the spring, [itex]U_{sp}[/itex]. The gravitational potential energy [itex]U_{g}[/itex] will change, and the kinetic energy [itex]K[/itex] will change. There will also be energy lost due to friction (heating the spring), [itex]W_{nc}[/itex]. By conservation of energy, the change in total energy of the mass + spring must all go into the non-conservative work [itex]W_{nc}[/itex]. So if we let [itex]E_1[/itex] be the total energy after compressing the spring a little, then

[itex]E_1 + W_{nc} = E_0[/itex]

where

[itex]E_1 = K_1 + U_{g,1} + U_{sp, 1}[/itex]

where [itex]K_1, U_{g,1}, U_{sp,1}[/itex] are the kinetic energy, gravitational potential energy, and spring potential energy at that moment. Putting it all together:

[itex]K_1 + U_{g,1} + U_{sp,1} + W_{nc} = K_0 + U_{g,0}[/itex]
 

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