Conservation of Energy Equation

[oneplusone]

In an AP Physics C course for mechanics, what other variables are usually added to this equation? :U_g+U_{sp}+K+W_{nc} = U_g+KAlso, why is a spring's potential energy only on the left hand side? Would it ever go on the right hand side? (final).

 

[mikeph]

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.

 

[stevendaryl]

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


U_g+U_{sp}+K+W_{nc} = U_g+K


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, E_0 will be:

E_0 = U_{g,0} + K_0

where U_{g,0} is its gravitational potential energy, and K_0 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, U_{sp}. The gravitational potential energy U_{g} will change, and the kinetic energy K will change. There will also be energy lost due to friction (heating the spring), W_{nc}. By conservation of energy, the change in total energy of the mass + spring must all go into the non-conservative work W_{nc}. So if we let E_1 be the total energy after compressing the spring a little, then

E_1 + W_{nc} = E_0

where

E_1 = K_1 + U_{g,1} + U_{sp, 1}

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

K_1 + U_{g,1} + U_{sp,1} + W_{nc} = K_0 + U_{g,0}