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Sections 10.3-10.8

Not all forces can lead to potential energy. Potential energy can be extracted so it must be that when the objects come back to their initial position, the change in potential energy is zero.

In terms of work this require that the work done on a closed path is zero.

Only two forces satisfy this criteria in Phys 211 and they are called conservative forces.

Gravity with potential U_G =mgy
Spring force with potential U_{Sp} = \frac12 k\left(\Delta s\right)^2

Tension and thrust force will always do work while kinetic (or rolling) friction will always lead to thermal energy increase. Finally the normal force and static friction never transfer energy.

The full energy principle is then

\Delta E_{sys} = \Delta K + \Delta U + \Delta E_{th} = W_{ext}

K_i + U_{G,i} + U_{Sp,i} + W_{ext} = K_f + U_{G,f} + U_{Sp,f} + \Delta E_{th}

Note that W_{ext} is from external forces only. Kinetic friction should always be internal and contribute to \Delta E_{th} which we never write as an initial and final since we do not have the tools yet to quantify the amount of thermal energy in an object (see Phys 213).

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