Potential energy:

??.?? : Gravity (near earth)
1. Total mechanical energy (??=??+??=12????2+??????)
2. ??.?? : spring
Total mechanical energy for the mass-spring system is:
(??=??+??=12????2+12????2)
3. ??.?? : Gravitational (general )
Total mechanical energy
(??=??+??=12????2???????????
If several conservative forces acting on an object: ????? , ????? and ?????
????????????=?????? .?????+?????? .?????+?????? .?????
??=????+????+???? [sum all the individual ??.?? for each force]
6.9 Non-Conservative Force
If non-conservative forces act on an object, then the changes in the ????+???? of the conservative force will be equal to the work done by the friction force
???+???=??????????????????
[???? change in KE, ???? change in ????]
??1=??1+??1 , ??2=??2+??2
(??2???1)=??????????????????
12????22+??(??2)?12????12+??(??1)=???????
6.10 Force ? Potential Energy
We have seen how to calculate the ???? given a conservation force
??(??1)???(??0)=????? ??1??0.?????
We can calculate the force given the ????, assume ??0 and ??1 are related by the infinitesimal displacement ?????, then refferentainting expression for ??(??1):