How Do Work-Energy Principles Apply When Potential Energy Changes?

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The work-energy principles state that Wnet equals the change in kinetic energy (ΔK) and Wnc represents the work done by non-conservative forces, which is related to the change in total mechanical energy (ΔE). Equation (1) is valid as long as all forces are accounted for, even when potential energy changes. However, Wnc is not always smaller than Wnet, and it is incorrect to assume Wnc is zero when Wnet is zero. An example illustrates this: a block sliding down an incline at constant speed experiences net work of zero due to friction, which is a non-conservative force that does work. Understanding these principles is crucial for analyzing systems where potential energy varies.
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(1) Wnet = ΔK
(2) Wnc = ΔE

1. Is equation (1) always correct even if the potential energy of the object is also changing? A
2. Is equation (2) always going to have a small value than Wnet? And is Wnc always 0 if Wnet is zero?
 
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henry3369 said:
1. Is equation (1) always correct even if the potential energy of the object is also changing?
Yes, as long as you include the work done by ALL forces acting. This is the so-called "work-energy" theorem. (There are some subtleties, which I won't confuse you with.)

henry3369 said:
2. Is equation (2) always going to have a small value than Wnet?
No.

henry3369 said:
And is Wnc always 0 if Wnet is zero?
No.

Example: Imagine a block sliding down an incline at constant speed. (Friction is obviously acting.) The net work including all forces will be zero. But the work done by friction (the non-conservative force in this example) will not be zero.
 

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