# Work Energy Theorem (WET)

1. Oct 10, 2008

### Phan

Technically, I don't really have a problem specifically that I need help on solving, but there is a crucial concept that I cannot grasp about the WET, and until I can do so, most WET problems are a pain to me.

My professor gave us two types of formulas for the work energy theorem, stating that there are more and each will get progressively better and designed for use on more situations. The first one we got, and the one most highschool students receive, is:

W = delta (K),
where W is work and the RHS is the change in kinetic energy.

The second equation is:
Wnc = (delta K) + (delta Ug) + (delta Us),
where Wnc is non conservative work, Ug is gravitational work, and Us is spring work.

Since the professor really only gave one example for each theorem, I decided to take the liberty and try several more textbook questions. From what I have found out, the first theorem could be used for almost any of the problems that I encountered, as I could keep putting in different forces:

ex. Delta K = Wg + Ws + Wa

From my understanding, the work for the first equation means conservative work, which I suppose means that work with a constant force. The thing is, the individual values of W that I have used in various equations are non-conservative at times, such as the work of a spring.
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If this is the case, why is the second equation used for situations where there is no friction (my professor did an example like that in class)? Furthermore, how does one use the second theorem? This is a question that my professor has given:

A 100kg car goes up a 10deegree hill at a constant a. Starts at 10m/s, travels 2km, the final speed is 2.5m/s. There is slipping, creating a frictional energy of 2120kG, what is the energy expended by the car?
.

What was done was that the Wnc (or LHS) was set to Wapp - Wfric, both of which are non-conservative forces. So, if this is the case, why is the general equation not set so that the Spring Force (Us) is taken out and included on the Wnc side?

I believe that my hopelessness is a result of my weak physics background, and I am thus confused by these two equations in general. When should I use theorem #1 or theorem#2, and how do they differ specifically?

Finally, a non-conservative force is one in which the start and end point doesn't matter or is not path dependent (ala force is constant), whereas a conservative force is one in which the path taken is taken into account (force is variable)? I am not sure if I am correct about these two ideas, since they seem critical to the understanding of the theorems stated earlier.

It is Thanksgiving Weekend and my professor has gone home, I didn't intend to ask him about these concepts since I thought I could grasp them after re-reading my notes, but 2hours of various problems and internet searching has not helped at all. Any help here would be appreciated D:

PS. For whoever that answered my Bosun question, I appreciate your help. I'm too lazy to dig up the thread and reply to it, so know that I genuinely benefited from your post :D

2. Oct 10, 2008

### Staff: Mentor

A few tips...

As long as you include the total work done on the particle due to all forces acting on it, this will apply. The forces don't have to be conservative. (This equation is generally called the "work-energy theorem".)

This is a variation of conservation of energy. If there is no non-conservative work, then the LHS is zero and mechanical energy--the sum of the three energy terms on the RHS--is conserved.

If I understand what you are saying, I agree. (This is similar to my comment above.)

No, on two counts: (1) As I already stated, the forces do not have to be conservative; (2) conservative does not mean "constant".

A non-conservative force is a dissipative force such as sliding friction or an applied force such as someone pushing on a box.
Spring force is a conservative force.

When there is no friction--or other non-conservative force--then the second equation is just plain old conservation of mechanical energy.

Two reasons: (1) Spring force is a conservative force, as I already stated; (2) There are no springs in this problem!
The work done by a conservative force only depends on the end points and not on the path taken. For example, no matter how you move a mass from a to b, the work done by gravity is the same. But the work done by a non-conservative force--like friction--does depend on the path.

3. Oct 10, 2008

### Phan

Ok... so a conservative force is something like Gravity in which case it can 'store' energy, like potential gravitational energy?
A conservative force is one that cannot 'store' energy, similar to when you are pushing something against friction the kinetic energy is lost to it? If so, where does the kinetic energy go if it is used up and not stored?

And in general, usually frictional forces are non conservative and gravitational and electric forces are conservative?

4. Oct 11, 2008

### Staff: Mentor

Yes.
You meant non-conservative force here. The energy "lost" in work done by a non-conservative force is not really lost, just transformed into to other forms such as thermal energy (for the most part). You start out with a certain amount of macroscopic mechanical energy (gravitational, kinetic, spring) and some ends up as thermal energy due to friction.
Yes.