Discussion in 'MCAT: Medical College Admissions Test' started by BengaliTiger, Mar 8, 2007.

1. ### BengaliTiger 7+ Year Member

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Can someone explain to me how work can be both a conservative force (which is indepedent of path) and a path function (which depends upon the pathway used to achieve any state)?

2. ### AK1kinase Newbie 7+ Year Member

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I had a similar question I asked my physics professor. His short answer was that its position dependent and not necessarily path dependent. For example, change in potential energy according to the work energy theorm constitue work. Potential energy is considered conservative because it depends only on initial and final position and is independent of pathway. Not sure if this will help but it has been noted by EK that consevative / non-conservative forces are not likely to be tested directly by the MCAT.

3. ### bigserve99 Member 10+ Year Member

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I'm not sure exactly what you mean, but

work is always path dependent!

BY DEFINITION: Work = F dot d or Fd cos(theta)

When one talks of work done against gravity for example: if you lift an object straight up at a constant velocity to height h. You have done work by imparting a force (mg) for a distance h....thereby giving you work done (mgh), which happens to equal the gain in graviational potential energy.

In the kinetic work energy theorem (assuming mass is constant): When kinetic energy is changed, a force (and hence acceleration (+ or -)) had to applied over a distance d in order to change the velocity. If this force happened to be gravity, so be it. It still does work along the F dot d or Fd cos (theta). F due to gravity just happens to always point straight down.

P delta V work is also path dependent. See heat engines for an example of this.

Regardless it is always path dependent.

EDIT: Now I understand your concern.....I think you are trying to differentiate between potential energies, which are functions of the potential energy fields (electric, gravitational etc.) from which they are derived and the work done by the force. Still work is always path dependent. The potential energies associated with an object/particle are more accurately correlated with their position in that particular energy field (gravitational, electro-magnetic). I'm sure you can consider them interchangable if you want to. But I choose not to take the chance of mis-cataloguing the energy changes. To each their own I suppose.

4. ### Mark84 5+ Year Member

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Yes that is the definition of work, but thats not exactly what he was saying. In the case of dealing with work and potential energy, the path taken to get from A to B does not matter. A ball falling from 20ft to 0ft and a ball rolling from 20ft to 0 down a hill feet both do the same amount work when dealing with potential energy.

EDIT: specified rolling down a hill

5. ### bigserve99 Member 10+ Year Member

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yah, I hear ya.

6. OP

### BengaliTiger 7+ Year Member

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I was actually reading through EK when I saw that work was a path function. It definitely makes sense (thanks y'all). I guess the reason I was confused initally was that all the PR materials I have define work to be a conservative force, which is a force that does not depend on the path but only initial and final position. Otherwise, it does not really elaborate any further.

Okay, I'll stop here, don't want to create any further confusion.

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