Work path dependency

Hemichordate

Peds
10+ Year Member
I know that in general, work is path dependent, but is it still dependent for a conservative force?

What are some examples of situations where work is dependent/independent of path?

kentavr

10+ Year Member
Work is path independent under conservative force. I would say it is a definition of conservative force.(http://en.wikipedia.org/wiki/Conservative_force).
Add friction to the system and good bye conservatism .

RogueUnicorn

rawr.
7+ Year Member
I know that in general, work is path dependent, but is it still dependent for a conservative force?

What are some examples of situations where work is dependent/independent of path?

dependent - PV work in some cases.

independent - gravity pulling a rock down from a certain height to a lower height

kentavr

10+ Year Member
dependent - PV work in some cases.

independent - gravity pulling a rock down from a certain height to a lower height
I would doubt that PV work is conservative. The heat transfer happens that breaks the conservative condition.

kentavr

10+ Year Member
I would doubt that PV work is conservative. The heat transfer happens that breaks the conservative condition.
Conservative force should be changing KE or PE energy. As soon as you start playing with internal energy(T) all work cannot be recovered. That's the point of 2nd termodynamic law. In other words, if work can be transfered in non recovery form(friction or heat/temperature) then it is not conservative.

RogueUnicorn

rawr.
7+ Year Member
I would doubt that PV work is conservative. The heat transfer happens that breaks the conservative condition.
yup. (the one exception i believe is adiabatic which depend only on initinal and final T/V/P)

kentavr

10+ Year Member
yup. (the one exception i believe is adiabatic which depend only on initinal and final T/V/P)
Agree. Adiabatic process is conservative. But that is the only one line in PV diagram. Step away from this line in you lost conservation.

thebillsfan

Unseasoned Veteran
10+ Year Member
5+ Year Member
i read in EK that "technically" gravity does not work, and further, that no conservative force actually does any work because the mechanical energy is conserved. that is, the sum of PE and KE is conserved. on the mcat, can we assume that gravity and other conservative forces DO perform work, and that this work is the change in KE even if the total mechanical energy doesnt change?

RogueUnicorn

rawr.
7+ Year Member
i read in EK that "technically" gravity does not work, and further, that no conservative force actually does any work because the mechanical energy is conserved. that is, the sum of PE and KE is conserved. on the mcat, can we assume that gravity and other conservative forces DO perform work, and that this work is the change in KE even if the total mechanical energy doesnt change?
i don't understand. the work part is converting the PE into KE... W=Fd

thebillsfan

Unseasoned Veteran
10+ Year Member
5+ Year Member
right but EK says that conservative forces have no change in mechanical energy. mechanical energy is PE plus KE.

so are you defining work not as change in mech energy but change in KE? on second thought, does ANYONE define is at a change in mech energy, or would that be incorrect?

RogueUnicorn

rawr.
7+ Year Member
right but EK says that conservative forces have no change in mechanical energy. mechanical energy is PE plus KE.

so are you defining work not as change in mech energy but change in KE? on second thought, does ANYONE define is at a change in mech energy, or would that be incorrect?
the work energy theorem specifically refers to kinetic energy. i mean, the whole definition of conservative force explicitly is DEFINED by no change (i.e. conserved) in mechanical energy

thebillsfan

Unseasoned Veteran
10+ Year Member
5+ Year Member
okay...so would you say then that gravity technically does zero work?

RogueUnicorn

rawr.
7+ Year Member
okay...so would you say then that gravity technically does zero work?
no gravity does work. technically or not. W=Fd.

inaccensa

10+ Year Member
Agree. Adiabatic process is conservative. But that is the only one line in PV diagram. Step away from this line in you lost conservation.

What line arer you talking about? Phase change?

kentavr

10+ Year Member
What line arer you talking about? Phase change?
No.
Adiabatic line on PV diagram for gas. When there is no heat exchange with environment. Let see does picture link works (green line there) If link doe not works, then http://en.wikipedia.org/wiki/Adiabatic_process

kentavr

10+ Year Member
right but EK says that conservative forces have no change in mechanical energy. mechanical energy is PE plus KE.

so are you defining work not as change in mech energy but change in KE? on second thought, does ANYONE define is at a change in mech energy, or would that be incorrect?
1. Work is F * dX (always)
2. Change in KE may be equal work or may not. (depends)

Now the hard part.
If force belong to the same nature as potential energy. (Gravity force in gravity field) then PE+KE=const and work of this force changes PE to KE.
However if force is outsider (space rocket fuel in gravity field) then work will change PE+KE. and d(PE+KE) = F*dS
HTH
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