Homework Help: Work energy theorem and gravitational potential energy

Miike012 · Nov 10, 2011

In my book it is talking about conservation forces and work energy theorem.

In the book it said....
"suppose gravitational potential energy alone does work (constant force)

*Then Wnet = Wg ......... ending statement Ef = Ei....

My question.... Does the work energy theorem only deal with conservation forces??? Because why would they say if this is the only force (being a conservation force) then it equals Wnet...?

PhanthomJay · Nov 10, 2011

Miike012 said: ↑

In my book it is talking about conservation forces and work energy theorem.

In the book it said....
"suppose gravitational potential energy alone does work (constant force)

*Then Wnet = Wg ......... ending statement Ef = Ei....

My question.... Does the work energy theorem only deal with conservation forces??? Because why would they say if this is the only force (being a conservation force) then it equals Wnet...?

On the contrary, the work-energy theorem states that
W_net = W_c +W_nc = KE_final - KE_initial

If gravity alone is the only force doing work, then W_nc = 0, and the equation for that special case boils down to
W_net = W_g = KE_final - KE_initial. Watch signage.

Miike012 · Nov 10, 2011

thank you,.

Miike012 · Nov 10, 2011

Another Question:
Correct me if I am wrong... conservation of energy states that energy of a system is conserved.. thus the gain i Kinetic energy is equal to the loss in potential energy of all the forces acting on the body....

Question... in general non conservation forces ( like friction ) cause a non constant kinetic energy, and this loss or gain in Kinetic energy can not be gained by non conservation forces as potential energy because potential energy is not associated with non conservation forces.. thus energy through out the system is not conserved... Is this a correct statement????
Thank you.

Rome_Leader · Nov 11, 2011

Assuming there are no other sources of loss (e.g. sound, temperature change, etc.) which is an idealized but very common situation when working out problems. If we are using your initial problem where only gravitational potential is concerned, then yes, what you gain in kinetic as you fall will be reflected in an equal loss of gravtiational potential (reflected in the change of height).

For question two, there are other ways you can gain energy, as I've mentioned above. Heat, sound, etc. But no, conservation of energy for the system does not strictly apply in this sense, because there are losses from system to surroundings due to friction and other possible changes.

PhanthomJay · Nov 11, 2011

Energy can neither be created nor destroyed, only transformed to different types of energy.

Since W_nc = ΔKE + ΔPE, then when only conservative forces, such as gravity and ideal springs, do work,
W_nc = 0, and therefore,

ΔKE + ΔPE = 0.

This is the conservation of mechanical energy equation, which, when only conservative forces act and there are no non-conservative forces acting that do work, tells us that in such a system the energy is always constant...it is neither lost nor gained, but transformed from one type to the other, whether the system is isolated (a closed system) from its surroundings or an open system (un-isolated from its surroundings).

When non-conservative forces, like friction or applied forces, act and do work, then the change in mechanical energy is not 0, and energy is apparently lost or gained to or from its surroundings (open system). It should follow, therefore, knowing that energy cannot be destroyed, that the work done by nonconservative forces can be represented as
-ΔE₀, where ΔE₀ is the other energy (heat, sound, chemical, etc.) transferred out of or into the system. This can be also looked at as a closed system, where
ΔKE + ΔPE + ΔE₀ = 0,
the total conservation of energy equation, where again energy of a system is always a constant, but transformed to different forms.