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My textbook states the following:

$$W_{net}=W_{non−conservative}+W_{conservative}$$ $$W_{non−conservative}=ΔKE+ΔPE$$ $$W_{conservative}=−ΔPE$$ $$W_{net}=ΔKE$$

$$W=FDcos(Θ)$$

However, my teacher states that $$W=ΔE=ΔUg+ΔU_{spring}+ΔKE+ΔE_{thermal}$$

Which I think can be rewritten as: $$W=ΔPE+ΔKE+ΔE_{thermal}$$

But I'm at a loss for where to go from here.

I understand how the textbook derived it's equations but I'm failing to see how exactly my teacher came up with $W=\Delta E$

Any help is greatly appreciated.

Edit: For reference, I'm using the OpenStax textbook. The summary for the section I'm referencing can be found here: https://openstax.org/books/college-physics-ap-courses-2e/pages/7-section-summary

pldsdc
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2 Answers2

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Work is the transfer of energy from one mathematical object with an associated energy value to another mathematical object with an associated energy value. We can subdivide, group, and label each mathematical object however it's convenient.

It's no more conceptually complicated than figuring out the total transfer of water from one container or collection of containers to another container or collection of containers, or the total transfer of money from one account or collection of accounts to another account or collection of accounts, etc, etc.

It's also equally impossible to exhaustively list all the possible mathematical objects that can have energy as it is to exhaustively list all possible water containers. What if you want to know the work done by the electric field produced by blue-haired astronauts on the translational kinetic energy of three roller-skating linguists and the chemical potential energy contained in their eyeballs?

I remain at a loss as to why introductory physics textbooks present work in such a counterproductive way.

If we want to express the work done by every energy-holding mathematical object in the whole rest of the universe on every energy-holding mathematical object associated with the system under consideration (or vice-versa with oppositely signed $\Delta E$) then your instructor's simple $$W = \Delta E$$ is correct.

g s
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Basically what you do is, you consider change in potential energy is work done by something (otherwise energy cant come out of nothingness, due to law of conservation) so...

ΔP.E. = work done by gravity, or work done to gravity,

and when you take that to LHS, that gets added up with work done. Similarly for thermal energy. Basically, work energy theorem is just another way of writing conservation of energy...

Chethas Pai
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