potential/kinetic energy and Work

[muchomaas]

I recently got a problem wrong on a practice test because I failed to remember that Work=delta_KE. So if you lift a book from the ground and put it on a table, no work is done since the kinetic energy change is 0. While this in itself seems like a silly way to define something called work, I'll accept it.

Now (I'm actually studying for a physics final) when you are looking at the work done, say, to move a charge from one point in a non-uniform electric field to another, you define the work as the change in POTENTIAL energy. What's up with that? When is work defined by potential, rather than kinetic energy? Does it have something to do with conservative vs nonconservative forces?

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[Bernoull]

I recently got a problem wrong on a practice test because I failed to remember that Work=delta_KE. So if you lift a book from the ground and put it on a table, no work is done since the kinetic energy change is 0. While this in itself seems like a silly way to define something called work, I'll accept it.

Now (I'm actually studying for a physics final) when you are looking at the work done, say, to move a charge from one point in a non-uniform electric field to another, you define the work as the change in POTENTIAL energy. What's up with that? When is work defined by potential, rather than kinetic energy? Does it have something to do with conservative vs nonconservative forces?

The concept ur alluding to is work-Energy theorem which is LIMITED to SPECIFIC SITUATIONS.

There's 2 ways to change the energy of something, work and heat. dE=dW+dQ. Both Heat & Work are mechanisms for energy transfers. Heat is da natural process of transferring energy from a warmer body to a colder one. If there's no Heat, the only possilibility to transfer energy is work.

dW =dK+dP+dEi where dK is change in kinetic energy, dP is change in potential energy and dEi is change in internal energy. Ei changes with frictional forces, therefore if an energy transfer DOESN'T involve heat or friction, u have

dW=dP + dK or change in mechanical energy. Now when the energy change does not involve heat, friction or dP, THEN & ONLY THEN does the work-energy theorem apply which states dW =dK,
I hope u appreciate how limited this theorem is and consequently how limited its utility is also.

With this background info, to directly answer ur question, (when there's no heat or friction), work changes with both dP and dK so you must consider BOTH.

Also work is the dot product of force and displacement, W=FdcosQ, and the reason why vertically raising a book involves 0J of work is bcos Q=0 and cos0=0, this is purely vector mathematics and is not intuitive bcos OBVIOUSLY u expend energy to raise a book..