Change potential energy without doing work?

[Willowhawk]

Change potential energy without doing work?

I'm sure this is a very elementary question, however, this is just one thing that has been confusing me in my General Physics w/ Calculus 1 class...


They say, that if you are lifting a book at a constant velocity, no work is being done. This is because the acceleration going up, and gravity constant would have to be equal for the book to be moving at a constant velocity. This by itself i understand.

however.

later on in the course, we learned that Work=(delta kenetic energy)(force)..

and -(delta potential energy)=(delta kenetic energy)

also, by increasing the height of an object, you increase its potential energy.

SO.

as the book is rising, its gaining height...at this time its gaining potential energy... if its gaining potential energy, that also means that its kinetic energy is decreasing, which would change the numbers in the work formula...

how can one change potential energy without doing any work?

again: a person raising a book vertically at a constant velocity is doing no work, yet changing the books potential energy. Potential energy is inversely related to kinetic enerby. Kinetic energy is a major variable in the work formula, thus it would have to change the value of work. If the value of work is changing here, how come the person is doing no work?


maybe i haven't made a whole lot of sense typing it out, but it's confusing the hell out of me... if anyone can decipher what I've written here and come up with an explanation/clarification, i would very much appreciate it.

 

[Galileo]

You are doing work if you lift, say, a book from a low to a higher position (You pick it off the floor and put it on the table). You are exerting a force in the direction of motion (upwards), so the work done by you is positive and this work is equal to the change in potential energy of the object.
Before and after the deed the book is at rest. The book has gained potential energy, so the total energy has increased. That's okay, since this is not a closed system. You applied the external force by lifting the book. But if the book falls off the table, only gravity is acting on it, and it will do positive work on the book, increase its kinetic energy and decrease its potential energy according to energy conservation.

 

[charng]

I can understand how this concept can be confusing. Let me try to explain it in a simpler way.

Potential energy is the energy an object has due to its position or configuration. In the case of lifting a book at a constant velocity, the book is not gaining any additional energy. Its potential energy is simply changing because of its position in relation to the Earth's gravitational field. This change in potential energy does not require any work to be done, as the book is not accelerating and its velocity is not changing.

On the other hand, when an object is lifted against the force of gravity, work is being done because the object is gaining energy due to the applied force. In this case, the potential energy of the object is increasing because work is being done to overcome the force of gravity.

In summary, changing potential energy without doing work is possible when the object is not accelerating and its position or configuration is simply changing in relation to a force field. This does not violate the work-energy theorem, as the object is not gaining any additional energy. I hope this explanation helps to clarify the concept for you.