# Change potential energy without doing work?

1. Oct 19, 2005

### 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 havent 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 explaination/clarification, i would very much appreciate it.

2. Oct 19, 2005

### 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.

Last edited: Oct 19, 2005