# Work done in lifting a box

I am having a small misunderstanding regarding the concept of work, and I am hoping someone could clear things up for me.

I am reading Principles of Physics by Serway and Jewett, and it has an example of a person lifting a box vertically. It states that the work done by the person lifting the box is mgh, where h is the height the box is lifted, and correspondingly the work done by gravity is -mgh. Thus, the total work is 0.

From the perspective of work as energy transfered to the system, this does not make sense to me; the total work done is 0, yet we seem to have transfered energy into the system because we now have gravitational potential energy. If no work was done overall, then where has this additional energy come from?

Any responses are greatly appreciated.

Regards,
-Xaenn

nrqed
Homework Helper
Gold Member
I am having a small misunderstanding regarding the concept of work, and I am hoping someone could clear things up for me.

I am reading Principles of Physics by Serway and Jewett, and it has an example of a person lifting a box vertically. It states that the work done by the person lifting the box is mgh, where h is the height the box is lifted, and correspondingly the work done by gravity is -mgh. Thus, the total work is 0.

From the perspective of work as energy transfered to the system, this does not make sense to me; the total work done is 0, yet we seem to have transfered energy into the system because we now have gravitational potential energy.
right
If no work was done overall, then where has this additional energy come from?

Any responses are greatly appreciated.

Regards,
-Xaenn

The energy came from the person lifting the box. And it was transferred to the box/Earth system

Understood. I was thinking it was an issue of identifying the proper system, but I just wasn't being able to do so having not thought about classical mechanics for so long.

Thanks for the quick response.

russ_watters
Mentor
Yes, your issue is with defining the system. If you define the box as the system, there is work done on it. If you define the system as the box and the person, there is no net work done on the system: all the work is internal to the system.

Now I am clear on the fact that the energy came from the person lifting the box. However, I still have a bit of confusion, so perhaps someone can clarify a bit further.

Yes, your issue is with defining the system. If you define the box as the system, there is work done on it.

Letting the box be our system, we have two forces acting on it, gravity and the person lifting it up. According to the text the work done by each of these forces on the box is equal and opposite. Thus, there should be no net work, so the energy of the box should not change. This doesn't make sense, but where is the flaw in this reasoning?

jtbell
Mentor
One method of analyzing this situation is via the work-energy theorem: the change in an object's kinetic energy equals the net work done by all forces. If you lift the box at constant speed by exerting a constant force on it, then you do positive work on the box, the gravitational force does negative work on the box, the net work is zero, and the box's kinetic energy is the same before and after.

The other way is to consider that the change in an object's total energy (kinetic plus potential) equals the net work done by non-conservative forces (the forces that don't have a potential energy associated with them). In this case the gravitational force is conservative, but the force you exert is not. So, as you lift the box, the work done by non-conservative forces (you) is not zero, and as a result, the total energy of the box increases. The kinetic energy remains constant as before, but the gravitational potential energy increases.

To put it another way, you count the work done by gravity either as work or as change in gravitational potential energy, not both at once.

tiny-tim
Homework Helper
Welcome to PF!

… yet we seem to have transfered energy into the system because we now have gravitational potential energy. If no work was done overall, then where has this additional energy come from?
Now I am clear on the fact that the energy came from the person lifting the box. …

… there should be no net work, so the energy of the box should not change. This doesn't make sense, but where is the flaw in this reasoning?

Hi xaenn! Welcome to PF! I think it depends where the outside force came from.

If the box is connected to a heavy weight, over a pulley, and the person releases a brake so that the weight falls and the box rises, and then the person re-applies the brake, then I think you'd agree that the energy given to the box has come from the energy lost by the weight.

So the weight provides the outside force.

Similary, if the person simply lifts the box, the person is producing an outside force … which he can't get back!

We're so used to lifting things that we forget that there's no such thing as a free lunch … and that it's the lunch that provided the energy to move the box! Now, if the lunch was chicken … where did the chicken come from?  … you owe me lunch!

To put it another way, you count the work done by gravity either as work or as change in gravitational potential energy, not both at once.

Many thanks for your explanation. It was extremely insightful, and illuminates the fact that my problem was an incorrect notion of work. Now that you have mentioned things such as the work kinetic energy theorem I do remember it from my days ago in physics.

Hi xaenn! Welcome to PF! Thank you. So far I've been very pleased with the quick and helpful responses I've gotten, with no mention of this being a very elementary or "noobish" question. I think I'll stick around for awhile.

I've always liked physics quite a bit, but unfortunately I studied the wrong major in college (engineering). As of late I've begun to try and brush up on physics purely out of interest, so I think this will be a good place to supplement that. Then again, it may just so happen that I'll come across a question about lasers and I'll be the one to do some explaining (even though I am sure there are many people here with a much more in-depth understanding than I).