Is Work Done When Lifting a Box of Books Despite Equal Forces?

[ilkjester]

Homework Statement

You slowly lift a box of books from the floor and put it on a table. Earth's gravity exerts a force, magnitude mg, downward, and you exert a force, magnitude mg, upward. the two forces have equal magnitudes and opposite directions. It appears that no work is done, but you know you did work. Explain what work is done.

Homework Equations

The Attempt at a Solution

I don't get why its saying there was no work done. If work is force times distance. Then you exerted a force and moved the box. Does the force of gravity pulling down cancel out your force lifting it up.

 

[Mindscrape]

Your problem statement is weird. Maybe what it is trying to get at that you are doing work against gravity or something. The bottom line is that there is work done lifting the box. The only way the problem would make sense is if you were moving the box perpendicular to gravity, in which case the work comes from your muscles.

 

[ilkjester]

Your problem statement is weird. Maybe what it is trying to get at that you are doing work against gravity or something. The bottom line is that there is work done lifting the box. The only way the problem would make sense is if you were moving the box perpendicular to gravity, in which case the work comes from your muscles.

So you think the question is just weird. Because I don't know why the book says no work was done either.

 

[Mindscrape]

I'm really not sure what the book you have is trying to explain, but use the definition of work

W = \int F \cdot ds

Your force is a constant, mg, and the displacement is in the direction of the force, so the dot product is simply the magnitudes. W = F * displacement = mg*s

So what I think it is getting at is that if your force is the same as gravitational force, you are not actually lifting up the books (despite the problem saying you slowly lift the books), so there is actually no displacement. Yet, you are exerting a lot of energy to get that heavy box of books going, even if you can't get it. The work you are feeling is biological work, friction in your muscles and such.

 

[ilkjester]

I'm really not sure what the book you have is trying to explain, but use the definition of work

W = \int F \cdot ds

Your force is a constant, mg, and the displacement is in the direction of the force, so the dot product is simply the magnitudes. W = F * displacement = mg*s

So what I think it is getting at is that if your force is the same as gravitational force, you are not actually lifting up the books (despite the problem saying you slowly lift the books), so there is actually no displacement. Yet, you are exerting a lot of energy to get that heavy box of books going, even if you can't get it. The work you are feeling is biological work, friction in your muscles and such.

Yeah I understand that. The question is just weird I guess. Thanks for the help.