a box of books of 100 kg. is push at constant speed in a straight line over a rough floor with kenitic energy 0.20.find the work done by the force that pushes the box if the box moves by 3 meters across the floor?
Gah! I hate it when I make a "trivial" mistake on what ends up being a simple problem if I had just looked at it in the right way.
Okay, here's a revised version of what I wrote this (Monday) morning... Okay, it's completely rewritten, hiding my shame!
$\displaystyle f_k = \mu _k N$
When we do a Free Body Diagram on the box, we find that the magnitude of the normal force on the box is simply equal to the magnitude of the weight. So:
$\displaystyle f_k = \mu _k N = \mu _k mg$
Work done by friction, then, is:
$\displaystyle W = \vec{f_k} \cdot \vec{s}$
Kinetic friction is always defined to be in the direction opposite the displacement. So $\displaystyle \vec{f_k}$ and $\displaystyle \vec{s}$ are at 180 degrees to one another, sooooooooo:
$\displaystyle W = \vec{f_k} \cdot \vec{s} = f_ks \cdot cos(180^o) = -f_k s = -\mu _k mgs$
You can plug in the numbers from here. And the "-" sign is very important as it implies energy is leaving the system, so you have to include it.
-Dan