1. ## physics

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?

2. Originally Posted by alderon
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!

$f_k = \mu _k N$

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:
$f_k = \mu _k N = \mu _k mg$

Work done by friction, then, is:
$W = \vec{f_k} \cdot \vec{s}$

Kinetic friction is always defined to be in the direction opposite the displacement. So $\vec{f_k}$ and $\vec{s}$ are at 180 degrees to one another, sooooooooo:
$W = \vec{f_k} \cdot \vec{s} = f_ks \cdot cos(180^o) = -f_k s = -\mu _k mgs$

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