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  1. #1
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    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?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by alderon View Post
    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
    Last edited by topsquark; October 8th 2007 at 06:43 PM.
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