{cloak:id=intc}External influences from the earth (gravity), the floor (normal force) and the rope (tension).{cloak}
{toggle-cloak:id=modc} *Model:* {cloak:id=modc}[Point Particle Dynamics].{cloak}
{toggle-cloak:id=appc} *Approach:*
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{toggle-cloak:id=diagc} {color:red} *Diagrammatic Representation* {color}
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We begin with a free body diagram for the box:
!normalfbd3.png!
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{toggle-cloak:id=mathc} {color:red} *Mathematical Representation* {color}
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From the free body diagram, we can write the equations of [Newton's 2nd Law|Newton's Second Law]. We ignore the x-direction, since there are no forces acting.
{latex}\begin{large}\[ \sum F_{y} = T + N - mg = ma_{y}\]\end{large}{latex}
Because the box is sliding over level ground, it is not moving at all in the _y_ direction. Thus, it certainly has no y-acceleration. Setting _a_~y~ = 0 in the _y_ direction equation gives:
{latex}\begin{large}\[ T + N - mg = 0 \]\end{large}{latex}
Solving for the normal force gives:
{latex}\begin{large}\[ N = mg - T = \mbox{78 N}\]\end{large}{latex}
{tip}When three or more forces act in a direction with zero acceleration, it is always a good idea to check your answer by putting the numbers on the free body diagram and making sure that they balance. In this case, T (20 N) and N (78 N) act to balance mg (98 N).{tip}
{note}Follow up question: The floor no longer supports the entire weight of the box (98 N) because the rope is carrying some of the weight (20 N). How will the _person's_ normal force be affected in this situation? If the floor is carrying so much less weight, what part of the building is now feeling an extra load?{note}
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