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h2. Part A

!normalbox1.png|width=40%!

A 10 kg box slides at a constant speed of 2 m/s along a smooth floor.  What is the magnitude of the normal force exerted on the box by the floor?

System:  Box as [point particle] subject to external influences from the earth (gravity) and the floor (normal force).

Model:  [Point Particle Dynamics].

Approach:  We begin with a free body diagram for the box:

!normalfbd1.png!

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}\[ \sum F_{y} = N - mg = ma_{y}\]\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 above equation gives:

{latex}\begin{large}\[ N = mg = \mbox{98 N}\]\end{large}{latex}